China Satellite Navigation Conference (CSNC 2021) Proceedings Volume II [II] 9789811631412, 9789811631429

Table of contents :
Preface
Organization
Editorial Board
Topic: S01: Professional GNSS Applications
Chairman
Vice-chairman
Topic: S02: GNSS Applications for the Mass Market
Chairman
Vice-chairman
Topic: S03: GNSS and Their Augmentations Chairman
Vice-chairman
Topic: S04: Satellite Orbits and Precise Positioning
Chairman
Vice-chairman
Topic: S05: Time Frequencies and Precision Timing
Chairman
Vice-chairman
Topic: S06: Autonomous Navigation and Intelligent Operation
Chairman
Vice-chairman
Topic: S07: GNSS Signal Processing
Chairman
Vice-chairman
Topic: S08: GNSS User Terminals
Chairman
Vice-chairman
Topic: S09: PNT Architectures and New PNT Technologies
Chairman
Vice-chairman
Topic: S10: Policies, Standards and Intellectual Property Rights
Chairman
Vice-chairman
Scientific Committee
Senior Advisor: (By Surnames Stroke Order)
Chairman
Vice-chairman
Executive Chairman
Committee Members: (By Surnames Stroke Order)
Executive Members: (By Surnames Stroke Order)
Organizing Committee
Director
Deputy Director
Secretary-General
Deputy Secretary-General
Deputy Secretary
Committee Members: (By Surnames Stroke Order)
Contents
GNSS and Their Augmentations Chairman
Analysis of GPS Signal Power Enhancement Effect Based on Data from Multiple Ground Stations
1 Introduction
2 Recent GPS Signal Power Enhancement
3 Analysis Method of Power Mutation Moments
4 Power-Enhanced Satellites Availability Analysis
5 Conclusion
References
The Research on Double-Difference Ionospheric Interpolation Based on Gaussian Process Regression
1 Introduction
2 Problem of Double-Difference Ionospheric Interpolation for Local Base Station Networks
3 Gaussian Process Regression
4 Selection of the Kernel of Double-Difference Ionospheric Delay
4.1 Kernel of Zenith Ionospheric Delay
4.2 Kernel of Double-Difference Ionospheric Delay
5 Experimental Results
5.1 Experimental Data
5.2 Comparison of Three Interpolation Algorithms
6 Conclusion
References
Monitoring Station Data Quality Analysis Method
1 Introduction
2 Data Quality Analysis Indicator and Method
2.1 Multipath Error
2.2 Cycle Slip Ratio
2.3 Observation Data Availability
3 Data Sources
4 Result Analysis
4.1 Multipath Error
4.2 Cycle Slip Ratio
4.3 Observation Data Availability
5 Data Continuity Analysis
5.1 Data Continuity Definition
6 Result Analysis
7 Conclusion
References
Research on the Distortion Threat Model and Threat Space of BDS B1C and B2a Signals
1 Introduction
2 ICAO Threat Model and BDS Signal
2.1 Current Threat Model in ICAO
2.2 BDS B1C/B2a Signals and the Processing Strategies
3 The Choice of Model Frame for BDS Signal
4 Threat Space Analysis
4.1 Analysis Methodology
4.2 Threat Space Analysis for B1C
4.3 Threat Space Analysis for B2a
4.4 Summaries for Threat Space
5 Summary
References
Applicability Analysis of DFMC SBAS Receiver Design Constraints to BDS B1C and B2a Signals
1 Introduction
2 BDS Signals and the Threat Model
2.1 B1C/B2a Signals and the Processing Strategies
2.2 B1C/B2a Signal Threat Model
3 DFMC SBAS Receiver Design Constraints
3.1 User Receiver Design Constraints
3.2 Monitoring Station Receiver Recommendation
4 Constraints Applicability Analysis
4.1 Analysis Method
4.2 Simulation Conditions
4.3 Simulation Results
5 Summary
References
Analysis of the Applicable Minimum Filter Gain Roll-Off of DFMC SBAS Receiver for BDS Signals
1 Introduction
2 Receiver Design Constraints Introduction
2.1 General Content of Constraints
2.2 DFMC SBAS Receiver Constraints
2.3 Filter Gain Roll-Off
3 Evaluation Method and Conditions
3.1 Evaluation Method
3.2 Evaluation Conditions
4 Results and Analysis
4.1 Results for B1C Signal
4.2 Results for B2a Signal
5 Summary
References
Weakening Test of Pseudo-range Bias Based on Parameters-Constrained of BDS Monitoring Receiver
1 Introduction
2 The Influence on Pseudo-range Bias from Receiver Parameters
3 Constraint Adjustment Test Based on Receiver Parameter
4 Conclusion
References
Signal Quality Monitoring Algorithms of DFMC SBAS for Dual-Frequency Civil Signals of BDS
1 Introduction
2 BDS Signals for Civil Aviation and Threat Models
2.1 B1C and B2a Signals
2.2 Threat Models
3 Progress of Signal Quality Monitoring Techniques
3.1 SQM Techniques Based on Pseudo-Range Observables
3.2 SQM Techniques Based on Multi-Correlator Observables
3.3 SQM Techniques Based on Chip Domain Observables
4 Hybrid SQM Algorithm and Evaluation
4.1 Hybrid SQM Algorithm
4.2 Evaluation on Hybrid SQM Algorithm
5 Simulations and Analyses
5.1 Simulations and Analyses on B1C Signal
5.2 Simulations and Analyses on B2a Signal
6 Conclusions and Future Work
References
Optimal Design of LEO Constellation for Communication and Navigation Fusion Based on Genetic Algorithm
1 Introduction
2 Constellation Design
2.1 Constellation Configuration Selection
2.2 Orbital Altitude Determination
3 Optimization Method
3.1 Constellation Configuration Selection
3.2 Calculation Method
3.3 Optimize Objective Function Design
3.4 Optimization Algorithm
4 Constellation Optimization
4.1 Simulation Scene Setting
4.2 Optimization Results
5 Conclusions
References
Observations of Ionospheric Disturbances Based on CORS Data Over North America
1 Introduction
2 GNSS Extracts Total Electron Content
2.1 GNSS Observation Data and STEC Extraction
2.2 Carrier Phase Smoothing Pseudorange Extraction STEC
2.3 PPP Algorithm to Extract STEC
3 TID Detection
3.1 Detrending Ionospheric Trends
3.2 Two-Dimensional DSTEC Map
3.3 Regional MSTID Characterization
4 Conclusion
References
Spectrum Compatibility Analysis Between LEO Navigation Augmentation Signals and GNSS Signals
1 Introduction
2 Satellite Navigation Signal
2.1 Signal System and Constellation Parameters
2.2 Signal Model and Real PSD
2.3 Doppler Frequency Offset Between GNSS Signal and LNAS
3 Spectrum Compatibility Analysis Method
3.1 Theoretical Formula
3.2 Characteristic Analysis
4 Simulation Analysis
4.1 Parameter Configuration
4.2 Global Simulation Results
5 Conclusion
References
A Robust Positioning and Adaptive RAIM FDE Algorithm for Multiple Outliers Based on Non-Gaussian Distribution
1 Introduction
2 Gaussian Mixture Model
2.1 Convert Weighted Least Squares to Ordinary Least Squares
2.2 The Gaussian Mixture Model
2.3 Positioning Using EM Algorithm
2.4 Initial Value Selection
2.5 Calculation of the Protection Level
3 Experiments
3.1 Experimental Design
3.2 Positioning Error Analysis
3.3 Protection Level Analysis
3.4 Time Complexity
4 Conclusions
References
Sparse Reconstruction of the Ionosphere in the Equatorial Anomaly Region During the Solar Eclipse Based on Beidou Ground Based Augmentation System
1 Introduction
2 Ionospheric Tomography Reconstruction Method
3 Research Area and Data Source
4 Results and Analysis
5 Conclusion and Discussion
References
Research on Single Frequency BDSBAS Message Scheduler Improvement
1 Introduction
2 Research on International Standards of SBAS Messages
3 Research on SBAS Message Scheduler At Home and Abroad
4 BDSBAS Fixed Time Sequence Dynamic Message Scheduler
4.1 BDSBAS Broadcast Message Analysis After Officially Providing Service
4.2 Introduction of Fixed Time Sequence Dynamic Message Scheduler
5 Feasibility Verification of BDSBAS Message Scheduler
6 Conclusion
References
Improved BDS RAIM Algorithm Based on M-Estimation
1 Introduction
2 Improved RAIM Algorithm for M-Estimation
2.1 RAIM Algorithm Based on Least Square Approach
2.2 Basic Principles of M-Estimation
2.3 Improved M-Estimation Algorithm
3 Experimental Verification and Result Analysis
4 Conclusion
References
Analysis of the BDS-3 Complete System on Positioning Performance in Polar Region
1 Introduction
2 Data Sources and Processing Strategies
3 Coverage Performance Analysis
3.1 Number of Visible Satellites
3.2 DOP Value
3.3 PDOP Availability
4 Data Quality Analysis
4.1 Signal-To-Noise Ratio
4.2 Pseudo Range Multipath
5 User Equivalent Ranging Error Analysis
6 Positioning Performance Analysis
7 Summary
References
Development of High-Precision Ionospheric Monitoring System in China: Taking ROTI Map as an Example
1 Introduction
2 High-Precision Ionospheric Real-Time Monitoring System in China
2.1 System Architecture
2.2 Network-Cloud-Map-End Integrated Solutions
2.3 High-Precision Ionospheric Map Service
3 Taking ROTI Map as an Example
3.1 Algorithm for ROTI Map Processing
3.2 ROTI Map During a Strong Magnetic Storm
4 Conclusion and Outlook
References
LEO Constellation Design Based on Dual Objective Optimization and Study on PPP Performance
1 Introduction
1.1 LEO Satellite Features
1.2 Analysis of the Influence of Atmospheric Drag on the Number of Low-Orbit Satellites
1.3 Optimal Design of Low-Orbit Navigation Constellation Based on Dual Objective Optimization
1.4 Research on the Performance of Low-Orbit/GNSS Multi-system PPP
1.5 Conclusion
References
Research on Civil GNSS Signal Authentication Service Design
1 Introduction
2 Technical and Service Perspective
3 Design Considerations
4 Performance Metrics Framework
4.1 Navigation Performance Metrics
4.2 Authentication Metrics
4.3 Security Metrics
5 Preliminary Design of an Authentication Proposal for BDS
5.1 BDSSA Design Features
5.2 BDSSA Protocol
5.3 BDSSA Message Structure
5.4 Preliminary Performance Analysis
6 Conclusion
References
Key Technical Characteristics and Performance of BeiDou Navigation Augmentation System Based on LEO Constellation
1 Introduction
2 System Architecture
2.1 Space Segment
2.2 Ground Segment
2.3 User Segment
3 Key Technical System and Performance Analysis
3.1 Construction and Maintenance of LEO Spatio-Temporal Reference
3.2 LEO Satellite Navigation Augmentation Constellation
3.3 Augmented Navigation Signal System
3.4 The Precise Positioning Method Based on the Mixed Constellation Augmentation
4 Conclusion
References
Satellite Navigation System Time Delay Automatic Calibration Technology and Ground Verification
1 Introduction
2 Satellite Navigation System Delay Classification
2.1 Satellite and Ground Equipment Delay
2.2 Inter-station Link Delay
2.3 Inter-satellite Link Delay
3 Automatic Time Delay Calibration Method
3.1 Automatic Calibration Method of Transmission Delay
3.2 Automatic Calibration Method of Receiving Equipment Delay
4 Ground Test Verification Results
4.1 Equipment Self-calibration Result
4.2 Automatic Time Delay Calibration Result
5 Summary
References
Preliminary Assessment of BDS-3 PPP Service Performance
1 Introduction
2 Technical Features
3 Assessment Method of the Service Performance
3.1 SISRE
3.2 Service Coverage
3.3 PPP Accuracy and Convergence Time
4 Analysis of BDS-3 PPP Service Performance
4.1 Data Source
4.2 Analysis of SISRE
4.3 Analysis of Service Coverage
4.4 Analysis of Positioning Accuracy and Convergence Time
5 Conclusions
References
Influence of Different ISB Processing Strategies on the Accuracy of Undifferenced FCBs and PPP-AR Positioning
1 Introduction
2 BDS/GPS/Galileo Undifferenced and Uncombined PPP
3 Parameter Processing Strategy
3.1 ISB Processing Strategy
3.2 FCB Processing Strategy
4 Results and Discussion
4.1 Characteristic Analysis of FCBs
4.2 Positioning Result Analysis
5 Conclusions
References
Co-channel Interference Cancellation Method Based on Deep Neural Network for LEO Satellite Systems
1 Introduction
2 System Model
2.1 RF Channel Model
2.2 Co-frequency Interference Signal Model of LEO Satellite Enhancement Signal
3 Interference Cancellation Method
3.1 Interference Cancellation Model
3.2 Network Model
4 Performance Analysis
5 Conclusion
References
A Pseudo-satellite Implementation Method Using High Precision Time Synchronization
1 Introduction
2 Principle Analysis
3 Function Composition and Working Process of Pseudo-satellite System
3.1 Composition and Function
3.2 Working Process
4 Design and Implementation of Internal Algorithm
4.1 Design and Implementation of Pseudo-satellite Signal Generator
4.2 Time Synchronization Algorithm and Synchronization Process
4.3 Ephemeris Parameter Calculation Process
5 Test and Result Analysis
6 Conclusion
References
Coordinated Precoding Based on Distributed CSI for Multi-station and Multi-satellite MIMO Uplink System
1 Introduction
2 Cooperative Precoding Algorithm for Multi-station and Multi-satellite
2.1 Optimization of the Total Rate of Signals from Multi-station and Multi-satellite
2.2 RB-WMMSE Algorithm Based on Distributed CSI
3 Simulation and Analysis
4 Conclusion
References
Energy Efficiency Optimization Algorithm for Single Station Multi-satellite MIMO Uplink System
1 Introduction
2 Energy Efficiency Optimization Algorithm
2.1 Energy Efficiency Optimization Model
2.2 Power Allocation Algorithm Based on Energy Efficiency Maximization
3 Simulation and Result Analysis
3.1 Energy Efficiency Under Different SNR
3.2 Energy Efficiency Under Different Satellite Numbers
3.3 Energy Efficiency Under Different Satellite Numbers
4 Conclusion
References
Unmasking Bayesian RAIM Algorithm for Identifying Simultaneous Two-Faulty Satellites
1 Introduction
2 Bayesian Model for Identifying Simultaneous Two-Faulty Satellites
3 Bayesian Method of Identification for Simultaneous Two-Faulty Satellites Based on Posterior Probability
3.1 Posterior Distribution of Errors
3.2 The Formula of Posterior Probability
3.3 The Implementation Steps of Bayesian Method for Identifying Simultaneous Two-Faulty Satellites
4 Example and Analysis
4.1 Verification of Fault Identification
4.2 Statistics of Correct Identification Rate of Faults
5 Conclusion
References
The Realization and Performance Evaluation of Real-Time Precise Point Positioning Based on BDS-3 PPP-B2b Augmentation Information
1 Introduction
2 PPP-B2b Augmentation Information
3 Real-Time PPP Algorithm
4 Real-Time PPP Experiment
5 Conclusion
References
Autonomous Navigation and Intelligent Operation
Research on Improvement Method of Systematic Deviation of Autonomous Navigation Message of BDS
1 Introduction
2 Source Analysis of Systematic Deviation of Message
2.1 Correction of Satellite Centroid and Antenna Phase Center
2.2 Relativistic Effect Correction
2.3 Channel Transmit Receive Delay Correction
3 Solution of Channel Transmit and Receive Delay Correction Error
3.1 Epoch Reduction of Inter Satellite Distance Observations
3.2 Calculated Value of Inter Satellite Distance
3.3 Calculation of the Difference Between the Observed and Theoretical Values of Ephemeris and Clock
4 Simulation Calculation of Channel Transmit and Receive Delay Error
5 Conclusion
References
A DBZP Acquisition Method for High-Dynamic and Weak GPS Signal Aided by SINS
1 Introduction
2 Performance Analysis of DBZP Algorithm in High-Dynamic Environments
3 A DBZP Acquisition Method for High-Dynamic and Weak GPS Signal Aided by SINS Information
3.1 Calculation of Aiding Information
3.2 A DBZP Acquisition Method Based on Navigation Bit Estimation
4 Simulation Verification
4.1 Simulation Conditions
4.2 Simulation Results and Analysis
5 Conclusions
References
The Dispersion Effect of Pseudo-noise Ranging and Time Delay Measurement for Ka Inter-satellite Link
1 Introduction
2 Pseudorange Delay of Dispersive Networks
2.1 Group Delay and Pseudorange Delay
2.2 Transmission Function of Networks
2.3 Frequency Conversion on Transmission Function
2.4 The Numerical Calculation Methods of Pseudorange Delay
3 ISL Antenna Pseudorange Delay Measurement
3.1 ISL Antenna Group Delay Measurement
3.2 Determination of Pseudorange Delay by PSI Method
4 Conclusion
References
Research on Collision Avoidance Between UAV Flocks Using Behavior-Based Approach
1 Introduction
2 Model Introductions
3 Flock Control Function Design
3.1 Aggregation and Separation Function Design
3.2 Velocity Alignment Function Design
3.3 Obstacle Avoidance
4 Simulation Experiment
4.1 Algorithm Performance Comparison
4.2 Parameter Analysis
4.3 Operation Time Analysis
5 Summary
References
Digital Track Map Aided Multi-sensor Fusion for Train Occupancy Identification in Complicated Track Sections
1 Introduction
2 Method
2.1 GNSS/INS Coupled Algorithm
2.2 Digital Track Map Generation
2.3 GNSS/INS/DTM Coupled Track Occupancy Identification Method in Complicated Track Sections
3 Experiment and Result Analysis
4 Conclusion
References
GNSS Multipath Detection Based on Decision Tree Algorithm in Urban Canyons
1 Introduction
2 Data Sources and Labelling
2.1 Data Sources
2.2 Data Labelling
2.3 Labelling Result
3 Selection and Calculation of Features
4 Model Training and Classification Results
4.1 Model Training
4.2 Verification of Classification Results
5 Conclusion
6 Future Outlook
References
Decentralized Collaborative Localization Algorithm Based on Covariance Propagation
1 Introduction
2 Recursion Law of State Vector and Covariance Between Synergies
3 Design of Decentralized Collaborative Localization System
3.1 Problem Hypothesis
3.2 Collaborative Localization System Equation
3.3 System Design
4 Experimental Results and Performance Analysis
5 Conclusions
References
DVT-SLAM: Deep-Learning Based Visible and Thermal Fusion SLAM
1 Introduction
2 Visual SLAM
3 Methodology
3.1 Visible-Infrared Image Fusion Network DVT-GAN
3.2 DVT-SLAM Based on the Visible-Infrared Fusion Image
4 Experiments and Results
4.1 Dataset
4.2 Visible - Thermal Image Fusion
4.3 Dvt-Slam
5 Conclusion
References
Satellite Thrusters’ Control Allocation and Application Used for Integrated Attitude-Orbit Control System
1 Introduction
2 The Integrated Attitude-Orbit Control Method Used by Thrusters
2.1 The Layout of Thrusters
2.2 The Control Allocation Problem of Thrusters
2.3 The Vector Approximation Algorithm Under the Integrated Attitude-Orbit Control
2.4 The Pipeline of Control Allocation Execution Under the Integrated Attitude-Orbit Control
2.5 The Stability of Integrated Attitude and Orbit Control
3 The Simulation Results
4 The on Orbit Results
5 Conclusions
References
Real-Time Robot Localization Based on 2D Lidar Scan-to-Submap Matching
1 Introduction
2 Related Work
3 Localization with Scan-to-Submap Matching
3.1 Cartographer
3.2 Definitions
3.3 CeresScanMatcher
4 Indoor Scan-Based Mapping
5 Experimental Results
5.1 Simulation Platform
5.2 Real Mobile Robot Platform
6 Conclusion
References
Research on Strategy of Access Node Selection for Space-Based Relay Network Based on Navigation Satellites
1 Introduction
2 Queuing Delay Analysis of Navigation Satellite Network
2.1 Access Node Selection Scheme
2.2 Theoretical Analysis of Network Queuing Delay
3 Simulation Analysis
3.1 Simulation Parameters and Scene Design
3.2 Simulation of Network Queuing Delay
3.3 Access Node Coverage Simulation
4 Conclusion
References
Research on Error Online Calibration Method of Inertial/Stellar Refraction Integrated Navigation System
1 Introduction
2 Error Modeling of Inertial/Starlight Refraction Integrated Navigation System
2.1 Reference Coordinate System
2.2 System Error Model
3 Error Online Calibration Method
4 Simulation Analysis
4.1 Simulation Analysis of Error Online Calibration
4.2 Simulation Analysis of Strapdown Inertial/Starlight Refraction Integrated Navigation
5 Conclusion
References
Investigation on Centralized Autonomous Orbit Determination Using Inter-satellite Ranging
1 Introduction
2 Centralized Orbit Determination
2.1 Satellite Grouping
2.2 Reference Satellite
2.3 Processing Procedures
3 Numerical Tests
4 Simulation Results
4.1 Testing the Centralized OD Strategy
4.2 Testing with Different Reference Satellites
5 Discussion and Conclusion
References
Research on Invariant Extended Kalman Filter Based 5G/SINS Integrated Navigation Simulation
1 Introduction
2 Invariant Extended Kalman Filter
2.1 The Differential Equation of the Full State in the ECEF Frame and Its Invariance
2.2 The Left-Invariant Error State Differential Equation of the SINS in the ECEF Frame
3 SINS/5G Integrated Navigation
3.1 The 5G Positioning Model and Left-Invariant Observation Equation
3.2 SINS/5G Integrated Navigation Measurement Updating
4 Experiment
4.1 Generate Simulation Data
4.2 Integrated Navigation Simulation Experiment
5 Conclusion
References
Analysis of Management and Control and Scheduling Mode for Mega Constellation
1 Introduction
2 Analysis of Operating Scenarios of Mega Constellation
2.1 Requirements for the Mega Constellation Control Center
2.2 Requirements for Existing Satellite Control Center
2.3 Analysis of Disadvantages of the Constellation Independent Control Mode
3 Analysis of Resource Sharing Management and Control Mode
3.1 Analysis of Resource Sharing Requirements
3.2 Design of Resource Sharing Management and Control Mode
4 Simulation Analysis
4.1 Simulation Condition
4.2 Ground Resources Effectiveness Evaluation Indicators
4.3 Simulation Results
5 Conclusion
References
Deployment Location Algorithm of Navigation Base Station Based on GDOP Analysis
1 Introduction
2 Method of Location Deployable
2.1 Application Principle Relationship
2.2 Segmentation Method of Area
3 Deployment Location Algorithm of Base Stations
3.1 Sampling Method of Served-Areas
3.2 Deployment Location Algorithm
3.3 Important Influencing Factors
4 Simulation and Analysis
4.1 The Deployable Area Contains the Served Area
4.2 The Deployable Area Is on the Side of the Served Area
5 Conclusion
References
Research on Loran-C ASF Correction Method Based on GA-BP Neural Network
1 Introduction
2 Design of Loran-C ASF Correction Method Based on GA-BP Neural Network
2.1 ASF Revises Database Design Strategy
2.2 BP Neural Network Training Method Based on GA
3 Loran-C ASF Correction Method Based on GA-BP Neural Network
3.1 The Initial Weights and Thresholds of BP Neural Network Are Obtained by Genetic Algorithm
3.2 2BP Neural Network Algorithm
3.3 Propagation Delay Correction of Non-real Time ASF
4 Simulation Example
5 Summary
References
On Precise Inertial Force Modeling for Autonomous Orbit Propagation in Earth-Centered Fixed System for Earth Satellites
1 Introduction
2 The Equation of Motion and the Inertial Force
2.1 The Equation of Motion in the Rotating Frame
2.2 The Coriolis Force and the Centrifugal Force
2.3 The Euler Force
3 Numerical Tests
3.1 Results of Test no. 1
3.2 Results of Test no. 2
4 Discussion and Conclusion
References
A Beidou Laser Link Allocation Scheme Based on Network Throughput Optimization
1 Introduction
2 Conception of Spatial Network of Next Generation BDS
2.1 High-Speed Laser Link Between Satellites
2.2 Inter-satellite Backbone Network
2.3 Design and Analysis of Laser Backbone Network
3 Optimal Design of Next Generation Beidou Space Laser Backbone Network
3.1 Low, Medium and High Mixed Constellation Design
3.2 Improved Laser Backbone Network Design
4 Performance Analysis
4.1 Throughput When the Heterogeneous Network is not Communicating
4.2 Throughput of Inter-orbit Network Communication
5 Concluding Remarks
References
Mechanism Analysis and Mitigation of Visual Navigation System Vulnerability
1 Introduction
2 Definition and Root Cause Analysis of VN Vulnerability
2.1 Scene (Source Segment)
2.2 Scene-Camera Optical Environment (Propagation Segment)
2.3 Camera (User Segment)
2.4 VN Software (Algorithm Segment)
2.5 Summary of VN Vulnerability Factors and Their Impact
3 VN Vulnerability Detection and Mitigation Techniques
3.1 Real-Time Vulnerability Detection
3.2 VN Vulnerability Mitigation
4 Experimental Results and Discussion
4.1 Examples of VN Vulnerability
4.2 Validation of Detection and Mitigation Techniques
5 Conclusion
References
Pedestrian Collaborative Inertial-Only SLAM
1 Introduction
2 Single-Pedestrian Inertial-Only SLAM
2.1 Map Representation and Estimation
2.2 Pedestrian Inertial Odometer and Motion Model
2.3 Particle Weight Calculation and Importance Sampling
3 Collaborative Inertial-Only SLAM
4 Experiments and Analysis
5 Conclusion
References
An Efficient and Robust Indoor Magnetic Field Matching Positioning Solution Based on Consumer-Grade IMUs for Smartphones
1 Introduction
2 Overview of Magnetic Field Positioning Solution
3 Magnetic Field Map Generation Stage
4 Real-Time Positioning Stage
5 Test Results and Analysis
6 Conclusion and Outlook
References
Research on Signal Acquisition Technique of Inter-satellite Links of Navigation System
1 The Introduction
2 Performance Analysis of Traditional Capture Algorithms
2.1 Serial Search Technology Based on Time-Domain Autocorrelation
2.2 Cycle Correlation Capture Technology Based on FFT
2.3 Fast Acquisition Technology of Segmented Matched Filtering Based on FFT
2.4 Influence of Inter-satellite Links on Traditional Signal Acquisition Methods
3 Fast Acquisition Technique Based on Fractional Fourier Transform
4 Conclusion
References
PNT Architectures and New PNT Technologies
Performance Verification of Capsule Networks in LOS/NLOS Identification for UWB Positioning
1 Introduction
2 System Model
2.1 Problem Formulation
2.2 LOS/NLOS Identification Framework
2.3 CapsNet Architecture
2.4 Dynamic Routing Mechanism
2.5 Margin Loss
3 Experiment and Analysis
3.1 Experimental Setup
3.2 Evaluation Metric
3.3 Analysis of CapsNet
4 Conclusion
References
Map Matching with WiFi-RSSI GRU Indoor Room Switching Classifier
1 Introduction
2 GRU-Based WiFi RSSI Room Switching Classifier
2.1 Introduction of GRU Algorithm
2.2 GRU Based WiFi RSSI Room Switching Classifier.
3 Map Matching with GRU Based WiFi RSSI Room Switching Classifier.
3.1 Map Matching Based on HMM Algorithm
3.2 HMM Map Matching Algorithm Optimized by GRU Algorithm
4 Simulation and Experiment
5 Conclusion
References
DOP Analysis for Indoor Hybrid TDOA/TOA Positioning Based on Mobile Communication Network
1 Introduction
2 System Model
3 DOP for Hybrid TDOA and TOA Positioning
4 Simulation Results and Analysis
4.1 Simulation Scenario
4.2 Simulation Results
4.3 Result Analysis
5 Conclusion
References
A New Algorithm of Tightly-Coupled GNSS/INS Integrated Navigation Based on Factor Graph
1 Introduction
2 GNSS Measurement Model
3 GNSS/INS Factor Graph Model
3.1 INS Factor
3.2 GNSS Factor
3.3 Experiment
4 Conclusion
References
ISM Band Multi-source Signal Perception Based on Time-Frequency Image Feature Analysis
1 Introduction
2 Time-Frequency Domain Transformation of Signals
2.1 Fourier Transform
2.2 Short-Time Fourier Transform
3 Signal Recognition Using Image Classification Method
3.1 Steps of SVM Image Classification
3.2 Speed Up Robust Features
3.3 K-Means Algorithm
3.4 BOW Model
4 Simulation
4.1 Signal Generation and Time-Frequency Conversion
4.2 Image Preprocessing
4.3 Recognition Results of SVM
5 Conclusion
References
Estimate of Initial Installation Angle of INS in Vehicle MEMS-INS/GNSS Integrated Navigation System
1 Introduction
2 Principle of the Installation Angle Estimate
2.1 Axis Transformation
2.2 Estimate of the Horizontal Installation Angle
2.3 Estimate of the Heading Installation Angle
3 Error Analysis
4 Field Tests
5 Conclusion
References
An Improved Wireless Positioning Algorithm Based on the LSTM Network
1 Introduction
2 Related Work
3 Positioning Algorithm Using Encoder-Decoder Framework
3.1 Data Processing
3.2 Extract Features
3.3 Algorithm Framework
4 Experiment Evaluation
4.1 Data Description
4.2 Software and Hardware Equipment
4.3 Model Comparison
5 Conclusion
References
Research on Space/ground Based Pulsar Timescale for PNT
1 Introduction
2 Basic Principle of Pulsar Time
3 Time Stability Analysis of Space-Based Pulsars
3.1 TIME Stability Analysis of Ground Based Pulsars Based on IPTA Timing Data
3.2 Time Stability Analysis of Space-Based Pulsars Based on the Observation Data of NICER Project
3.3 PT Stability Analysis Based on FAST Simulation Data
4 Conclusion and Discussion
References
Research on Positioning Method in the Lunar Space
1 Introduction
2 The Scene and Link Design of Lunar Station
3 Design of Lunar Positioning Signal
3.1 Signal Model
3.2 Angle Measurement Signal Receiving Algorithm
4 Simulation and Error Analysis
4.1 The Simulation of Angle Measurement Algorithm
4.2 Error Analysis
5 Conclusion
References
Parameter Estimation of Pulsar Position Based on Least Square
1 Introduction
2 Pulsar Timing Model
2.1 Timing Residuals
2.2 Solution of Pulsar Right Ascension and Declination Based on Least Square
3 Experiment and Analysis
3.1 The Influence of Planetary Ephemeris on Timing Residuals
3.2 Effect of Pulsar Position Error on Timing Residuals
3.3 Calculation and Analysis of Right Ascension and Declination Errors of Pulsars
4 Conclusions
References
Analysis and Suggestions on the Resilience of GNSS Timing
1 Introduction
2 Existing Problems of GNSS Timing
2.1 GNSS Anomalies
2.2 Jamming and Spoofing
3 Progress of GNSS Resilient Timing
4 Reflection on Resilient Timing
References
Machine Measuring Method for Norm-Position of Targets
1 Introduction
2 Norm Position
2.1 Definition of Norm Position
2.2 Key Technologies for Norm-position Machine Measurement
2.3 Resolution Methods for Norm Position
3 Study of Measurement Methods
3.1 Principles and Methods
3.2 Experimental Verification
3.3 Discussion
4 Analysis of Applications
4.1 Real Scenario Information Management
4.2 Unmanned Precision Operation
4.3 Reverse Control of Targets
References
Author Index

Citation preview

Lecture Notes in Electrical Engineering 773

Changfeng Yang Jun Xie   Editors

China Satellite Navigation Conference (CSNC 2021) Proceedings Volume II

Lecture Notes in Electrical Engineering Volume 773

Series Editors Leopoldo Angrisani, Department of Electrical and Information Technologies Engineering, University of Napoli Federico II, Naples, Italy Marco Arteaga, Departament de Control y Robótica, Universidad Nacional Autónoma de México, Coyoacán, Mexico Bijaya Ketan Panigrahi, Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Samarjit Chakraborty, Fakultät für Elektrotechnik und Informationstechnik, TU München, Munich, Germany Jiming Chen, Zhejiang University, Hangzhou, Zhejiang, China Shanben Chen, Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, China Tan Kay Chen, Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore Rüdiger Dillmann, Humanoids and Intelligent Systems Laboratory, Karlsruhe Institute for Technology, Karlsruhe, Germany Haibin Duan, Beijing University of Aeronautics and Astronautics, Beijing, China Gianluigi Ferrari, Università di Parma, Parma, Italy Manuel Ferre, Centre for Automation and Robotics CAR (UPM-CSIC), Universidad Politécnica de Madrid, Madrid, Spain Sandra Hirche, Department of Electrical Engineering and Information Science, Technische Universität München, Munich, Germany Faryar Jabbari, Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA Limin Jia, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Alaa Khamis, German University in Egypt El Tagamoa El Khames, New Cairo City, Egypt Torsten Kroeger, Stanford University, Stanford, CA, USA Yong Li, Hunan University, Changsha, Hunan, China Qilian Liang, Department of Electrical Engineering, University of Texas at Arlington, Arlington, TX, USA Ferran Martín, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain Tan Cher Ming, College of Engineering, Nanyang Technological University, Singapore, Singapore Wolfgang Minker, Institute of Information Technology, University of Ulm, Ulm, Germany Pradeep Misra, Department of Electrical Engineering, Wright State University, Dayton, OH, USA Sebastian Möller, Quality and Usability Laboratory, TU Berlin, Berlin, Germany Subhas Mukhopadhyay, School of Engineering & Advanced Technology, Massey University, Palmerston North, Manawatu-Wanganui, New Zealand Cun-Zheng Ning, Electrical Engineering, Arizona State University, Tempe, AZ, USA Toyoaki Nishida, Graduate School of Informatics, Kyoto University, Kyoto, Japan Federica Pascucci, Dipartimento di Ingegneria, Università degli Studi “Roma Tre”, Rome, Italy Yong Qin, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Gan Woon Seng, School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore, Singapore Joachim Speidel, Institute of Telecommunications, Universität Stuttgart, Stuttgart, Germany Germano Veiga, Campus da FEUP, INESC Porto, Porto, Portugal Haitao Wu, Academy of Opto-electronics, Chinese Academy of Sciences, Beijing, China Junjie James Zhang, Charlotte, NC, USA

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More information about this series at http://www.springer.com/series/7818

Changfeng Yang Jun Xie •

Editors

China Satellite Navigation Conference (CSNC 2021) Proceedings Volume II

123

Editors Changfeng Yang China Satellite Navigation Engineering Centre Beijing, China

Jun Xie China Academy of Space Technology Beijing, Beijing, China

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-16-3141-2 ISBN 978-981-16-3142-9 (eBook) https://doi.org/10.1007/978-981-16-3142-9 © Aerospace Information Research Institute 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

BeiDou Navigation Satellite System (BDS) is China’s global navigation satellite system which has been developed independently. BDS is similar in principle to Global Positioning System (GPS) and compatible with other global satellite navigation systems (GNSS) worldwide. The BDS will provide highly reliable and precise positioning, navigation and timing (PNT) services as well as short-message communication for all users under all-weather, all-time and worldwide conditions. China Satellite Navigation Conference (CSNC) is an open platform for academic exchanges in the field of satellite navigation. It aims to encourage technological innovation, accelerate GNSS engineering and boost the development of the satellite navigation industry in China and in the world. The 12th China Satellite Navigation Conference (CSNC 2021) is held during May 26–28, 2021, in Nanchang, China. The theme of CSNC2021 is “Spatio-Temporal Data Empowers Bright Future,” including technical seminars, academic exchanges, forums, exhibitions and lectures. The main topics are as follows:

Conference Topics S01 S02 S03 S04 S05 S06 S07 S08 S09 S10

Professional GNSS Applications GNSS Applications for the Mass Market GNSS and Their Augmentations Satellite Orbits and Precise Positioning Time Frequencies and Precision Timing Autonomous Navigation and Intelligent Operation GNSS Signal Processing GNSS User Terminals PNT Architectures and New PNT Technologies Policies, Standards and Intellectual Property Rights

v

vi

Preface

The proceedings (Lecture Notes in Electrical Engineering) have 201 papers in ten topics of the conference, which were selected through a strict peer-review process from 471 papers presented at CSNC2021, in addition, another 202 scientific committee of China Satellite Navigation Conference (CSNC). Papers were selected as the electronic proceedings of CSNC2021, which are also indexed by “China Proceedings of Conferences Full-text Database (CPCD)” of CNKI and Wan Fang Data. We thank the contribution of each author and extend our gratitude to 281 referees and 55 session chairmen who are listed as members of the editorial board. The assistance of CNSC2021’s organizing committees and the Springer editorial office is highly appreciated.

Organization

Editorial Board Topic: S01: Professional GNSS Applications Chairman Dangwei Wang

Beijing UniStrong Science and Technology Co., Ltd., Beijing, China

Vice-chairman Dun Wang Shuangcheng Zhang Caicong Wu Weiqiang Li

Space Star Technology Co., LTD. Beijing, China Chang’an University, Shaanxi, China China Agricultural University, Beijing, China Institute of Space Sciences, Spanish National Research Council

Topic: S02: GNSS Applications for the Mass Market Chairman Wenjun Zhao

Beijing Satellite Navigation Center, Beijing, China

Vice-chairman Shaojun Feng Changhui Xu Taosheng Wang

Qianxun Spatial Intelligence Inc., Shanghai, China Chinese Academy of Surveying and Mapping, Beijing, China BeiDou Application & Research Institute Co., Ltd. of Norinco Group, Beijing, China

vii

viii

Baoguo Yu Yang Gao

Organization

The 54th Research Institute of China Electronics Technology Group Corporation, Hebei, China University of Calgary, Alberta, Canada

Topic: S03: GNSS and Their Augmentations Chairman Rui Li

Beihang University, Beijing, China

Vice-chairman Long Yang Wenxiang Liu Xingxing Li Yansong Meng Liwen Dai

Beijing Future Navigation Technology Co., Ltd., Beijing, China National University of Defense Technology, Hunan, China Wuhan University, Hubei, China Xi’an Branch of China Academy of Space Technology, Shaanxi, China John Deere, Torrance CA, USA

Topic: S04: Satellite Orbits and Precise Positioning Chairman Xiaogong Hu

Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, China

Vice-chairman Jianwen Li Jianghui Geng Bofeng Li Xiaolin Meng

Information Engineering University, Henan, China Wuhan University, Hubei, China Tongji University, Shanghai, China The University of Nottingham, Nottingham, UK

Topic: S05: Time Frequencies and Precision Timing Chairman Aimin Zhang

National Institute of Metrology, Beijing, China

Vice-chairman Liang Wang

The 203th Research Institute of China Aerospace Science and Industry Corporation, Beijing, China

Organization

Lijun Du Xiaohui Li Patrizia Tavella

ix

Xi’an Branch of China Academy of Space Technology, Shaanxi, China National Time Service Center, Chinese Academy of Sciences, Shaanxi, China Bureau International des Poids et Mesures, Paris, France

Topic: S06: Autonomous Navigation and Intelligent Operation Chairman Xingqun Zhan

Shanghai Jiao Tong University, Shanghai, China

Vice-chairman Haihong Wang Wenbin Gong

Yuxin Zhao Caibo Hu Naser EI-Sheimy

Institute of Telecommunication and Navigation Satellites, CAST, Beijing, China Innovation Academy for Microsatellites of Chinese Academy of Sciences, Shanghai, China Harbin Engineering University, Heilongjiang, China Beijing Satellite Navigation Center, Beijing, China University of Calgary, Alberta, Canada

Topic: S07: GNSS Signal Processing Chairman Xiaochun Lu

National Time Service Center, Chinese Academy of Sciences, Shaanxi, China

Vice-chairman Yang Li

Zheng Yao Xiaomei Tang Sherman Lo

The 29th Research Institute of China Electronics Technology Group Corporation, Sichuan, China Tsinghua University, Beijing, China National University of Defense Technology, Hunan, China Stanford University, San Francisco, USA

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Organization

Topic: S08: GNSS User Terminals Chairman Hong Li

Tsinghua University, Beijing, China

Vice-chairman Zishen Li Liduan Wang Chengjun Guo Sang Jeong Lee

Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing, China ComNav Technology Ltd., Shanghai, China University of Electronic Science and Technology of China, Sichuan, China Chungnam National University, Daejeon, South Korea

Topic: S09: PNT Architectures and New PNT Technologies Chairman Zhongliang Deng

Beijing University of Posts and Telecommunications, Beijing, China

Vice-chairman Jiangning Xu Jinsong Ping

Dongyan Wei Jinling Wang

Naval University of Engineering, Hubei, China The National Astronomical Observatories of the Chinese Academy of Sciences, Beijing, China Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing, China The University of New South Wales, Sydney, Australia

Topic: S10: Policies, Standards and Intellectual Property Rights Chairman Junlin Yang

Beihang University, Beijing, China

Vice-chairman Miao Tian

China Satellite Navigation Office International Corporation Center, Beijing, China

Organization

Huiying Li

Yuxia Zhou

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Electronic Intellectual Property Center, Ministry of Industry and Information Technology, Beijing, China China Academy of Aerospace Standardization and Product Assurance, Beijing, China

Scientific Committee Senior Advisor: (By Surnames Stroke Order) Qingjun Bu Liheng Wang Yuzhu Wang

Guoxiang Ai Lehao Long Shuhua Ye Jiadong Sun Daren Lv Yongcai Liu Jingnan Liu Houze Xu Jinan Li Zuhong Li Guirong Min Rongjun Shen Chi Zhang Xixiang Zhang

China National Administration of GNSS and Applications, Beijing, China China Aerospace Science and Technology Corporation, Beijing, China Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China China Aerospace Science and Technology Corporation, Beijing, China Shanghai Astronomical Observatories, Chinese Academy of Sciences, Shanghai, China China Aerospace Science and Technology Corporation, Beijing, China The Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China China Aerospace Science and Industry Corporation, Beijing, China Wuhan University, Hubei, China Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Hubei, China The Former Electronic Information Foundation Department of General Equipment Department China Academy of Space Technology, Beijing, China China Academy of Space Technology, Beijing, China China Satellite Navigation System Committee, Beijing, China The Former Electronic Information Foundation Department of General Equipment Department The 29th Research Institute of China Electronics Technology Group Corporation, Sichuang, China

xii

Lvqian Zhang Junyong Chen Benyao Fan Dongjin Luo Huilin Jiang Guohong Xia Peikang Huang Chong Cao Faren Qi Rongsheng Su Shusen Tan Ziqing Wei

Organization

China Aerospace Science and Technology Corporation, Beijing, China National Administration of Surveying, Mapping and Geo-information, Beijing, China China Academy of Space Technology, Beijing, China China People’s Liberation Army, Beijing, China Changchun University of Science and Technology, Jilin, China China Aerospace Science and Industry Corporation, Beijing, China China Aerospace Science and Industry Corporation, Beijing, China China Research Institute of Radio Wave Propagation (CETC 22), Beijing, China China Academy of Space Technology, Beijing, China China People’s Liberation Army, Beijing, China Beijing Satellite Navigation Center, Beijing, China Xi’an Institute of Surveying and Mapping, Shaanxi, China

Chairman Changfeng Yang

China Satellite Navigation System Committee, Beijing, China

Vice-chairman Yuanxi Yang Shiwei Fan

China National Administration of GNSS and Applications, Beijing, China China Satellite Navigation Engineering Center, Beijing, China

Executive Chairman Jun Xie Lanbo Cai

China Academy of Space Technology, Beijing, China China Satellite Navigation Office, Beijing, China

Organization

xiii

Committee Members: (By Surnames Stroke Order) Xiancheng Ding Qun Ding

Quan Yu Zhijian Yu Jian Wang Shafei Wang Wei Wang Lihong Wang Chengqi Ran Weimin Bao Yueguang Lv Zhaowen Zhuang Chong Sun Yadu Sun Tianchu Li Xianyu Li Minglin Li Hui Yang Longxu Xiao Yirong Wu Weiqi Wu Haitao Wu Manqing Wu Bin Wu Jun Zhang

China Electronics Technology Group Corporation, Beijing, China The 20th Research Institute of China Electronics Technology Group Corporation, Beijing, China Peng Cheng Laboratory, Shenzhen, China Taiyuan Satellite Launch Center of China’s Manned Space Project, Shanxi, China Alibaba Group, Zhejiang, China Academy of Military Sciences PLA China, Beijing, China China Aerospace Science and Technology Corporation, Beijing, China Legislative Affairs Bureau of the Central Military, Beijing, China China Satellite Navigation Office, Beijing, China China Aerospace Science and Technology Corporation, Beijing, China Science and Technology Commission of the CPC Central Military Commission National University of Defense Technology, Hunan, China Beijing Institute of Tracking and Communication Technology, Beijing, China Aerospace Engineering Research Institute of the PLA Strategic Support Force National Institute of Metrology, Beijing, China Research Institute of the PLA Rocket Force China Society for World Trade Organization Studies, Beijing, China China Academy of Space Technology, Beijing, China Research Institute of the PLA Rocket Force The Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing, China Xichang Satellite Launch Center, Sichuan, China Aerospace, Chinese Academy of Sciences, Beijing, China China Electronics Technology Group Corporation, Beijing, China Beijing Institute of Tracking and Communication Technology, Beijing, China Beijing Institute of Technology, Beijing, China

xiv

Zhijie Chen Zhonggui Chen

Jinping Chen Baojun Lin

Zhixin Zhou Jianping Zhou Jianhua Zhou Jiancheng Fang Wenjun Zhao Jiang Hu Jie Jiang Shuren Guo Huikang Huang Xibin Cao Wenhai Jiao Yi Zeng Yi Cai

Organization

National Core Laboratory of Airspace Technology The 5th Research Institute of China Aerospace Science and Technology Corporation, Beijing, China Beijing Satellite Navigation Center, Beijing, China Innovation Academy for Microsatellites of Chinese Academy of Sciences, Shanghai, China Space Engineering University, Beijing, China Chief Designer of China’s Manned Space Project Beijing Satellite Navigation Center, Beijing, China Beihang University, Beijing, China Beijing Satellite Navigation Center, Beijing, China BeiDou Application & Research Institute Co., Ltd. of Norinco Group, Beijing, China China Academy of Launch Vehicle Technology, Beijing, China China Satellite Navigation Engineering Center, Beijing, China Ministry of Foreign Affairs of the People’s Republic of China, Beijing, China Harbin Institute of Technology, Heilongjiang, China China Satellite Navigation Engineering Center, Beijing, China China Electronics Corporation, Beijing, China BeiDou Ground-based Augmentation System Chief Engineer

Executive Members: (By Surnames Stroke Order) Jun Shen Dangwei Wang Rui Li Xiaogong Hu Aimin Zhang Xingqun Zhan

Beijing UniStrong Science and Technology Co., Ltd., Beijing, China Beijing UniStrong Science and Technology Co., Ltd., Beijing, China Beihang University, Beijing, China Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, China National Institute of Metrology, Beijing, China Shanghai Jiao Tong University, Shanghai, China

Organization

Xiaochun Lu Hong Li Zhongliang Deng Junlin Yang

xv

National Time Service Center, Chinese Academy of Sciences, Shaanxi, China Tsinghua University, Beijing, China Beijing University of Posts and Telecommunications, Beijing, China Beihang University, Beijing, China

Organizing Committee Director Chengqi Ran

China Satellite Navigation Office, Beijing, China

Deputy Director Jun Yang Xiaohua Qu Yun Xiao

China Satellite Navigation Office, Beijing, China Jiangxi Provincial Office of Civil-Military Integration, Jiangxi, China Nanchang Municipal People’s Government, Jiangxi, China

Secretary-General Haitao Wu

Satellite Navigation Headquarters, Chinese Academy of Sciences, Beijing, China

Deputy Secretary-General Weina Hao

Satellite Navigation Headquarters, Chinese Academy of Sciences, Beijing, China

Deputy Secretary Yao Wang Wenhai Jiao Mingquan Lu Jun Lu Weiquan Guo Bin Yang

Nanchang Municipal People’s Government, Jiangxi, China China Satellite Navigation Engineering Center, Beijing, China Tsinghua University, Beijing, China China Satellite Navigation Engineering Center, Beijing, China Jiangxi Provincial Office of Civil-Military Integration, Jiangxi, China Nanchang Municipal Office of Civil-Military Integration, Jiangxi, China

xvi

Organization

Committee Members: (By Surnames Stroke Order) Li Wang Ying Liu Guangfu Sun Di Xiao Caicong Wu Taosheng Wang Jun Shen Lu Chen Xiuwan Chen Junlin Yang Dongning Lin Baoming Zhou Jinjun Zheng Wenjun Zhao Qile Zhao Yamin Dang Min Shui Wei Xiong

International Cooperation Research Center, China Satellite Navigation Office, Beijing, China China Satellite Navigation Engineering Center, Beijing, China National University of Defense Technology, Hunan, China Beidou Union Technology Co., Ltd., Beijing, China China Agricultural University, Beijing, China China Satellite Navigation Engineering Center, Beijing, China Beijing UniStrong Science and Technology Co., Ltd., Beijing, China Beijing Institute of Space Science and Technology Information, Beijing, China Peking University, Beijing, China BDS/GNSS Policy and Regulation Research Center, Beijing, China Beijing Shunyi District Economic and Information Commission, Beijing, China Nanchang Municipal Office of Civil-Military Integration, Jiangxi, China China Academy of Space Technology, Beijing, China Beijing Satellite Navigation Center, Beijing, China Wuhan University, Hubei, China Chinese Academy of Surveying and Mapping, Beijing, China The National Remote Sensing Center of China, Beijing, China Jiangxi Provincial Office of Civil-Military Integration, Jiangxi, China

Contents

GNSS and Their Augmentations Chairman Analysis of GPS Signal Power Enhancement Effect Based on Data from Multiple Ground Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chao Xie, Deyong Xian, Teng Li, Guotai Wang, and Qian Wang

3

The Research on Double-Difference Ionospheric Interpolation Based on Gaussian Process Regression . . . . . . . . . . . . . . . . . . . . . . . . . . Zhendong Dai, Peilin Liu, Rendong Ying, and Qiang Liu

11

Monitoring Station Data Quality Analysis Method . . . . . . . . . . . . . . . . . Hongyi Ren, Zhigang Huang, Rui Li, and Tiantian Yang

22

Research on the Distortion Threat Model and Threat Space of BDS B1C and B2a Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yang Gao, Xiaowei Cui, Henglin Chu, Qibing Xu, and Yuqi Liu

33

Applicability Analysis of DFMC SBAS Receiver Design Constraints to BDS B1C and B2a Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Henglin Chu, Yang Gao, Kefan Wei, and Xiaowei Cui

45

Analysis of the Applicable Minimum Filter Gain Roll-Off of DFMC SBAS Receiver for BDS Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yang Gao, Xiaowei Cui, Kefan Wei, and Henglin Chu

55

Weakening Test of Pseudo-range Bias Based on ParametersConstrained of BDS Monitoring Receiver . . . . . . . . . . . . . . . . . . . . . . . Xiaochao Feng, Lei Gong, Kuixing Liu, Qian Ma, Shuai Gao, and Xin Qi

66

Signal Quality Monitoring Algorithms of DFMC SBAS for Dual-Frequency Civil Signals of BDS . . . . . . . . . . . . . . . . . . . . . . . . Xiang Wang, Xiaowei Cui, Kefan Wei, Gang Liu, Yang Gao, and Mingquan Lu

75

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xviii

Contents

Optimal Design of LEO Constellation for Communication and Navigation Fusion Based on Genetic Algorithm . . . . . . . . . . . . . . . Jinquan Huang, Ying Liu, Xiaohui Liu, Xiaozhou Ye, Xiangjun Li, Wei Xiao, Wenxiang Liu, and Yong Zuo

92

Observations of Ionospheric Disturbances Based on CORS Data Over North America . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Junru Ye, Yan Chen, and Haiyang Fu Spectrum Compatibility Analysis Between LEO Navigation Augmentation Signals and GNSS Signals . . . . . . . . . . . . . . . . . . . . . . . . 114 Sixin Wang, Xiaohui Liu, Xiaomei Tang, Feixue Wang, and Zhaowen Zhuang A Robust Positioning and Adaptive RAIM FDE Algorithm for Multiple Outliers Based on Non-Gaussian Distribution . . . . . . . . . . 130 Lihua You and Bo Bi Sparse Reconstruction of the Ionosphere in the Equatorial Anomaly Region During the Solar Eclipse Based on Beidou Ground Based Augmentation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Yun Sui, Haiyang Fu, Denghui Wang, Shaojun Feng, Feng Xu, and Yaqiu Jin Research on Single Frequency BDSBAS Message Scheduler Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 Jingcan Zhang, Rui Li, and Junjun Wang Improved BDS RAIM Algorithm Based on M-Estimation . . . . . . . . . . . 163 Ershen Wang, Xidan Deng, Jing Guo, Pingping Qu, and Tao Pang Analysis of the BDS-3 Complete System on Positioning Performance in Polar Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 Shunxi Fan, Yi Fan, Xianbing Wu, Kang Zheng, Deyan Xu, Yue Mao, and Xiaolin Jia Development of High-Precision Ionospheric Monitoring System in China: Taking ROTI Map as an Example . . . . . . . . . . . . . . . . . . . . . 187 Chengli She, Haitao Liu, Jun Yu, Peiyuan Zhou, and Hongzheng Cui LEO Constellation Design Based on Dual Objective Optimization and Study on PPP Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 Xin Nie, Min Li, Fujian Ma, Lei Wang, and Xu Zhang Research on Civil GNSS Signal Authentication Service Design . . . . . . . 208 Xiaomin Jia, Ranran Su, Wentao Liang, Fei Shen, Chong Zheng, Zheng Wang, Xuan Wang, and Linfeng Xu

Contents

xix

Key Technical Characteristics and Performance of BeiDou Navigation Augmentation System Based on LEO Constellation . . . . . . . 219 Xing Li, Lang Bian, Xia Guo, and Yansong Meng Satellite Navigation System Time Delay Automatic Calibration Technology and Ground Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 Wei Wang, Yilong Liu, Jun Lu, Ying Chen, Haitao Wei, Guoyi Zhang, and Chengpan Tang Preliminary Assessment of BDS-3 PPP Service Performance . . . . . . . . . 241 Chenghe Fang, Yinhu Ma, Changjiang Geng, Hongliang Cai, Yifang Zhao, Tianyang Sun, Qi Li, and Cheng Liu Influence of Different ISB Processing Strategies on the Accuracy of Undifferenced FCBs and PPP-AR Positioning . . . . . . . . . . . . . . . . . . 256 Wenlong Qi, Hongzhou Chai, Xu Kun, Wang Min, and Chong Yang Co-channel Interference Cancellation Method Based on Deep Neural Network for LEO Satellite Systems . . . . . . . . . . . . . . . . . . . . . . 270 Jie Sun, Zuping Tang, Jiaolong Wei, and Yiwen Ren A Pseudo-satellite Implementation Method Using High Precision Time Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 Ruifeng Zheng Coordinated Precoding Based on Distributed CSI for Multi-station and Multi-satellite MIMO Uplink System . . . . . . . . . . . . . . . . . . . . . . . 289 Shan Lu, Yi Zhang, Chengkai Tang, and Juan Zhang Energy Efficiency Optimization Algorithm for Single Station Multi-satellite MIMO Uplink System . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 Juan Zhang, Yi Zhang, Chengkai Tang, and Shan Lu Unmasking Bayesian RAIM Algorithm for Identifying Simultaneous Two-Faulty Satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 Ke Chen, Xinna Li, and Junzheng Li The Realization and Performance Evaluation of Real-Time Precise Point Positioning Based on BDS-3 PPP-B2b Augmentation Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 Lun Ai, Jie Wu, Binbin Wang, and Ruwei Zhang Autonomous Navigation and Intelligent Operation Research on Improvement Method of Systematic Deviation of Autonomous Navigation Message of BDS . . . . . . . . . . . . . . . . . . . . . . 327 Qiuli Chen, Haihong Wang, Xu Zhang, Yu Ding, and Weisong Jia

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A DBZP Acquisition Method for High-Dynamic and Weak GPS Signal Aided by SINS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 Junshuai Wang, Xinlong Wang, Fei Liu, and Xiaoming Hao The Dispersion Effect of Pseudo-noise Ranging and Time Delay Measurement for Ka Inter-satellite Link . . . . . . . . . . . . . . . . . . . . . . . . 347 Jianlou Zhuang, Jie Zhang, Chengbin Kang, Zhendong Li, and Zhijia Liu Research on Collision Avoidance Between UAV Flocks Using Behavior-Based Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 Changkun Wang, Jiqing Du, Lang Ruan, Jing Lv, and Shiwei Tian Digital Track Map Aided Multi-sensor Fusion for Train Occupancy Identification in Complicated Track Sections . . . . . . . . . . . . . . . . . . . . . 366 Tao Yang, Debiao Lu, Baigen Cai, Jiang Liu, and Yu Xiao GNSS Multipath Detection Based on Decision Tree Algorithm in Urban Canyons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 Yue Wang, Jiawei Xu, Rong Yang, and Xingqun Zhan Decentralized Collaborative Localization Algorithm Based on Covariance Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 Dongmin Wang, Dongqing Zhao, Minzhi Xiang, Ziru Huang, and Jinfei Li DVT-SLAM: Deep-Learning Based Visible and Thermal Fusion SLAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 Ruochen Wang, Ling Pei, Lei Chu, Qi Wu, Tao Li, Wenxian Yu, and Xujun Guan Satellite Thrusters’ Control Allocation and Application Used for Integrated Attitude-Orbit Control System . . . . . . . . . . . . . . . . . . . . 404 Xiaoyue Li, Tao Bai, and Baojun Lin Real-Time Robot Localization Based on 2D Lidar Scan-to-Submap Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 Qipeng Li, Jianzhu Huai, Dong Chen, and Yuan Zhuang Research on Strategy of Access Node Selection for Space-Based Relay Network Based on Navigation Satellites . . . . . . . . . . . . . . . . . . . . 424 Lingchuan Zeng, Weiyi Chen, Bingcheng Liu, Yan Bai, Xiaochun Lu, and Guang Yang Research on Error Online Calibration Method of Inertial/Stellar Refraction Integrated Navigation System . . . . . . . . . . . . . . . . . . . . . . . . 435 Qiaochu Lv, Xueying An, Dingjie Wang, and Jie Wu Investigation on Centralized Autonomous Orbit Determination Using Inter-satellite Ranging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 Jingshi Tang, Haihong Wang, Jinjun Zheng, Lin Liu, Qiuli Chen, Weisong Jia, Xu Zhang, and Chengbin Kang

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Research on Invariant Extended Kalman Filter Based 5G/SINS Integrated Navigation Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 Yarong Luo, Mengyuan Wang, Chi Guo, and Wenfei Guo Analysis of Management and Control and Scheduling Mode for Mega Constellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 Lei Lei, Wei Chen, Si-zhe Cai, Hui-li Gao, and Chen Chi Deployment Location Algorithm of Navigation Base Station Based on GDOP Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478 Jintao Yao, Hongli Li, and Bin Li Research on Loran-C ASF Correction Method Based on GA-BP Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487 Yuqi Wang, Wei Wang, and Rui Luo On Precise Inertial Force Modeling for Autonomous Orbit Propagation in Earth-Centered Fixed System for Earth Satellites . . . . . 496 Haihong Wang, Jingshi Tang, Jinjun Zheng, Qiuli Chen, Chengbin Kang, Weisong Jia, and Shaojun Bi A Beidou Laser Link Allocation Scheme Based on Network Throughput Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 Zheng Huang, Wenbin Gong, and FengWei Shao Mechanism Analysis and Mitigation of Visual Navigation System Vulnerability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 Yawei Zhai, Yuanwen Fu, Shizhuang Wang, and Xingqun Zhan Pedestrian Collaborative Inertial-Only SLAM . . . . . . . . . . . . . . . . . . . . 525 Yiming Ding, Zhi Xiong, Zhengchun Wang, Zhiguo Cao, and Wanling Li An Efficient and Robust Indoor Magnetic Field Matching Positioning Solution Based on Consumer-Grade IMUs for Smartphones . . . . . . . . . 535 Jian Kuang, Taiyu Li, and Xiaoji Niu Research on Signal Acquisition Technique of Inter-satellite Links of Navigation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546 Jian Wang, Xuan Wang, Yuqian Pan, Xiaofang Zhao, Xinuo Chang, and Zhendong Li PNT Architectures and New PNT Technologies Performance Verification of Capsule Networks in LOS/NLOS Identification for UWBPositioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 Zhichao Cui, Haiyu Zeng, Yufang Gao, Shiwei Tian, and Jian Cheng

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Map Matching with WiFi-RSSI GRU Indoor Room Switching Classifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566 Weijia Jiang, Zhongliang Deng, Xinyu Zheng, Jiehua Liu, and Yuetong Wang DOP Analysis for Indoor Hybrid TDOA/TOA Positioning Based on Mobile Communication Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576 Hanhua Wang, Zhongliang Deng, Xinyu Zheng, and Xiao Fu A New Algorithm of Tightly-Coupled GNSS/INS Integrated Navigation Based on Factor Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586 Xiaohui Liu, Yuelin Yuan, Jinquan Huang, Yamu Xiao, and Xingtong Li ISM Band Multi-source Signal Perception Based on Time-Frequency Image Feature Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596 Zhongliang Deng, Hang Qi, Enwen Hu, and Yanxu Liu Estimate of Initial Installation Angle of INS in Vehicle MEMS-INS/GNSS Integrated Navigation System . . . . . . . . . . . . . . . . . . 606 Hongsong Zhao, Juhong Xing, Mobo Qiu, and Yongsong Wang An Improved Wireless Positioning Algorithm Based on the LSTM Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616 Xiansheng Yang, Dong Chen, Jianzhu Huai, Xiaoxiang Cao, and Yuan Zhuang Research on Space/ground Based Pulsar Timescale for PNT . . . . . . . . . 628 Qingyong Zhou, Ziqing Wei, Linli Yan, Pengfei Sun, Kun Jiang, and Yidi Wang Research on Positioning Method in the Lunar Space . . . . . . . . . . . . . . . 637 Linshan Xue, Xue Li, Weiren Wu, and Yikang Yang Parameter Estimation of Pulsar Position Based on Least Square . . . . . . 646 Shi Chen, Li-rong Shen, Yong-qiang Shi, Xiao-ping Li, Zhe Su, and Hai-feng Sun Analysis and Suggestions on the Resilience of GNSS Timing . . . . . . . . . 656 Longxia Xu, Feng Zhu, and Xiaohui Li Machine Measuring Method for Norm-Position of Targets . . . . . . . . . . 666 Haitao Wu Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681

GNSS and Their Augmentations Chairman

Analysis of GPS Signal Power Enhancement Effect Based on Data from Multiple Ground Stations Chao Xie(B) , Deyong Xian, Teng Li, Guotai Wang, and Qian Wang Beijiing Satellite Navigation Center, P.O. Box 5128, Beijing 100094, China [email protected]

Abstract. Public data provided by the International GNSS Service (IGS) website shows that from 0:00 UTC on February 14, 2020, the power of the P(Y) code signal of some GPS satellites at the L2 frequency point has been increased significantly. An automatic analysis method of GPS satellite signal power sudden changes based on data from multiple ground stations is proposed. This method is based on the post-observation data of multiple ground stations and automatically analyzes the time of the sudden change in the power of the navigation satellite signal through computer software, so as to determine the satellite power enhancement period, and then analyze the availability of the satellite in the power enhancement state. The method can be applied to the analysis and research of the power enhancement effect of GPS system. Keywords: GPS · Power enhancement · Automatic analysis · Multiple ground stations

1 Introduction As the first satellite navigation system to be built and applied, GPS played an important role in a series of local wars in Iraq, Kosovo, Afghanistan, Libya and Syria. However, satellite navigation system has the characteristics of weak signal, easy interference and vulnerability to obstruct, making its military applications vulnerable, so the U.S. military began to study GPS anti-jamming and electronic warfare technology, and in 1997 first put forward the concept of “navigation warfare”, that is, “The NAVWAR program is tasked with protecting Pentagon and allied use of GPS during times of conflict, preventing its use by adversaries while maintaining normal availability to the civil user outside the area of conflict.” [1] This concept is widely accepted in the field of military navigation in various countries, thus opening up a comprehensive study and application of navigation warfare. As one of the means to improve the anti-jamming capability of the system navigation service, satellite signal power enhancement is an important defense measure for the satellite navigation user segment. In navigation confrontation, in order to avoid the interference of navigation signal by suppression and deception, the user’s anti-jamming ability is improved by increasing the power of navigation signal. In the case of constant © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 3–10, 2021. https://doi.org/10.1007/978-981-16-3142-9_1

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interference level, the satellite signal increase of 10 dB can reduce the disturbed area to one-tenth of the original, while the 20 dB signal power increase can reduce the disturbed area to one percent. To achieve the same interference effect, the other side can only increase the interference power, thus making the interference source easier to detect and remove. Therefore, satellite signal power enhancement technology is an important measure to improve the survivability of satellite navigation equipment. Many scholars have carried out relevant research on satellite navigation power enhancement. Sun Jin [2] analyzed the power enhancement amplitude and coverage of satellite navigation system from the system point of view. Lu Zhicheng [3, 4] analyzed the impact of satellite navigation system power enhancement on regional positioning service performance and reception signal quality. Xiao Zhibin [5] analyzed the satellite navigation interstellar signal assistance capability under the condition of power enhancement from the user’s point of view, but these methods are mainly based on simulation and theoretical analysis, lack of practical data support.

2 Recent GPS Signal Power Enhancement Recently, GPS signal power was enhanced again, and after-the-fact data analysis provided by IGS found that since 0:00 UTC on February 14, 2020, the L2 frequency P(Y) code signal power of some GPS satellites has been increased, and the signal power of several satellites has mutated in the next few days. Based on actual monitoring data, some scholars have used RTKLIB software to analyze the power enhancement of GPS signals during the 2018 U.S. strike on Syria. Based on this method, using RTKLIB software to draw the observation data of IGS monitoring station, we can see that the L2 frequency carrier-to-noise ratio has obvious jump. Taking the GPS03 satellite L2 frequency signal carrier-to-noise ratio curve observed by AIRA station on February 16, 2020 as an example, as shown in Fig. 1, the carrier-to-noise ratio value suddenly increased by about 10 dB at about 13:13 UTC time. Other sites around the AIRA station were also able to observe a sudden change in the GPS03 satellite’s carrier-to-noise ratio at the same time, so it is thought that the GPS03 satellite began to perform power enhancement at about 13:13. Similarly, the GPS03 satellite can be seen stopping the power enhancement at about 14:49, and its signal power returns to normal levels.

Fig. 1. Carrier-to-noise ratio curve of GPS satellite L2 frequency point P(Y) code signal with PRN of 03 observed by IGS AIRA station

Analysis of GPS Signal Power Enhancement

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3 Analysis Method of Power Mutation Moments However, only relying on RTKLIB software for data analysis will lead to problems of high manual participation, low efficiency, and poor real-time performance. Given the huge amount of data, the quality of data analysis is difficult to guarantee. And this method cannot process multiple ground-based observatory data at the same time. Therefore, it is difficult to detect errors in the case of errors, which can easily lead to inaccurate or incomplete data analysis results. In order to solve the above problems, an automatic analysis method of GPS power change time based on multi-ground station data is proposed, which is based on the post-observation data of multiple ground stations, and the moment of sudden change of navigation satellite signal power is calculated by automatic analysis by computer software. The object of analysis is the observation of GPS satellites by M ground stations in a period of time, the start of the time period is recorded as, the end moment is recorded as, and is used to represent a moment in the time period, k is 1,2,…,N. The analysis method flow, as shown in Fig. 2, includes the following steps: Step 1, because the low elevat angle satellite signal changes by a large margin, so if not processed, there may be more false alarm. Therefore, first of all, the satellite signal load-to-noise ratio data received by the ground station is filtered, and the carrier-tonoise ratio data of satellites with pitch angle below the threshold (the threshold value is recorded as He,c ) are discarded. Step 2, initialize the site index and the moment index variable, so that tk = t1 , J = 1. Step 3, Differential calculations are performed on the carrier noise ratio data of the satellites received by ground station J at tk moment. For the current moment tk , in the observation data file, read the carrier-to-noise ratio CNRJ ,k of the satellite s received by the ground station J, and tk-1 moment’s carrier-tonoise ratio CNRJ ,k−1 . By making a difference between the two values, the load-to-noise ratio change CNRJ ,k for the tk-1 to tk period is obtained by formula 1. CNRJ ,k = CNRJ ,k − CNRJ ,k−1

(1)

Step 4, to determine whether the ground station J observed the signal power of the satellite s jump. If the difference CNRJ ,k is greater than threshold H CNR (the typical value range of H CNR is 3 dB to 6 dB), it’s considered that the ground station J observes the sudden increase of the satellite signal power at tk moment, and if CNRJ ,k < -H CNR , it’s considered that the ground station J observes the satellite signal power suddenly decrease at tk moment. Step 5, select the next ground station, repeat step 3 to step 4, until traversing all M ground stations. The number of ground stations where the satellite’s power enhancement and weakening can be observed at tk time is counted separately. Step 6, observation data from multiple ground stations is used to determine whether the tk time satellite s signal power has mutated. If the number of ground stations where the signal power of the satellites is suddenly increased at tk time is greater than the threshold N 0 (the typical value range of N 0 is 2 to 10), the signal power of the satellites is considered to be suddenly increased at tk ; and similarly, If the number of ground

6

C. Xie et al. Begin The satellite signal load-to-noise ratio data received by the ground station are filtered and the carrier-to-noise ratio data of satellites with pitch angle below the threshold are discarded. Initialize site indexes and moment index variables. Differential calculations are performed on the carrier noise ratio data of the satellites received by ground station J at tk moment.

Determine whether ground station J has observed a jump in the signal power of the satellite s.

Select the next ground station and repeat steps 3 through 4 until all M ground stations are traversed. The number of ground stations where the satellite's power suddenly increased and suddenly weakened was observed at tk time, respectively.

Multiple ground stations were used to determine whether the signal power of satellites had mutated.

Traversing each GPS satellite, repeating steps 3 through 6 to determine whether the power of all GPS satellites at tk time has mutated.

Traversing the t1 to tN moments, repeat steps 3 through 7 to arrive at a list of GPS satellites with signal power mutations during that time period.

End

Fig. 2. Flow chart of automatic analysis method for GPS signal power sudden change based on data from multiple ground stations

stations where the signal power of the satellites is suddenly reduced at tk time is greater than the threshold N 0 , the signal power of the satellites is considered to be suddenly reduced at tk ; otherwise, the signal power of the satellites is considered not to have mutated at that moment.

Analysis of GPS Signal Power Enhancement

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Step 7, traversing the GPS satellites, repeat steps 3 to 6, to determine whether all GPS satellite signal power mutation occurred at tk time. Step 8, traversing the t1 to tN moment, i.e. tk = t1 , . . . , tN , repeating steps 3 to 7, arrives at a list of GPS satellite information that has a signal power mutation during that time period, which contains the satellite PRN number, mutation type (enhanced or weakened), and mutation occurrence time.

4 Power-Enhanced Satellites Availability Analysis In order to conduct an in-depth analysis of the enhancement effect of the GPS L2 P(Y) code signal, the GPS observation data files of 461 sites on February 16, 2020 were downloaded from the IGS website. Using the above analysis method, set the threshold N 0 of the number of sites that simultaneously observe the sudden change of the satellite signal power to 10, the carrier-to-noise ratio jump threshold H CNR to 5 dB, and the satellite cut-off angle threshold He,c is set to 10°. The observation data of GPS is automatically analyzed, and the timetable of the sudden change in the power of the L2 P(Y) code signal for the GPS satellites on the day is obtained, as shown in Table 1. The signal power enhancement time of the GPS satellite with PRN of 03 is about 13:13, which is consistent with the result of the manual interpretation method in Fig. 2, thus verifying the correctness of the method. It can be seen from Table 1 that between 0:00 and 24:00 on February 16th, there were 64 sudden changes in the power of the L2 P(Y) code signal of GPS satellites. A total of 19 GPS satellites were involved, and their PRNs were 1, 3, 5, 6, 7, 8, 9, 10, 12, 15, 17, 24, 25, 26, 27, 29, 30, 31 and 32. Among them, the 6 satellites with RPN of 7, 9, 10, 12, 29, and 30 suddenly strengthened once and weakened once, and the remaining 13 satellites strengthened and weakened twice each. According to Table 1 and Fig. 3, the cumulative time of the 19 GPS satellite signals in the power-enhanced state is counted. Among them, the GPS satellite with a PRN of 10 has the longest enhancement time of 15 h and 35 min, and the GPS satellite with a PRN of 12 has the shortest enhancement time of 7 h and 52 min. The average enhancement time of all 19 satellites is 10 h and 8 min. Based on the publicly obtained GPS almanac, the availability of GPS satellites in an enhanced state will be analyzed. First, divide the grid points on the surface of the earth at intervals of 5° × 5° in space, and take a time point every 5 min in time. For all the time and space points of the day, take 5° pitch angle as the observable cut-off angle, and calculate the visibility and PDOP of the satellites in the power-enhanced state. Then, with PDOP ≤ 6 as the availability condition, for these earth grid points, the availability within 24 h is counted. Finally, use the contourf() function of MATLAB software to draw availability distribution map of satellites in power-enhanced state on February 16, as shown in Fig. 4. It can be seen that the power enhancement effect of GPS L2P(Y) code signal has obvious regional characteristics.

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Table 1. The timetable of the sudden change in the power of the L2 P(Y) code signal for the GPS satellites number

PRN

Type

Moment

number

1

31

Enhanced

0:06

33

2

3

Enhanced

0:20

34

3

25

Enhanced

1:11

4

24

Weakened

5

17

Enhanced

6

27

7 8

PRN

Type

Moment

5

Weakened

11:48

6

Enhanced

11:48

35

7

Weakened

12:51

1:14

36

3

Enhanced

13:13

1:58

37

1

Weakened

13:26

Weakened

2:06

39

30

Weakened

14:03

26

Enhanced

2:18

40

32

Enhanced

14:12

9

Enhanced

2:40

41

29

Enhanced

14:22

9

8

Weakened

2:59

42

3

Weakened

14:49

10

10

Weakened

3:36

43

15

Weakened

15:02

11

6

Enhanced

4:00

44

5

Enhanced

15:03

12

25

Weakened

4:00

45

31

Enhanced

16:14

13

7

Enhanced

4:18

46

32

Weakened

16:29

14

32

Weakened

4:43

47

17

Weakened

16:31

15

17

Weakened

4:47

48

24

Weakened

17:34

16

30

Enhanced

5:35

49

26

Enhanced

17:49

17

27

Enhanced

5:36

50

6

Weakened

17:58

18

1

Weakened

5:45

51

15

Enhanced

18:02

20

31

Weakened

6:18

52

10

Enhanced

19:11

21

5

Enhanced

7:03

53

12

Weakened

19:38

22

26

Weakened

7:37

54

27

Enhanced

19:59

23

3

Weakened

7:57

55

31

Weakened

20:22

24

6

Weakened

8:12

56

25

Weakened

20:35

25

17

Enhanced

9:22

57

5

Weakened

20:50

26

1

Enhanced

9:27

58

24

Enhanced

21:08

27

15

Enhanced

9:40

59

32

Enhanced

21:18

28

27

Weakened

9:55

60

8

Enhanced

21:24

29

9

Weakened

10:51

61

29

Weakened

22:42

30

8

Weakened

11:13

62

26

Weakened

23:11

31

24

Enhanced

11:14

63

15

Weakened

23:22

32

12

Enhanced

11:46

64

1

Enhanced

23:26

Analysis of GPS Signal Power Enhancement

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Fig. 3. Time distribution of the power enhancement state of GPS satellites on February 16, 2020

Fig. 4. All-day availability distribution map of GPS power-enhanced satellites on February 16, 2020

5 Conclusion By downloading GPS observation data released by IGS, the power enhancement phenomenon of GPS P(Y) code signal is found. In order to analyze the power change of GPS signal, a method for analyzing the sudden change of the GPS signal power based on

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the data of multiple ground stations is proposed. Through this method, a full-day GPS satellite power change schedule on February 16, 2020 is analyzed. Then, the availability distribution map of the GPS power enhancement satellites for that day is drawn, which can be applied to the analysis of the power enhancement effect of GPS.

References 1. Covault, C.: Navigation warfare-as the value of GPS increases, so do attempts to jam the system [EB/OJ] (Jan 2010). https://www.defensemedianetwork.com/stories/navigation-warfare/ 2. Sun, J., Chu, H., Dong, H., et al.: Research to power-enhanced technology and coverage areas of global navigation satellites. Acta Geodaetica et Cartographica Sinica 5, 27–31 (2019) 3. Zhicheng, L., Zengjun, L., Feixue, W.: An Analysis of Effect of Enhancement on Performance of Region Positioning Service. 33(1), 55–61 (2012) 4. Zhicheng, L., Junwei, N., Zengjun, L., et al.: Effects of enhancing power on received signal quality in satellite navigation system. Chin. J. Space Sci. 33(1), 101–107 (2013) 5. Zhibin, X., Xin, Z., Xiaomei, T., et al.: Analysis of inter-satellite signal assistance capacity under satellite power enhancement. J. Central S. Univ. Sci. Technol. 45(2), 468–473 (2014) 6. Qi, H., Zhu Kejia, F., et al.: Monitoring and assessment of GPS signals during US attacking on Syria. J. Navig. Position. 7(3), 7–10 (2019) 7. Tianqiao, Z., Xiliang, Z., Gang, W.: The effect of ADC on GNSS signal in continuous wave interference. Sci. Technol. Eng. 13(7) (2013) 8. White, J.F.: High Frequency Techniques: An Introduction to RF and Microwave Engineering, p. 339. Publishing House of Electronics Industry, Beijing (2009)

The Research on Double-Difference Ionospheric Interpolation Based on Gaussian Process Regression Zhendong Dai, Peilin Liu(B) , Rendong Ying, and Qiang Liu Brain-Inspired Application Technology Center, Shanghai Jiao Tong University, Shanghai, China [email protected]

Abstract. Ionospheric delay is an important factor affecting the high precision satellite positioning. Under short baseline conditions, it is possible to directly eliminate most of the ionospheric delay by using double-difference (DD) observation, while under long baseline conditions, it is necessary to use the ionospheric information from the base station network to perform interpolation. A DD ionospheric interpolation method under long baseline conditions based on Gaussian process regression is proposed in this paper. In our theory, we introduced the difference between the geographic longitude of the subsolar point and the ionospheric pierce point, and use it together with geographic coordinates as the input of kernel function. Kernel of the zenith ionospheric delay at the pierce point is reasonable assumed, and kernel of the DD ionosphere delay is derived based on it. Experimental results show that using the kernel proposed in this paper to perform Gaussian process regression interpolation, its effect can be better than the traditional Kriging and linear interpolation algorithms, and the accuracy is generally within 1 cm. Keywords: Ionospheric delay · Double-difference · Base station network · Gaussian process regression · Interpolation

1 Introduction For GNSS (Global Navigation Satellite System) positioning, the ionosphere will significantly affect the propagation delay of satellite signals, thus affecting the positioning accuracy [1]. Accurate ionospheric delay estimation can effectively improve the accuracy of single point positioning, and for high-precision positioning applications, it can also reduce the convergence time of carrier phase ambiguity resolution [3]. Dual frequency receivers can eliminate the influence of ionospheric delay by using ionosphere-free combination, but for the single frequency receivers, additional information is needed to correct the ionospheric delay. The first method is to model TEC distribution through mathematical function model, and there are different model choices according to different spatial-temporal scales [4]. For global ionospheric TEC, spherical harmonics can be used as its mathematical model, while for the regional ionospheric TEC, polynomial functions [13], low-degree spherical harmonic functions [7], spherical © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 11–21, 2021. https://doi.org/10.1007/978-981-16-3142-9_2

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cap harmonics functions [8] can be used. Due to the obvious diurnal variation characteristics of local Ionospheric TEC, the polynomial function can be combined with the periodic trigonometric series function to obtain the generalized trigonometric series function model for estimation [9]. The disadvantage of the above estimation method based on the mathematical function model is that it cannot effectively reflect the highfrequency variation components of the local ionosphere. Especially when the ionosphere is active, the difficulty of modeling is that the physical characteristics do not conform to the conventional model assumption. Some widely used models, such as Klobuchar model broadcast by GPS, can only correct 50% of the ionospheric delay [5]. The second method is to get accurate TEC estimation from the observations of the existing base station network, and then reconstruct the TEC of the whole region through interpolation. The common methods include inverse distance weighted method [2], planar fitting method [6], and Kriging interpolation method [10, 11], which is widely studied and used in the current wide area augmentation system (WAAS). This kind of interpolation based method can make more effective use of the spatial correlation between stations, and has a more accurate estimation of the local ionospheric information. With the continuous in-depth study of machine learning and other big data processing methods in recent years, some interpolation regression related algorithms are becoming more mature, and have been widely used in various fields. Gaussian process regression is one of the most widely used methods. Gaussian process is actually a set of nonparametric model based on Bayesian, and with the increase of the amount of data, the interpretation ability of the model is more powerful [12]. However, at present, there are few researches on ionospheric delay interpolation using Gaussian process regression, and many new algorithms proposed are also based on traditional Kriging method. Therefore, the research on ionospheric delay interpolation based on Gaussian process regression is very meaningful. In this paper, the DD ionospheric interpolation algorithm based on Gaussian process regression is studied, which aims to solve the problem of DD ionospheric estimation in local base station network. In practical applications, users often do not need the overall trend of the global ionosphere, but only need the precise ionospheric variation of a specific location, so the observation of local base station network can meet the requirements. In addition, due to the few number of stations in the local base station network, the number of observations in a single epoch is small, so it is difficult to get satisfactory results. It is necessary to process the data of multiple epochs for interpolation, so as to solve the problem of data sparsity.

2 Problem of Double-Difference Ionospheric Interpolation for Local Base Station Networks This section describes the problem of DD ionospheric interpolation in local base station network. Figure 1 is a diagram of the base station network, including multiple base stations and a rover station, and the base station nearest to the rover station can be selected as the master base station. The DD ionospheric delay of each base station relative to the main base station can be calculated by GNSS dual frequency observation.

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For rover stations, if we don’t use high-quality and long-time observation, it is impossible to directly calculate the DD ionospheric delay relative to the main base station, which can only be obtained by interpolating the DD ionospheric delay of the surrounding base stations according to the longitude and latitude coordinates of the base station. After the estimated DD ionospheric delay is obtained by interpolation, the corrected DD observation can be obtained by subtracting the estimated DD ionospheric delay directly from the DD observation of the rover station relative to the main base station, and then it can be used in the subsequent positioning algorithm.

Fig. 1. Diagram of base station network

3 Gaussian Process Regression Gaussian process regression is a kind of supervised learning regression method. It is a non-parametric model that uses the prior of Gaussian process for regression analysis of data. In this section, we will elaborate the basic concepts and principles of Gaussian process, and how to determine the hyperparameters of kernel. Let’s assume that we have training data input satisfying Gaussian process S = {xi , yi | i = 1, 2, . . . , n}, where x is the input vector of D dimension, y represents the corresponding observation output. Then the input matrix X and the target output observation y can be obtained by combining all n data. A Gaussian process can be uniquely expressed as    (1) f (x) ∼ GP m(x), k x, x   where m(x) is the mean function of the Gaussian process and k x, x is the covariance function of the Gaussian process, which is often called kernel. If there is additive white Gaussian noise ε in the observation, we have y = f (x) + ε

(2)

where the variance of noise is σn2 . Suppose X and X∗ represent the input matrix of training data and test data respectively, y represents the observation vector of training data and f∗ represents the target

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output of test data, then their joint distribution can be expressed as      K(X , X ) + σn2 I K(X , X∗ ) y ∼ N 0, K(X∗ , X ) K(X∗ , X∗ ) f∗

(3)

where N (m, C) is a Gaussian distribution with mean m and covariance matrix C. K is the covariance matrix calculated by kernel function. Then the conditional distribution can be calculated   f∗ | X∗ , X , y ∼ N f ∗ , cov(f∗ ) (4) where  −1 f ∗ = K(X∗ , X ) K(X , X ) + σn2 I y

(5)

 −1 cov(f∗ ) = K(X∗ , X∗ ) − K(X∗ , X ) K(X , X ) + σn2 I K(X , X∗ )

(6)

Then f ∗ is the regression prediction result calculated at the test data point according to the training data, and cov(f∗ ) is the corresponding variance, which can be used to estimate the confidence of the prediction result. Here we can introduce the marginal probability density, which can be expressed as

p(y | X , θ ) = p(y | f, X )p(f | , X )d f (7) where the prior p(f | , X ) satisfies Gaussian distribution, and θ is the hyperparameters, then n 1 1 log p(f | X , θ ) = − f T K −1 f − log|K| − log(2π) 2 2 2

(8)

By calculating the integral of Eq. (7), we can get

n −1 1  1

log p(y | X , θ ) = − yT K + σn2 I y − log K + σn2 I − log(2π ) 2 2 2

(9)

The gradient descent method can be used to optimize the marginal probability density and get the appropriate hyperparameters.

4 Selection of the Kernel of Double-Difference Ionospheric Delay Our ultimate goal is to construct a reasonable kernel of DD ionospheric delay. However, due to the complex statistical characteristics of the ionospheric delay after DD operation, it is difficult to be directly determined. Therefore, we need to first assume a reasonable kernel of zenith ionospheric delay, and then derive the kernel of DD ionospheric delay based on it.

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4.1 Kernel of Zenith Ionospheric Delay In the traditional linear ionospheric interpolation and Kriging interpolation algorithm, the input as the interpolation independent variable is two-dimensional geographic coordinates. This kind of method only interpolates the data on a single epoch according to the correlation between geographical coordinates, but does not consider the relationship between epochs, thus weakening the effect of interpolation. Therefore, this paper proposes an algorithm that can take multiple epoch data as input, and through subsequent analysis, we can know that its physical meaning represents the correlation of solar activity. The simplest way to deal with multi-epoch data interpolation is to directly add time dimensional, so the input can be formed as x0 = [λ, ϕ, t]T

(10)

where λ is the longitude, ϕ is the latitude, t is the UTC time in hour. The method above is an improvement to the original two-dimensional interpolation, but there is still room for improvement. We take the difference between the longitude of the ionospheric pierce point and the geographical longitude of the subsolar point as the third dimension, we can get x = [λ, ϕ, ϕ − ϕs ]T

(11)

where ϕs = − 360 24 t + 180 is the longitude of the subsolar point. It can be found that this method actually adds time epoch t to the third dimension of the input too. However, this method has more advantages under the actual observation conditions of the sun moving from east to west with the epoch variation. Geographical longitude and latitude can reflect the influence of the geomagnetic field on the ionosphere, that is, the smaller the difference between the geographical coordinates, the higher the correlation of the ionosphere delay due to the similarity of the geomagnetic field. On the other hand, taking the difference between the longitude of ionospheric pierce point and subsolar point as the input can also reflect the influence of solar radiation on the ionosphere. So far, we have determined the input of interpolation, from the traditional twodimensional interpolation to three-dimensional interpolation, making full use of the correlation of data between epochs, and reasonably introduced the influence of subsolar point. In order to quantify the relationship input data and output correlation,   between it is necessary to determine the kernel k x, x . Here we can assume that the kernel is expressed as      T    1 (12) k x, x = cov y, y = σ 2 exp − x, x D x, x 2 where σ is a scalar value and D is a 3 × 3 diagonal matrix, both of which are hyperparameters to be optimized by maximizing the marginal probability density. 4.2 Kernel of Double-Difference Ionospheric Delay In the previous section, the zenith ionospheric kernel function was determined. In this section, we will derive the DD ionospheric kernel based on it.

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Suppose that the top view of the distribution of ionospheric pierce point is shown in Fig. 2, which contains eight pierce point corresponding to two different DD ionospheric delays. x is the three-dimensional input designed in Sect. 4.1, and y is the zenith ionospheric delay. The superscript is used to distinguish the DD observations of two different epochs. The subscripts 1, 2, 3 and 4 represent the ionospheric pierce point between rover station and rover satellite, reference station and rover satellite, rover station and reference satellite, reference station and reference satellite, respectively. We can get two DD observations ∇y = F1 y1 − F2 y2 − (F3 y3 − F4 y4 )

(13)

  ∇y = F1 y1 − F2 y2 − F3 y3 − F4 y4

(14)

Fig. 2. Schematic diagram of the DD ionosphere pierce point distribution

where F1 , F2 , F3 , F4 are the corresponding trigonometric projection functions, which are related to the elevation angle of the satellite relative to the receiver, and are used to convert the STEC in the line of sight direction to VTEC in the vertical direction, which is F(E) =

STEC = VTEC

1−



1 Re Re +H

cos(E)

2

(15)

where, E is the elevation angle, Re is the radius of the earth, H is the height of the ionosphere. Because the ionospheric delay is proportional to TEC, the zenith ionospheric delay can be transformed into oblique ionospheric delay by using this projection function. Due to the introduction of the trigonometric projection function, the corresponding input should also include the value, and include the three-dimensional input of four pierce points, namely T  x∇ = x1T , x2T , x3T , x4T , F1 , F2 , F3 , F4

(16)

          T x∇ = x1T , x2T , x3T , x4T , F1 , F2 , F3 , F4

(17)

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According to the definition, the kernel of DD ionosphere can be expressed as      k∇ x∇ , x∇ = cov ∇y, ∇y (18) Because

⎛ ⎞      cov⎝ Ai , Bj ⎠ = cov Ai , Bj i

j

i

(19)

j

we can substitute (13), (14) into (18) and using (19) to get 4 4       k∇ x∇ , x ∇ = aij Fi Fj k xi , x j

(20)

i=1 j=1

where aij is selected as 1 or 1. If we only consider local base station network conditions, the correlation of ionospheric delay between different stations (same satellite) is relatively large, while the correlation of ionospheric delay between different satellites (same station) is relatively small, which can be ignored, so we have     (21) k xi , xj = 0, k xj , xi = 0, ∀i = 1, 2 j = 3, 4 In addition, the elevation angles of different base stations to the same satellite can be regarded as approximately equal, that is 







F1 ≈ F2 , F3 ≈ F4 , F1 ≈ F2 , F3 ≈ F4

(22)

Using (21) and (22), (20) can be transformed into            k∇ x∇ , x ∇ = F1 F1 k x1 , x 1 + k x2 , x 2 − k x1 , x 2 − k x2 , x 1          + F3 F3 k x3 , x 3 + k x4 , x 4 − k x3 , x 4 − k x4 , x 3 (23)   which is the DD ionospheric kernel function, where k x, x is the kernel of zenith ionospheric delay determined by (12). After determining the kernel and the form of input and output, the DD ionosphere delay can be interpolated directly by the Gaussian process regression described in Sect. 3.

5 Experimental Results 5.1 Experimental Data In this paper, the proposed algorithm is verified by the real measured base station network data. The base station network is located at the junction of Jiangxi, Guangdong and Hunan provinces in China, which is in the low latitude region. Compared with the high latitude region, the ionospheric variation is more intense, which is hard to estimate and has more research value. As shown in Fig. 3, the network consists of six base stations and one

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rover station. The master station is JXDY and the rover station is GDNX. Note that the rover station used here can obtain high quality observation to calculate accurate DD ionospheric delay, but it is only used as reference of the interpolation result. Ten groups of the DD ionospheric delay of base station network are obtained from the observation data of 6 GPS and 6 Beidou satellites on August 3, 2019. Each group corresponds to the DD ionospheric delay of a satellite pair. Because the proposed kernel function needs to ensure that the reference satellite of training input is the same, in order to ensure that the reference satellite does not change in the interpolation process, the observation time of each group of satellites is generally 1–3 h. The GPS reference satellite is PRN 5 and the Beidou reference satellite is PRN 10. For each group of data, we use the base station’s DD ionospheric delay to interpolate at the rover station, and compare with the rover station’s DD ionospheric reference value calculated by its high quality observation.

Fig. 3. Base station network distribution

5.2 Comparison of Three Interpolation Algorithms Figures 4 and 5 show the DD ionospheric interpolation results of GPS satellites and Beidou satellites under the three methods, and compare them with the reference values calculated based on rover observations. Table 1 lists the RMS errors of the DD ionospheric interpolation of different satellites under the three methods. By comparing the data in Table 1, we can see that the RMS error of the results obtained by Gaussian process regression interpolation is significantly better than the results obtained by Kriging and linear interpolation methods, and the errors are mostly within 1 cm. In most cases, The Kriging interpolation method is slightly better than the linear interpolation result. This is because the Kriging interpolation considers the correlation between the DD ionospheric delays of the base station. The kernel of Gaussian process regression proposed in this paper makes further use of multiple epoch observations to link the correlation of double difference ionospheric delay between different epochs relative to the position of subsolar point. This result also proves that the DD

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ionospheric kernel proposed in this paper can significantly improve the accuracy of the interpolation algorithm.

Fig. 4. Comparison of interpolation methods of GPS satellite DD ionospheric

Fig. 5. Comparison of interpolation methods of BEIDOU satellite DD ionospheric

In addition, by comparing the interpolation error of GPS and Beidou, it can be found that the interpolation error of Beidou is generally less than that of GPS. Considering that the value of double difference ionospheric delay has nothing to do with the type of satellite constellation itself, it is mainly related to the azimuth and orbit of the satellite. Here, Beidou satellites all choose geosynchronous orbit satellites (Beidou 01–04) and inclined geosynchronous orbit satellites. Therefore, it can be reasonably inferred that the interpolation accuracy of geosynchronous orbit and inclined geosynchronous orbit is better than that of medium orbit earth satellite.

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Table 1. RMS Interpolation error of DD ionosphere for different satellites under three methods Satellite

Gaussian process regression Kriging Linear

GPS02

0.0052

0.0104

0.0150

GPS06

0.0117

0.0237

0.0215

GPS13

0.0065

0.0251

0.0246

GPS15

0.0106

0.0280

0.0524

GPS29

0.0069

0.0118

0.0218

Beidou01 0.0060

0.0071

0.0149

Beidou02 0.0038

0.0045

0.0083

Beidou03 0.0034

0.0075

0.0076

Beidou04 0.0059

0.0200

0.0135

Beidou08 0.0044

0.0064

0.0111

6 Conclusion This paper mainly studies the DD ionospheric delay interpolation algorithm based on Gaussian process regression. As the kernel is an important factor affecting the Gaussian process regression, a special kind of kernel is constructed according to the physical characteristics of the ionosphere and the mathematical form of the DD ionospheric delay. In addition to the geographic longitude and latitude coordinates of the target point, the input of this kernel also includes the difference between the longitude of the ionospheric pierce point and the longitude of the subsolar point. Compared with the traditional Kriging interpolation and linear interpolation algorithm which only uses single epoch data, it makes full use of the correlation between epochs. Based on the assumption of a simple kernel of zenith ionospheric delay, this paper derives the kernel of DD ionospheric delay according to its mathematical form. The experimental results show that the effect of Gaussian process regression interpolation using the kernel proposed in this paper is significantly better than that of the traditional Kriging and linear interpolation algorithm, and its accuracy is generally less than 1 cm. In addition, for all three methods, interpolation results of Beidou geosynchronous orbit satellite and inclined geosynchronous orbit satellite are better than that of GPS medium orbit satellite.

References 1. Bock, Y., Melgar, D.: Physical applications of GPS geodesy: a review. Rep. Prog. Phys. 79(10), 106801 (2016) 2. Chao, Y.: Real time implementation of the Wide Area Augmentation System for the Global Positioning System with an emphasis on ionospheric modeling 3. Geng, J., Meng, X., Dodson, A.H., Ge, M., Teferle, F.N.: Rapid re-convergences to ambiguityfixed solutions in precise point positioning. J. Geodesy 84(12), 705–714 (2010) 4. Huang, L., Zhang, H., Xu, P., Geng, J., Wang, C., Liu, J.: Kriging with unknown variance components for regional ionospheric reconstruction. Sensors 17(3), 468 (2017)

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5. Klobuchar, J.A.: Ionospheric time-delay algorithm for single-frequency GPS users. IEEE Trans. Aerosp. Electron. Syst. 3, 325–331 (1987) 6. Komjathy, A., Sparks, L., Mannucci, A.J., Pi, X.: An assessment of the current WAAS algorithm in the South American region 7. Li, Z., Wang, N., Wang, L., Liu, A., Yuan, H., Zhang, K.: Regional ionospheric TEC modeling based on a two-layer spherical harmonic approximation for real-time single-frequency PPP. J. Geodesy 93(9), 1659–1671 (2019). https://doi.org/10.1007/s00190-019-01275-5 8. Liu, J., Chen, R., Wang, Z., Zhang, H.: Spherical cap harmonic model for mapping and predicting regional TEC. GPS Solutions 15(2), 109–119 (2011) 9. Li, Z., Yuan, Y., Wang, N., Hernandez-Pajares, M., Huo, X.: SHPTS: towards a new method for generating precise global ionospheric TEC map based on spherical harmonic and generalized trigonometric series functions. J. Geodesy 89(4), 331–345 (2014). https://doi.org/10.1007/ s00190-014-0778-9 10. Orús, R., Hernández-Pajares, M., Juan, J.M., Sanz, J.: Improvement of global ionospheric VTEC maps by using kriging interpolation technique. J. Atmos. Solar Terr. Phys. 67(16), 1598–1609 (2005) 11. Oliver, M.A., Webster, R.: A tutorial guide to geostatistics: computing and modelling variograms and kriging. CATENA 1(113), 56–69 (2014) 12. Seeger, M.: Gaussian processes for machine learning. Int. J. Neural Syst. 14(02), 69–106 (2004) 13. Zhang, H.P., Ping, J.S., Zhu, W.Y., Huang, C.: Brief review of the ionospheric delay models. Prog. Astron. 24(1), 16–26 (2006)

Monitoring Station Data Quality Analysis Method Hongyi Ren1 , Zhigang Huang1(B) , Rui Li1 , and Tiantian Yang2 1 School of Electronic Information Engineering, Beihang University, Beijing, China 2 Technical Center of Air Traffic Management Bureau of CAAC, Beijing, China

Abstract. The Beidou augmentation system currently mainly provides services for stationary users and low-dynamic users. With the continuous development of autonomous driving technology, it will provide services for L4 autonomous driving users in the future. Autonomous driving users are highly dynamic users, and the service is closely related to the user’s life safety, so it is necessary to ensure the accuracy and continuity of the monitoring station data. In the existing Beidou augmentation system reference station construction and acceptance technical specifications, the three indicators of multipath error, cycle slip ratio and observation data availability can be used to evaluate the data quality of the receiver. These three indicators can only reflect the correctness and completeness of the data, but cannot reflect the continuity of the data. In order to reflect the ability of monitoring stations to work continuously, this paper proposes data continuity indicators to evaluate the data quality of monitoring station receivers, which can provide new ideas for the subsequent evaluation of the reliability of monitoring station data. Keywords: Ground-based augmentation system · Monitoring station · Data quality · Data continuity

1 Introduction Since the Beidou Satellite Navigation System (BDS) officially provided services, China has begun to build Ground-based Augmentation System (GAS). On June 23, 2020, the BDS global network was officially completed. Beidou augmentation system will also cooperate with the BDS to provide ground-based enhancement services in China. The Beidou augmentation system is a Continuously Operational Reference System (CORS) established by multi-base station network Real Time Kinematic technology (RTK). The GAS consists of a BDS augmentation station network, a communication network, a data processing and broadcasting system, etc. It provides augmentation service by widearea augmentation products, regional augmentation products and post-processing highprecision data products. Beidou augmentation system is mainly used in precision agriculture, conventional surveying and mapping, meteorological observation and other fields. The users in these fields are static users and low dynamic users [1]. With the continuous development of autonomous driving technology, Beidou augmentation system will © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 22–32, 2021. https://doi.org/10.1007/978-981-16-3142-9_3

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provide services for L4 autonomous driving users in the future. This service is closely related to the users’ life safety, so the accuracy and continuity of the monitoring station data is particularly important. At present, the International Civil Aviation Organization (ICAO) has achieved highlevel autonomous driving in the aviation applications field, and can ensure high integrity and high continuity of received data. This is related to the strict standards of ICAO when building Satellite-Based Augmentation System (SBAS) monitoring stations. If Beidou augmentation system is to provide services for high dynamic users related to life safety, the accuracy and continuity of the data must be close to the SBAS stations. Since Beidou augmentation system uses CORS stations, it is necessary to compare the data quality of CORS stations and SBAS station receivers in order to evaluate whether Beidou augmentation system can provide services for high dynamic users related to life safety such as autonomous driving. Because there is currently no data from the Beidou augmentation system monitoring station, the data from the similar system, Crustal Movement Observation Network Of China (CMONOC), is selected for comparison and analysis with the data from the WAAS monitoring stations and the US CORS stations. In the current Beidou augmentation system reference station construction and acceptance specifications, the indicators for evaluating receiver data quality are multipath error, cycle slip ratio and observation data availability [11]. The above indicators can only reflect correctness and completeness of data, not continuity. In order to reflect capability of continuous operation capability of monitoring stations, this paper introduces the data continuity indicators to evaluate the data quality of the receivers of each monitoring station, in order to provide a reference for the improvement of the construction standards of the Beidou reference stations.

2 Data Quality Analysis Indicator and Method 2.1 Multipath Error Multipath error is the ranging error caused by non-direct navigation signal. In calculation, it needs to rely on dual-frequency observation data, combining the pseudorange observation equation and carrier phase observation equation to eliminate the influence of tropospheric and ionospheric delay. Multipath error is the main error in the ranging signal. Affected by the multipath effect, the accuracy of the pseudorange and phase observations of GNSS will drop sharply, which can lead to signal loss in severe cases. The multipath effect seriously affects the positioning and navigation accuracy, so it needs to be considered in data quality analysis [2]. When calculating the multipath error, it is necessary to combine the pseudorange observation equation and the carrier phase observation equation, and use the dual-frequency observation data to calculate, as shown in Eq. (1.1) [3].  MP1 = ρ1 − [(f12 + f22 )/(f12 − f22 )]ϕ1 + [2f22 /(f12 − f22 )]ϕ2 (1.1) MP2 = ρ2 − [2f22 /(f12 − f22 )]ϕ1 + [(f12 + f22 )/(f12 − f22 )]ϕ2 In Eq. (1.1), MP1 and MP2 are calculation amount of k 1 and k 2 frequencies including multipath error and whole-cycle ambiguity information; ρ 1 and ρ 2 are k 1 and k 2

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frequencies pseudorange observation, the unit is meter; f 1 and f 2 are the frequencies of navigation signal k 1 and k 2 frequencies carrier, the unit is megahertz; ϕ 1 and ϕ 2 are k 1 and k 2 frequencies carrier phase observation, the unit is meter. Multipath error need to be calculated using sliding windows. When the same satellite is continuously observed and there is no cycle slip, the combined ambiguity parameter will not change, and the multipath error can be obtained by calculating according to Eq. (1.2) between multiple epochs without cycle slip [4].   2   Nsw Nsw    MPk = [1/(Nsw − 1)] MPk (ti )/Nsw ) (1.2) MPk (ti ) − ( i=1

i=1

In Eq. (1.2), MPk is the evaluation value of multipath error observed by the receiver at frequency k; N sw is the number of epochs in the sliding window, and the default is 50; MPk (t i ) is the calculation amount of multipath error and whole-cycle ambiguity information observed by the receiver of epoch t i at k frequency. Since the data of WAAS monitoring station is not smoothed, it needs to be smoothed. The sliding window of the smoother is generally set between 20–100 epochs, and the smoothing Equation is shown in Eq. (1.3) [5].

(1.3) ρs,k = (1/M )ρk + [(M − 1)/M ] ρs,k−1 + λ(ϕk − ϕk−1 ) In Eq. (1.3), ρ s,k is the carrier phase smoothing pseudorange of the kth epoch, ϕ k is the carrier phase observation of the kth epoch, the unit is cycle, and M is the smoothing time constant. The larger the M, the better the smoothing effect. Its value range is 20–100 epochs (seconds). This paper uses M = 100. 2.2 Cycle Slip Ratio Before calculating the cycle slip ratio, the number of cycle slips should be calculated. Cycle slip is a counting error which occurs when the receiver performs continuous carrier phase measurement, due to some reason, and leads to a whole cycle slip of the phase observation value. Cycle slip ratio refers to the ratio of the number of epochs of the complete observation value of the receiver’s observation data to the number of epochs in which cycle slips occur during the observation of all observable satellites in a certain period of time. When calculating cycle slip ratio, cycle slip detection is required to obtain the number of epochs where the cycle slip occurs. When detecting cycle slips, a combination of Melbourne-Wubbena method and ionospheric residual error method is used. If multiple satellites have cycle slips in a certain epoch, there are two methods for calculating the number of cycle slips. The first method is that the number of cycle slips is equal to the number of satellites in the epoch. The second method is that no matter how many satellites in the epoch have cycle slips, the number of cycle slips is calculated only once. The two methods will be denoted as cycle slip ratio 1 and cycle slip ratio 2 when analyzing the results below.

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25

2.3 Observation Data Availability Observation data availability refers to the ratio of the number of epochs containing complete observations in the receiver observation data to the number of theoretical epochs for all observable satellites in a certain period of time. The theoretical epoch refers to the epoch that may be obtained by observing all observable satellites in a period of time. This paper defines an epoch with an elevation angle greater than 15° as a theoretical epoch. The epoch with complete observations means that all observable satellites are observed within a period of time, and there are no missing epochs for all frequency pseudoranges and carrier phase observations [6]. This paper uses L1 and L2 dual-frequency observation data of each station for the statistics of observation data availability. Therefore, the epoch without missing observations of the L1 and L2 dualfrequency pseudoranges and carrier phases at the monitoring stations is defined as the complete observation epoch. There are two methods for calculating observation data availability. The first method is to consider the number of visible satellites in the calculation, and the second method is to not consider the number of visible satellites in the calculation. This paper uses the first method when calculating observation data availability. The observation data availability can be calculated using Eq. (1.4). ⎛ ⎞

n n   Cj Dj ⎠ × 100% (1.4) DIS = ⎝ j=1

j=1

In Eq. (1.4), DI s is the available rate of observation data; C j is the number of epochs in which the jth satellite has a complete observation value during the observation period; Dj is the total number of theoretical epochs of the jth satellite during the observation period; n is the total number of satellites observed in the observation period, this paper takes n = 31.

3 Data Sources Observation data comes from 15 monitoring stations, 8 WAAS stations (zau1, zkc1, zme1, zmp1, zfw1, zab2, zdv1 and zob1), 3 US CORS stations (alja, alla and nvpo) and 4 CMONOC stations (GSTS, JSYC, SXGX and YNTC). The location of the WAAS monitoring station (blue icon), the US CORS station (red icon) and the CMONOC station (purple icon) are shown in Fig. 1. The signal-to-noise ratio of each station is only related to the stability of receiver, and has nothing to do with environmental factors. Select continuous observational data from January 1, 2015 to January 30, 2015 for data quality analysis, and data sampling interval is 1 s. Among the 15 selected monitoring stations, 8 WAAS monitoring stations use NOV WAASGII receivers; 3 US CORS stations use LEICA receivers; 4 CMONOC stations use TRIMBLE receivers, GSTS, SXGX and YNTC stations use TRIMBLE NETR8 receiver, and JSYC station uses TRIMBLE NETR9 receiver. In addition, the lower the elevation angle of the satellite, the worse the quality of the signal received by the receiver. Therefore, when evaluating receiver data quality, each

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Fig. 1. Location of WAAS monitoring stations, US CORS stations and CMONOC stations

satellite should have a minimum elevation angle, and data below the minimum elevation angle should be excluded [7]. In practical applications, the elevation gate is generally limited to 5–15°. This article sets the minimum elevation angle to 15° when evaluating data quality.

4 Result Analysis 4.1 Multipath Error Calculate the 95% quantile of the multipath error of all satellites in the one-month data from WAAS monitoring station, US CORS station and CMONOC station. The results are shown in Table 1. The unit of multipath error is meter. From the statistical results, it can be seen that after smoothing the data from WAAS stations using Eq. (1.3), the multipath errors between WAAS stations and US CORS stations are relatively small, while the multipath errors of CMONOC stations are relatively large. The reason may be that the environmental interference of the station site of CMONOC is relatively large, while the environmental interference of the WAAS station and the US CORS station site is relatively small. 4.2 Cycle Slip Ratio The cycle slip ratio is calculated on the data of all satellites of WAAS station, US CORS station and CMONOC station for one month. The cycle slip detection method is a combination of Melbourne-Wubbena method and ionospheric residual error method. the results are shown in Table 2. It can be seen from the statistical results that cycle slip ratio calculated by two methods is not much different. What’s more, the cycle slip ratio of WAAS stations is between 1500–2200, US CORS stations is between 2400–3000, and CMONOC stations is between 1000–2800. It shows that the consistency of the cycle slip ratio of the WAAS station and the US CORS station is relatively strong, while the consistency of the cycle slip ratio of the CMONOC station is weak.

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Table 1. 95% quantile multipath error of L1 and L2 frequency at each station for one month Station name Raw data (L1) After smoothing (L1) Raw data (L2) After smoothing (L2) zau1

1.0180

0.1554

0.8133

0.1768

zkc1

0.8003

0.1286

0.6320

0.1364

zme1

0.9448

0.1539

0.7734

0.1567

zmp1

0.9834

0.1570

0.7409

0.1472

zfw1

1.0773

0.1744

0.9143

0.1876

zab2

0.8955

0.1511

0.7298

0.1417

zdv1

0.8819

0.1451

0.7803

0.1524

zob1

0.7475

0.1433

0.6274

0.1526

nvpo

0.1112

–

0.1373

–

alja

0.1489

–

0.1965

–

alla

0.1741

–

0.1996

–

GSTS

0.6042

–

0.2825

–

SXGX

0.4665

–

0.4328

–

YNTC

0.3572

–

0.2897

–

JSYC

0.3605

–

0.3143

–

4.3 Observation Data Availability Statistics on the observation data availability for one month of data at all stations are performed. The results are shown in Table 3. The epoch unit is second. It can be seen from the statistical results that the observation data availability at 6 of the 8 WAAS stations reached 0.999. The observation data availability from two of the three US CORS stations reached 0.999. The observation data availability from the four CMONOC stations has not reached 0.99, which was the lowest.

5 Data Continuity Analysis In the existing Beidou augmentation system standards, multipath error, cycle slip ratio and observation data availability can be used to evaluate data quality of station receiver. Analyzing the definitions of the three indicators, it is found that the multipath error essentially reflects receiver thermal noise. The cycle slip ratio reflects the ratio of the number of complete epochs of the data to the number of cycle slip epochs. The more cycle slips, the more epochs the receiver has error, but this indicator cannot reflect the time when the data cycle slips. The availability of observational data reflects whether the single epoch data of each satellite is complete, it does not consider the correctness of the data. These indicators cannot reflect the continuity of data, but autonomous driving users need to ensure the correctness and continuity of the received data, so that the Beidou augmentation system can monitor its integrity to ensure the life safety of autonomous

28

H. Ren et al. Table 2. Statistics of the one-month original data cycle slip ratio of each station Station name Cycle slip ratio 1 Cycle slip ratio 2 zau1

2166

2183

zkc1

1815

1882

zme1

1554

1644

zmp1

1585

1688

zfw1

1788

1814

zab2

1998

2018

zdv1

2135

2157

zob1

1727

1861

nvpo

2488

2502

alja

2961

2991

alla

2977

2997

GSTS

1072

1078

SXGX

1251

1286

YNTC

2475

2491

JSYC

2681

2708

driving users. In order to reflect observation data continuity and the continuous operation capability of each station, this paper proposes a data continuity indicator to evaluate receiver data quality. The following will use this indicator to compare the difference in data quality between WAAS stations, US CORS stations and CMONOC stations. 5.1 Data Continuity Definition In the existing GPS Standard Positioning Service Performance Standards, the concept of spatial signal continuity and outage is defined [8]. The paper draws on this definition and defines data continuity and interruption as follows: Data continuity refers to the situation where there is no interruption in the observation arc, which is measured by the indicator of data continuity probability. Interruption means that the number of available satellites in an epoch is less than 5 due to cycle slip or too few visible satellites, or a certain epoch dual-frequency pseudorange and carrier phase data are missing. When calculating data continuity probability, the sliding window method is generally used. Assuming that the data time period is [t start , t end ], the user’s sampling interval is T, and the sliding window time is denoted as t op , the total number of satellites observed in the observation period is n, this paper takes n = 31, the calculation equation of the data continuity probability Con is [9]:

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29

Table 3. Statistics of the availability of observation data for one month at each station Station name

Complete epochs

Theoretical epochs

Observation data availability

zau1

16836660

16837630

0.999942

zkc1

17026189

17028967

0.999837

zme1

16769180

16773937

0.999716

zmp1

16883339

16910956

0.998367

zfw1

17160542

17163652

0.999819

zab2

17190557

17192056

0.999913

zdv1

17037398

17039217

0.999893

zob1

16555748

16594309

0.997676

nvpo

19598451

19749312

0.992361

alja

19202394

19216828

0.999249

alla

19160275

19167356

0.999631

GSTS

14501292

19137082

0.757759

SXGX

15695267

17255934

0.909558

YNTC

16320075

19277386

0.846592

JSYC

19237450

19562306

0.983394

⎧ ⎤⎫ ⎡ ⎤ ⎡ −top +1 t+top −1 −top +1 n tend  n tend  ⎨ ⎬   ⎣ Con = bool(Statuj (k))⎦ /⎣ bool(Statuj (t))⎦ ⎩ ⎭ j=1 t=tstart ,inc=T

k=t,inc=T

j=1 t=tstart ,inc=T

(1.5) When using data continuity probability to calculate Eq. (1.5), it is need to calculate the number of available satellites for each epoch. First, count the satellites with an elevation angle greater than 15° and complete observations for each epoch, and take bool(Statuj (k)) function value of these satellites as 1, and bool(Statuj (k)) function value of other satellites as 0, where k is the epoch time and j is the satellite number. After that, perform cycle slip detection on the observation data of all satellites, record the satellites with cycle slips in each epoch, and set bool(Statuj (k)) function value of these satellites to 0. Finally, count the number of available satellites for each epoch excluding the satellites that have occurred cycle slips. If the number of available satellites in the epoch is greater than 5, bool(Statuj (k)) function value of the satellites that occurred cycle slips is set to 1. Otherwise, bool(Statuj (k)) function value of all satellites in this epoch is set to 0. When calculating the bool(Statuj (t)) function value of the denominator, it is need to count the elevation angle of each satellite in each epoch. When the elevation angle of the satellite j in the tth epoch is greater than 15°, the bool(Statuj (t)) function is set to 1, otherwise it is set to 0. It can be seen from Eq. (1.5) that the selection of sliding window time t op is very important for calculating data continuity probability. At present, the methods used for

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positioning mainly include Precise Point Positioning (PPP) and network RTK. The convergence time of PPP is too long to meet the real-time requirements of automatic driving. The network RTK technology uses multiple reference stations deployed on the ground to form a continuous GPS reference station network, comprehensively utilizes the observation information of each reference station, and establishes an accurate error model to generate a Virtual Reference Station (VRS) near the user that does not exist physically [10]. The VRS broadcast compensation value of power generation to user receiver at 15 s intervals. In order to generate an accurate ionospheric compensation value, it is necessary to ensure that the 15 s continuous dual-frequency observation data of each station is accurate, so the sliding window time t op is selected as 15 s. If dual-frequency observation data of the reference station is abnormal within 15 s, the data during this period cannot be used to generate the correct ionospheric compensation value, so that value of bool(Statuj (k)) function for the 15 s is set to 0. If there is no abnormality in the dualfrequency observation data of the reference station within 15 s, value of bool(Statuj (k)) function for the 15 s is set to 1.

6 Result Analysis Take the sampling interval T as 1 s, and the sliding window time t op as 15 s. Statistics on the continuity probability of one-month data of all monitoring stations, the statistical results are shown in Table 4. The epoch unit is second. From the definition of the data continuity probability, when the sliding window time t op is 1 s and receiver data achieves ideal reception, data continuity probability will be equal to observation data availability. Therefore, data continuity probability is less than or equal to observation data availability. Statistics on the difference between the two indicators, the D-value is shown in Table 4. The larger the difference between observation data availability and data continuity probability, the higher probability of data interruption and the worse data quality. It can be seen from the statistical results that the data continuity probabilities of 8 WAAS stations and 3 US CORS stations all exceed 0.99. However, the data continuity probability of the 4 CMONOC stations did not reach 0.99. The result shows that the continuity of WAAS station and US CORS station is good, and the continuity of CMONOC station is poor. It can be seen from the difference between the maximum and minimum data continuity probability that 8 WAAS stations are less than 0.5%, 3 US CORS stations are less than 0.8%, and 4 CMONOC stations reach 27%. It shows that the consistency of the receiver performance of WAAS station is the strongest, and the consistency of the receiver performance of CMONOC is weak. What’s more, from the results of D-value, it can be seen that the WAAS station and the US CORS station are between 0.11% and 0.47%, while the CMONOC station is between 0.40% and 5.72%. It shows that the data of the station of CMONOC is more prone to interruption, while the data of the WAAS monitoring station and the US CORS station are not easily interrupted. In summary, compared with the observational data availability indicator, the data continuity indicator considers the influence of cycle slips, the number of satellites available in a single epoch, and the ionospheric compensation value generated by VRS in network RTK every 15 s. Besides, the data continuity probability can be used to compare the differences in the data quality of the three types of monitoring stations. Therefore, when

Monitoring Station Data Quality Analysis Method

31

Table 4. Data continuity and D-value of each station Station name

Continuous sliding windows

Theoretical epochs

Data continuity probability (/s)

D-value

zau1

16811507

16835110

0.998598

0.001344

zkc1

16978428

17026419

0.997181

0.002656

zme1

16692489

16771473

0.995291

0.004425

zmp1

16801227

16908422

0.993660

0.004707

zfw1

17133409

17161034

0.998390

0.001429

zab2

17164660

17189438

0.998559

0.001354

zdv1

16984698

17036669

0.996949

0.002944

zob1

16524978

16593385

0.995877

0.001799

nvpo

19559835

19746162

0.990564

0.001797

alja

19178607

19213986

0.998159

0.001090

alla

19134760

19164553

0.998445

0.001186

GSTS

13405111

19133722

0.700601

0.057158

SXGX

15584279

17252686

0.903296

0.006262

YNTC

16240570

19274474

0.842595

0.003997

JSYC

19043588

19558778

0.973659

0.009735

evaluating the data quality of the monitoring station receiver, data continuity indicators should be added.

7 Conclusion This paper uses data of three types of monitoring stations to carry out statistical analysis on the three indicators proposed in Beidou augmentation system reference station construction and acceptance specifications for evaluating quality of receiver data. It is found that the original indicators can only reflect the correctness and completeness of the monitoring station data, but cannot evaluate the ability to continue working. Therefore, this paper proposes a data continuity indicator for assessing continuous working capacity of monitoring station, and carries out a statistical analysis of the indicator. The results show that this indicator can reflect the difference between three types of monitoring stations and the consistency of receiver performance. Therefore, in order to provide services to highly dynamic users related to life safety, data continuity indicators should be added to the existing augmentation system specifications. The deterioration of data quality is related to cycle slips, which are affected by factors such as multipath, interference, satellite power drop or increase, receiver reliability, and user movement. Because the terrain near each monitoring station and the electromagnetic interference received are different, it is necessary to conduct a specific analysis based on the situation of the monitoring station itself.

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Finally, thanks to China Seismological Bureau’s CMONOC data for providing data support for the creation of this paper.

References 1. China Satellite Navigation Office: BeiDou Navigation Satellite System Ground-based Augmentation Service Interface Control Document (Version 1.0) (July 2020). http://www.beidou. gov.cn/xt/gfxz/202008/P020200803362071652972.pdf 2. Li, Y., Li, J., Pan, L., et al.: Quality assessment of the Beidou-3 new signal B1C and B2a observation data. Adv. Earth Sci. 33(11), 1161–1168 (2018) 3. Pan, L., Cai, C.: Software design and implementation for Beidou data quality analysis. Eng. Surv. Mapp. 23(10), 67–71 (2004) 4. Feng, X., Jin, G., Fan, J., et al.: Experimentation and analysis of multipath effect in Pseudorange measurement of GNSS receiver. Mod. Electron. Tech. 5, 77–81 (2013) 5. Xie, G.: Principles of GPS and Receiver Design, p. 93. Electronic Industry Press, Beijing (2009) 6. Ding, Y.: Research on Evaluation Methods for Multi-GNSS Data Quality and Integrity. Southeast University, Nanjing (2017) 7. Lu, Y.: Principle and Implementation Technology of Beidou/GPS Dual Mode Software Receiver, pp. 313–315. Electronic Industry Press, Beijing (2016) 8. U.S. Department of Defense: Global Positioning System Standard Positioning Service Performance Standard (2008) 9. Liu, S., Jia, X.: Algorithm and evaluation models of GNSS signal-in-space continuity. J. Navig. Position. 4(01), 98–102 (2016) 10. Song, K., Zhou, S., Zhang, X.: The working principle of network RTK technology. Haihe Water Resour. 02, 61–62 (2007) 11. Liu, Z., Gong, Y., Zhou, L.: Impact of China’s high speed train window glass on GNSS signals and positioning performance. Satell. Navig. 1(1), 1–16 (2020). https://doi.org/10. 1186/s43020-020-00013-z

Research on the Distortion Threat Model and Threat Space of BDS B1C and B2a Signals Yang Gao1(B) , Xiaowei Cui2 , Henglin Chu1 , Qibing Xu3 , and Yuqi Liu4 1 Beijing Satellite Navigation Center, Beijing, China

[email protected]

2 Department of Electronic and Engineering, Tsinghua University, Beijing, China

[email protected]

3 Xi’an Institute of Space Radio Technology, Xi’an, China 4 The 29th Research Institute of China Electronics Technology Group Corporation,

Chengdu, China

Abstract. Navigation signal distortion is a potential threat to navigation services. Modeling signal distortion is a necessary condition to ensure service safety and an important content of mandatory requirements in International Civil Aviation Organization (ICAO) standards. This paper studies the distortion threat model and threat space of BDS B1C and B2a signals. Based on the existing ICAO standard distortion model frame, a threat space determination method considering both satellite physical characteristics and distortion error characteristics is proposed. At the same time, the good ranging bias detection performance provided by the satellite onboard monitoring receiver on BDS satellite is well used to reduce the distortion parameter range threatening service, thus the threat space of B1C and B2a signals is determined and made smaller compared with the that of similar signals in other systems, and the requirement of signal quality monitoring performance will be reduced in theory. The research results can provide reference for the formulation and verification of the relevant contents of ICAO standards for BDS B1C and B2a signals. Keywords: Navigation signal distortion · Threat model · Threat space · BDS B1C and B2a signals

1 Introduction The satellite navigation signal may be distorted due to the non-ideality or failure of satellite onboard components. This distortion has actually occurred in GPS L1C/A signal [1, 2], which brings potential threat to navigation service [3, 4]. Especially for life safety services for civil aviation such as the Satellite-Based Augmentation System (SBAS) service and Ground-Based Augmentation System (GBAS) service, such distortion may lead to disastrous consequences [5–7]. So, some methods such as Signal Quality Monitoring (SQM) must be adopted to detect and alarm the distortion to ensure adequate protection for users. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 33–44, 2021. https://doi.org/10.1007/978-981-16-3142-9_4

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Modeling the signal distortion and defining the specific distortion characteristics and distortion degree are the basis for the design and evaluation of SQM. In high integrity services such as civil aviation, the distortion threat model of navigation signal and the corresponding threat space are mandatory requirements in the International Civil Aviation Organization (ICAO) standard, and are the necessary conditions for satellite navigation system to be augmented by SBAS and GBAS to provide civil aviation services. The signal distortion model research started firstly on GPS signal due to its actually occurred distortion cases. Based on the observation of the actual distortion, a reasonable compromise is made between fidelity and simplicity, and a distortion model for L1C/A signal is proposed, and the parameter range of the model is determined based on the state of the satellite, that is, the threat space [8]. This model has been written into ICAO standard [9]. Galileo system has also carried out signal distortion modeling research in the process of joining ICAO standard. Since Galileo in orbit satellite has not experienced obvious distortion, it directly adopts the distortion model framework of existing ICAO standards, and determines the threat space of E1C and E5a signals completely based on the theoretical characteristics of errors caused by distortion [10]. Because the actual characteristics of satellites are not considered in the modeling work, the threat space is obviously larger than that of GPS. The BDS B1C and B2a signals plans to join the ICAO standards to be augmented by Dual-Frequency and Multi-Constellation Satellite-Based Augmentation System (DFMC SBAS). Therefore, it is necessary to define signal distortion threat model and threat space according to the requirements of the standard. This paper studies the distortion threat model and threat space for B1C and B2a signals. Since there is no actual distortion in BDS in orbit satellite B1C and B2a signals currently, this paper takes into account the complexity, maturity and commonality with other GNSS, and adopts the general distortion model framework in the current ICAO standards. On this basis, this paper further proposes a threat space determination method considering both the satellite physical characteristics and distortion error characteristics and fully utilizes the good ranging error detection performance provided by the BDS satellite carrying the onboard monitoring receiver, then gives the threat space for B1C and B2a signals. Because more factors are considered in this paper comparing with that for other GNSS systems, the threat space obtained is significantly reduced comparing with that of similar signal in other GNSS systems, and the performance requirements of SQM will be also reduced in theory. The results of this paper can provide reference for the formulation and verification of relevant contents of the ICAO standards for BDS B1C and B2a signals.

2 ICAO Threat Model and BDS Signal 2.1 Current Threat Model in ICAO Threat model proposed by ICAO for the GPS and GLONASS signals has three parts, which are Threat Model A (TM-A), Threat Model B (TM-B) and Threat Model C (TM-C) [9].

Research on the Distortion Threat Model and Threat Space

35

Threat Model A consists of code that all the positive chips have a falling edge that leads or lags relative to the correct end-time. This model is associated with a failure of digital part of satellite, and has a single parameter , which is the lead or lag of the falling edge expressed in μs or fractions of a chip. Threat Model B introduces the amplitude modulation and models the degradation in the analog section of satellite. Specifically, it consists of the output from a second order linear system dominated by a pair of complex conjugate poles, which are σ ± j · 2π fd , where σ is the damping factor in Mneper/s and fd is the resonant frequency in MHz. The unit step response of the system is given as: ⎧ ⎪ t 1), then a distortion detection is declared. In the simulation, 1 s integral time is used for one test, no additional smoothing is adopted.

Applicability Analysis of DFMC SBAS Receiver Design Constraints

51

4.3 Simulation Results 4.3.1 Simulation Result for B1C The simulation result for B1C is shown in Fig. 1. Max differential tracking error of the equivalent C/N0 4.5 C/N0=35dB-Hz

4

Differential tracking error (m)

3.5

C/N0=39dB-Hz

3 2.5 2

Error = 1.55m

1.5 1 0.5 0 46

44

42

40

38 C/N0 (dB-Hz)

36

34

32

30

Fig. 1. Simulation results in distortion situation for B1C signal

Figure 1 use the expression way proposed in [11], the x-axis is C/N0, which means the position of Testmetric = 1 for the corresponding C/N0 value; the y-axis is the maximum differential error for every point. In this figure, for every C/N0 value in x-axis, all the points in left area of this C/N0 value are the ones that cannot trigger alarms, as there Testmetric < 1. While all the points in the right area of this C/N0 value are the ones that can trigger alarms, as there Testmetric > 1. For B1C signals, according to [11], the maximum allowable differential error of B1C is 1.55m, which means, for a certain C/N0 value, if there are no point with error higher than 1.55 m in the left part, then the SQM performance meet the requirement under this C/N0. In contrary, if there are point with error higher than 1.55m in the left part, then the SQM performance does not meet the requirement under this C/N0. As shown in Fig. 1, to meet the SQM performance, the needed minimum C/N0 is 39 dB-Hz. According to [12], the minimum power of B1C on ground is -161 dBW with 5 degree elevation, and B1Cp-BOC (1, 1) component has 29/44 of the total power, thus the minimum C/N0 of B1C can be calculated as: -162.8dBW + (-5.5 dB) - (-228.6dBJ/K + 24.8dBK) = 35.5 dB-Hz here, -5.5 dB gain of the receiver antenna in 5° elevation and 300 K (24.8 dBK) thermal noise is assumed. As 35.5 dB-Hz is lower than the need minimum C/N0 value, it cannot meet the requirement by using only 1 s integral time. Thus, smoothing of metrics is needed to increase the equivalent C/N0. According to [11], 100 s smoothing of metrics can be adopt in SQM, and the gain can be conservatively estimated as 4 dB considering the multipath influence in actual conditions. Therefore, the B1C equivalent C/N0 after smoothing can

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reach to 39.5 dB-Hz, which is higher than the 39 dB-Hz minimum C/N0, and will meet the requirement. Further considering that the SBAS service itself requires at least three monitoring stations to be visible to satellites at the same time to carry out the differential information calculation, the coherent use of SQM data of three stations can introduce 4.7 dB gain, and the system design margin is about 39.5 dBHz + 4.7 dB-39.0 dBHz = 5.2 dB. 4.3.2 Simulation Result for B2a The simulation result for B2a is shown in Fig. 2. Max differential tracking error of the equivalent C/N0 4

Differential tracking error (m)

3.5

C/N0= 27dB-Hz

C/N0= 37dB-Hz

3 2.5 2

Error = 2.78m

1.5 1 0.5 0 44

42

40

38

36

34 32 C/N0 (dB-Hz)

30

28

26

24

Fig. 2. Simulation results in distortion situation for B2a Signal

The expression way of Fig. 2 is the same with that of Fig. 1. For B2a signals, according to [11], the maximum allowable differential error is 2.78 m. As the results show, to meet the SQM performance, the needed minimum C/N0 is 27 dB-Hz. According to [13], the minimum power of B2a on ground is -158 dBW with 5 degree elevation, and B2a pilot component has 1/2 of the total power, thus the minimum C/N0 of B2a pilot can be calculated as: -161dBW + (-5.5dB) - (-228.6 dBJ/K + 24.8-dBK) = 37.3 dB-Hz here, -5.5dB gain of the receiver antenna in 5° elevation and 300 K (24.8dBK) thermal noise is assumed. As the C/N0 (37.3 dB-Hz) of B2a is higher than the needed minimum C/N0 (27 dBHz), it can meet the SQM performance requirement by using only 1 s integral time. Further considering the coherent use of SQM data of three stations can introduce 4.7dB gain, and the system design margin is about 37.3 dB + 4.7 dB-27.0 dB = 15 dB.

5 Summary To meet the requirements that BDS B1C and B2a signals used in SBAS and other civil aviation services, this paper analysed the applicability of DFMC SBAS receiver design

Applicability Analysis of DFMC SBAS Receiver Design Constraints

53

constraints in the current ICAO standard draft for B1C and B2a signals for the first time. In this paper, based on B1C, B2a signal distortion threat model, signal power and other specific conditions, the minimum C/N0 that meets the requirements of SBAS service is simulated and obtained, and the system capacity margin is also evaluated. The results show that B1C and B2a signals can meet the user protection requirements by using the current DFMC SBAS receiver constraints. B1C signal has a margin of about 5dB, and B2a signal has a margin of 15 dB, which can further relax the constraints of receiver in theory. The conclusion of this paper can provide reference for the formulation and verification of the relevant contents of ICAO standards for B1C and B2a signals.

References 1. Enge, P., Phelts, R.E., Mitelman, A.M.: Detecting anomalous signals from GPS satellites. In: Proceedings of ICAO, GNSS/P, Toulouse, France (1999) 2. Edgar, C., Czopek, F., Barker, B.: A Co-operative anomaly resolution on PRN-19. In: Proceedings of ION GPS 1999, Nashville, Tennessee, pp. 2269–2271 (Sept 1999) 3. Phelts, R.E., Walter, T., Enge, P., Wong, G.: Signal deformation monitoring for dual-frequency WAAS. In: Proceedings of ION ITM, San Diego, California, pp. 93–106 (Jan 2013) 4. Vergara, M., Antreich, F., Enneking, C., et al.: A model for assessing the impact of linear and nonlinear distortions on a GNSS receiver. GPS Solutions 24(1), 5–15 (2020) 5. Wong, G., Phelts, R.E., Walter, T., Enge, P.: Characterization of signal deformations for GPS and WAAS satellites. In: Proceedings of ION GNSS, San Diego, California, pp. 3143–3151 (Sept 2010) 6. Shao, B., Ding, Q., Wu, X.: Estimation method of SBAS dual-frequency range error integrity parameter. Satell. Navig. 1, 11 (2020). https://doi.org/10.1186/s43020-020-00011-1 7. Mitelman, A.M.: Signal Quality Monitoring for GPS Augmentation Systems. Stanford University, California (2004) 8. Wong, G.: Impact of Nominal Signal Deformations on Satellite Navigation Systems. Stanford University, California (2014) 9. RTCA: DO 229E - Minimum Operational Performance Standards (MOPS) for GPS/WAAS Airborne Equipment (Dec 2016) 10. EUROCAE: ED-259A v0.5 - MOPS for Airborne Galileo GPS SBAS Satellite Receiving Equipment (Apr 2020) 11. Pagot, J.B.: Modelling and Monitoring of New GNSS Signal Distortions in the Context of Civil Aviation. Signal and Image Processing, Institute National Polytechnique de Toulouse (INPT), Toulouse, France (2016) 12. China Satellite Navigation Office. BDS-SIS-ICD B1C-1.0 BeiDou Nssavigation Satellite System Signal in Space Interface Control Document Open Service Signal B1C (Version 1.0). China Satellite Navigation Office, Beijing (Dec 2017) 13. China Satellite Navigation Office. BDS-SIS-ICD B2a-1.0 BeiDou Navigation Satellite System Signal in Space Interface Control Document Open Service Signal B2a (Version 1.0). China Satellite Navigation Office, Beijing (Dec 2017) 14. Yao, Z., Lu, M., Feng, Z.M.: Quadrature multiplexed BOC modulation for interoperable GNSS signals. Electron. Lett. 46(17), 1234 (2010) 15. International Civil Aviation Organization. ICAO International Standards and Recommended Practices. Annex 10 to the Convention on International Civil Aviation. Volume I Radio Navigation Aids Seventh Edition. International Civil Aviation Organization, Canada (July 2018). ISBN 978-92-9258-504-4

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16. Lu, J., Guo, X., Su, C.: Global capabilities of BeiDou navigation satellite system. Satell. Navig. 1, 27 (2020). https://doi.org/10.1186/s43020-020-00025-9 17. Li, R., Zheng, S., Wang, E., et al.: Advances in BeiDou navigation satellite system (BDS) and satellite navigation augmentation technologies. Satell. Navig. 1, 12 (2020). https://doi. org/10.1186/s43020-020-00010-2

Analysis of the Applicable Minimum Filter Gain Roll-Off of DFMC SBAS Receiver for BDS Signals Yang Gao1(B) , Xiaowei Cui2 , Kefan Wei3 , and Henglin Chu1 1 Beijing Satellite Navigation Center, Beijing, China

[email protected]

2 Department of Electronic and Engineering, Tsinghua University, Beijing, China

[email protected] 3 North Information Control Research, Academy Group Co. Ltd., Nanjing, China

Abstract. The minimum filter gain roll-off is an important content of receiver design constraints in Dual Frequency and Multi Constellation (DFMC) SatelliteBased Augmentation System (SBAS) service standard. BDS B1C and B2a signals plan to join this service standard, and this paper studies the minimum applicable filter gain roll-off for the two signals. SBAS implementation cost by using signal quality monitoring (SQM) method to provide users sufficient protection are evaluated under two typical filter gain roll-off values of 30 dB/octave and 24 dB/octave. The results show that: for B2a signal, under both the parameter values, the user can be sufficiently protected by using only one monitoring station SQM data; for B1C signal, under 30 dB/octave and 24 dB/octave, the user can be sufficiently protected by using at least 2 and 3 monitoring station SQM data in coherent way, respectively. Considering that the SBAS service itself requires at least three monitoring stations to be visible to satellites at the same time to carry out the differential information calculation, so when filter gain roll-off parameter is not less than 24 dB/octave, the system can meet the protection of users without increasing the number of visible monitoring stations. Thus, 24 dB/octave can be used as the minimum filter gain roll-off for B1C and B2a signals. The conclusion of this paper can provide a reference for the development of DFMC SBAS receiver design constraints for B1C and B2a signals. Keywords: BDS B1C and B2a signals · Dual-frequency and multi constellation satellite-based augmentation system · Receiver design constraints · Applicable minimum filter gain roll-off

1 Introduction In high integrity and life safety related navigation services such as Satellite Based Augmentation System (SBAS) service, it is necessary to define the user receiver design constraints [1–3] to avoid disastrous consequences caused by navigation signal distortion and to ensure that the SBAS system end can provide sufficient protection for users [4, 5]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 55–65, 2021. https://doi.org/10.1007/978-981-16-3142-9_6

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BDS B1C and B2a signals plan to join the International Civil Aviation Organization (ICAO) standard, be augmented by the Dual-Frequency and Multi-Constellation Satellite-Based Augmentation System (DFMC SBAS), and provide civil aviation services together with other Global Satellite Navigation System (GNSS). Therefore, it is necessary to comply with standard requirements to define the DFMC SBAS receiver design constraints for B1C and B2a signals. The receiver design constraints include the methods and parameters of signal filtering and pseudo code discriminating [6]. The minimum filter gain roll-off of the receiver front-end filter is an important content, which will affect the requirements of system end design and user receiver design. Generally, on the premise of providing sufficient protection for users, the larger the minimum filter gain roll-off is, the lower the difficulty of system end design is, but the higher the implementation cost and constraints of user receiver design are; the smaller the minimum filter gain roll-off is, the more difficult it is to realize the system end, but the lower the implementation cost and constraints of user receiver design are. Therefore, each GNSS should carefully evaluate and select the parameter to achieve a balance between the system end and the user receiver. Reference [7] analyzes the minimum filter gain roll-off of Galileo E1C and E5a signal receivers, and GPS and GLONASS also carry out relevant research. This paper studies the applicable minimum filter gain roll-off in DFMC SBAS receiver for BDS B1C and B2a signals. Based on the reference of monitoring station receiver filter gain roll-off (36 dB/octave), the parameter limit of that for the user receiver is relaxed. Two typical filter gain roll-off values of 30 dB/octave and 24 dB/octave are selected, the implementation cost of the system end using signal quality monitoring (SQM) method to provide users with protection is evaluated under the two parameters. The results show that: for B2a signal, under both the parameter values, the user can be sufficiently protected by using only one monitoring station SQM data; for B1C signal, under 30 dB/octave and 24 dB/octave, the user can be sufficiently protected by using at least 2 and 3 monitoring station SQM data in coherent way, respectively. Considering that the SBAS service itself requires at least three monitoring stations to be visible to satellites at the same time to carry out the differential information calculation, so when filter gain roll-off parameter is not less than 24 dB/octave, the system can meet the protection of users without increasing the number of visible monitoring stations. When the filter gain roll-off parameter is lower than 24 dB/octave, more visible monitoring stations are needed, which will bring extra burden to the system. Thus, considering the complexity balance of system end and user receiver, 24 dB/octave can be used as the minimum filter gain roll-off for B1C and B2a signals. The conclusion of this paper can provide a reference for the development of DFMC SBAS receiver design constraints for B1C and B2a signals.

2 Receiver Design Constraints Introduction 2.1 General Content of Constraints The SBAS user receiver design constraints are specified in relevant International Civil Aviation Organization (ICAO) standards, which mainly involve signal filtering and

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pseudo-random code discrimination, including front-end filter bandwidth range, maximum in band differential group delay, minimum filter gain roll -off, code discriminating method, code discriminating space, etc., the signal channel and signal component selected for ranging will also be specified. 2.2 DFMC SBAS Receiver Constraints DFMC SBAS service plans to augment the four core Global Satellite Navigation Systems, specific signals include: GPS L1C/A and L5 signals, GLONASS L1OC and L3OC signals, Galileo E1C and E5a signals, BDS B1C and B2a signals. Considering the interoperability of GNSS and simplifying the user receiver design, the DFMC SBAS receivers for each GNSS should adopt unified receiver constraints as far as possible. Currently, the preliminary conditions include [6]: (1) (2) (3) (4)

3dB front-end filter bandwidth: 12–24 MHz; In band differential group delay: no more than 150 ns; Pseudo code discrimination method: E-L discrimination is used; Pseudo code discrimination space: the discrimination space range of L1C/A, L1OC, E1C and B1C is 0.08–0.12 chip; that of L5, L3OC, E5a and B2a is 0.9–1.1 chip.

In terms of the channel for ranging, B1C adopts BOC (1,1) component [8, 9] of pilot channel for ranging, and B2a adopt the BPSK (10) modulated pilot channel [10] for ranging. 2.3 Filter Gain Roll-Off The filter gain roll-off parameter mainly describes the suppression characteristics of filter for out of band signal. The larger the value is, the higher the requirement for filter is, and the higher the implementation cost and difficulty of receiver are. Therefore, the minimum value of filter gain roll-off is usually taken as the constraint condition. Because the user receiver also needs to take into account the anti-interference, multipath mitigation and other performance, so in the premise of ensuring the service performance, the minimum filter gain roll-off should be reduced as far as possible to provide the user receiver design as loose conditions as possible. The typical values of filter gain roll-off in navigation receiver include 36 dB/octave, 30 dB/octave, 24 dB/octave, etc. it is necessary to distinguish the specific modulation mode, distortion threat model, signal power on the ground and other conditions of each system signal, conduct careful evaluation, and select the minimum value as the constraint boundary.

3 Evaluation Method and Conditions 3.1 Evaluation Method Stipulating the receiver design constraints in civil aviation standard is to avoid the influence of signal distortion on service integrity. Based on consideration, this paper analyzes

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the system implementation cost of using SQM to detect signal distortion to meet the requirements of civil aviation under different filter gain roll-off values. The minimum filter gain roll-off is determined based on the criterion of not significantly increasing the system implementation cost. The specific process is as follows: Step 1: select a filter gain roll-off value and form a complete set constraint together with the content in Sect. 2.2; Step 2: within the constraints of step 1, traverse each parameter range according to a certain step size to obtain a set of user receiver parameters covering the whole constraints space. Step 3: for B1C and B2a signals, according to a certain step interval, traverse all parameters in the signal distortion threat model. For each group of distortion parameters, the maximum differential error between the monitoring station receiver and all user receivers is calculated, and the monitoring results of the distorted signal by SQM method are simulated. Record the maximum differential error and SQM monitoring results under each distortion parameter. Step 4: for the distortion that causes the differential error to exceed the error tolerance, the minimum carrier to noise ratio (C/N0) condition that SQM can meet the detection performance requirements is estimated. Step 5: calculate the minimum C/N0 of B1C and B2a base on the minimum power on the ground of B1C and B2a signals and calculate the implementation cost of the system according to the minimum C/N0 required by SQM. Step 6: Select another filter gain roll off value in step 1 and repeat the above steps. The implementation cost of different filter gain roll-off parameters is compared. 3.2 Evaluation Conditions 3.2.1 Receiver Conditions 3.2.1.1 Monitoring Station Receiver Conditions Considering minimizing the differential error, the monitoring station receiver design is usually close to that of the user receiver. According to reference [6], the recommended monitoring station receiver design conditions are as follows: (1) The 3dB front-end bandwidth is 24 MHz; (2) The amplitude frequency response is that of 6-order Butterworth filter, and the filter gain roll off is about 36 dB/octave; (3) The in band differential group delay is 0 ns; (4) E-L discrimination method is used; (5) The discrimination space is 0.1 chip for B1C; (6) The discrimination space is 1.0 chip for B2a. 3.2.1.2 User Receiver Conditions User receiver specific conditions are as follows: Code discrimination: B1C code discrimination spacing includes 0.08, 0.10, 0.12 chips; B2a code discrimination spacing includes 0.9, 1.0, 1.1 chips. Filtering: in the analysis, two resonant filters with different gain roll-off values are used, the gain roll-off are 30 dB/octave and 24 dB/octave respectively. For each gain

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roll-off value filter, there are 7 filter bandwidths, including 12, 14, 16, 18, 20, 22 and 24 MHz, and for each bandwidth 3 in band differential group delay parameters (0 ns, 30 ns, 150 ns) are used. Taking the bandwidth of 24 MHz and group delay of 150 ns as an example, the frequency response characteristics of the resonant filter under two kinds of gain roll-off characteristics are shown in Fig. 1 and Fig. 2.

Fig. 1. Filter characteristic 1 (30 dB/octave, 24 MHz, 150 ns)

Fig. 2. Filter characteristic 2 (24 dB/octave, 24 MHz, 150 ns)

3.2.2 Threat Model and Threat Space Conditions BDS B1C and B2a signals adopts the general distortion model framework in ICAO standard [11], including Threat Model A (TM-A), Threat Model B (TM-B) and Threat Model C (TM-C). According to the study of satellite state and distortion error, the parameter ranges (the threat space) and simulation steps are shown in Table 1.

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Signal

TM-A simulation range  (chip)

TM-B simulation range σ (Mnepers/s) fd (MHz)

TM-C simulation range  (chip) σ (Mnepers/s) fd (MHz)

B1C

−0.05: 0.01: 0.05

0.1: 0.5: 20 (σ) 1: 1: 18 (fd )

−0.05: 0.01: 0.05() 0.1: 0.5: 20 (σ) 1: 1: 18 (fd )

B2a

−0.5: 0.1: 0.5

0.1: 0.5: 18 (σ) 4: 1: 18 (fd )

−0.5: 0.1: 0.5() 0.1: 0.5: 18 (σ) 4: 1: 18 (fd )

3.2.3 SQM Conditions 3.2.3.1 The Metric Design We used three metrics in the simulation, which are. (1) Simple ratio metric: Mx =

Ix I0

(2) Sum ratio metric: M−x+x =

I−x + I+x I0

M−x−x =

I−x − I+x I0

(3) Difference ratio metric:

where, I is the correlator output accumulation, ±x represent where the correlator locates, “−” sign is leading and “+” sign is lagging, I0 represent the prompt correlator output. 3.2.3.2 The Correlators Design (1) B1C correlator design: there are 13 correlators for B1C signal [12], including 1 prompt correlator, 6 early correlators and 6 late correlators, which can be written as: I−0.10 , I−0.08 , I−0.06 , I−0.04 , I−0.03 , I−0.02 , I0 , I+0.02 , I+0.03 , I+0.04 , I+0.06 , I+0.08 , I+0.10 . (2) B2a correlator design: There are 13 correlators for B2a signal [12], including 1 prompt correlator, 6 early correlators and 6 late correlators, which can be written as: I−1.0 , I−0.8 , I−0.6 , I−0.5 , I−0.4 , I−0.2 , I0 , I+0.2 , I+0.4 , I+0.5 , I+0.6 , I+0.8 , I+1.0 .

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3.2.3.3 The Test and Alarm Design Based on the previous descried correlators and metrics, we define the test method as follows: |Mdist − Mnorm | TestM = MDEM where, Mnorm is the metric for signal with distortion; Mdist is the corresponding metric for nominal signal; MDEM is the minimum detectable errors, which is depending on both detection performance requirement and noise power, and the relationship can be written as: MDEM = (Rmd + Rffd ) · σM where, Rmd is the missed detection multiplier factor, and Rmd = 3.09 is used as the typical value representing a missed detection probability of 1 × 10–3 /test [11]; Rffd is fault-free detection multiplier factor, and Rffd = 5.26 is used as the typical value representing a false detection probability of 1.5 × 10–7 /test [11]; σM is the Gaussian noise standard deviation in the metric, which is dependent on the C/N0 of the signal. For one test point in the Threat Space, if any test result of Mx ,M−x−x and M−x+x is larger than 1 (which means TestM > 1), then a detection of distortion is alarmed. One second integral time is used in the simulation for every test, no additional smoothing is adopted.

4 Results and Analysis 4.1 Results for B1C Signal The simulation results for B1C signal under 30 dB/octave and 24 dB/octave are shown in Fig. 3 and Fig. 4, respectively. Figure 3 and Fig. 4 use a way of expression referring to [6], the x-axis represent the C/N0, which means the position of TestM = 1 for the corresponding C/N0 value; the y-axis represents the maximum differential error of all the user receivers for every test point. In these figures, for one C/N0 value, all the points in left hand part of this C/N0 value are the ones that will not trigger alarms. While all the points in the right hand part of this C/N0 value are the ones that will trigger alarms. For B1C signal, the maximum allowable differential error of is 1.55 m [6, 13], which means, if there are no points with differential error higher than 1.55 m in the left part for one C/N0 value, under this C/N0 the SQM performance can meet the requirement. While if there are some points with differential error higher than 1.55 m in the left part for one C/N0 value, under this C/N0 the SQM performance does not meet the requirement. As Fig. 3 shows, in gain roll-off 30 dB/octave condition, to meet the SQM performance, the required minimum C/N0 is 41 dB-Hz. And as Fig. 4 shows, in gain roll-off 24 dB/octave condition, to meet the SQM performance, the required minimum C/N0 is 44 dB-Hz. According to [8], the minimum C/N0 of B1C is 35.5 dB-Hz, and considering 100 s smoothing of metrics gain estimated as 4 dB, after using smoothing, the B1C equivalent C/N0 can reach to 39.5 dB-Hz, which is still less that the minimum C/N0 SQM need. Thus, it should further use correlator outputs from several reference stations together. Considering the correlator outputs from different stations coherent accumulated:

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Differential tracking error (m)

4

Test points Differential Error = 1.55m Minimum C/N0 of B1C = 35.5dB-Hz Minimum C/N0 for SQM = 41.0dB-Hz

3.5 3 2.5 2 1.5 1 0.5 0 48

46

44

42

40 38 C/N0 (dB-Hz)

36

34

32

30

Fig. 3. SQM simulation results for B1C signal under 30 dB/octave Max differential tracking error of the equivalent C/N0 5 4.5

Differential tracking error (m)

4

Test points Differential Error = 1.55m Minimum C/N0 of B1C = 35.5dB-Hz Minimum C/N0 for SQM = 44.0dB-Hz

3.5 3 2.5 2 1.5 1 0.5 0 48

46

44

42

40 38 C/N0 (dB-Hz)

36

34

32

30

Fig. 4. SQM simulation results for B1C signal under 24 dB/octave

(1) For gain roll-off 30 dB/octave situation, 2 stations are needed to provide 3 dB gain to make the equivalent B1C minimum C/N0 to 42.5 dB-Hz, which can satisfy the 41 dB-Hz SQM required; (2) For gain roll-off 24 dB/octave situation, 3 stations are needed to provide 4.7 dB gain to make the equivalent B1C minimum C/N0 to 44.2 dB-Hz, which can satisfy the 44 dB-Hz SQM required.

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As in actual working situations, augmentation system needs at least 3 stations to observe a satellite at the same time to generate the corrections and integrity [14]. Therefore, when the gain roll-off is as low as 24 dB/octave, it is unnecessary to introduce additional monitoring stations to meet the detection performance of SQM, that is, no additional burden on the system. However, considering that the performance margin is only 0.2 dB, if the filter gain roll-off is further reduced, it will bring extra burden to the system. 4.2 Results for B2a Signal The simulation results for B2a signal under 30 dB/octave and 24 dB/octave are shown in Fig. 5 and Fig. 6, respectively. Max differential tracking error of the equivalent C/N0 6

Differential tracking error (m)

5

Test points Differential Error = 2.78m Minimum C/N0 of B2a = 37.0 dB-Hz Minimum C/N0 for SQM = 29.0dB-Hz

4

3

2

1

0 42

40

38

36

34 32 C/N0 (dB-Hz)

30

28

26

24

Fig. 5. SQM simulation results for B2a signal under 30 dB/octave

The expression way of Fig. 5 and Fig. 6 is the same with that of Fig. 4. For B2a signal, the maximum allowable differential error is 2.78 m [6, 13]. As shown in Fig. 5, in gain roll-off 30 dB/octave condition, to meet the SQM performance, the needed minimum C/N0 is 29 dB-Hz. And as shown in Fig. 6, in gain roll-off 24 dB/octave condition, to meet the SQM performance, the needed minimum C/N0 is 30 dB-Hz. According to [10], the minimum C/N0 of B2a pilot can be 37.3 dB-Hz, which is already higher than the needed minimum C/N0 (29 dB-Hz or 30 dB-Hz), thus, it can meet the SQM performance requirement by using one second integral time from single monitoring station, which will not bring extra burden for system.

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Differential tracking error (m)

5

Test points Differential Error = 2.78m Minimum C/N0 of B2a = 37.0 dB-Hz Minimum C/N0 for SQM = 30.0dB-Hz

4

3

2

1

0 42

40

38

36

34 32 C/N0 (dB-Hz)

30

28

26

24

Fig. 6. SQM simulation results for B2a signal under 24 dB/octave

5 Summary In this paper, the minimum filter gain roll-off in DFMC SBAS receiver constraints for BDS B1C and B2a signals is studied. The implementation cost of the system is evaluated under the two typical values of 30 dB/octave and 24 dB/octave. The results show that B1C signal is sensitive to the parameter selection. When the filter gain roll-off is 24 dB/octave, the system can meet the user protection without additional burden, but further reducing the filter gain roll-off requires more station SQM data and introduces additional burden on the system end. While for B2a signal, there is a large margin of this parameter. Considering the balance of the implementation cost of both the system end and the user receiver and using consistent parameters of B1C and B2a, 24 dB/octave can be selected as the minimum filter gain roll-off in the DFMC SBAS receiver constraints for BDS B1C and B2a signal. The conclusion in this paper can provide reference for the formulation and verification of the relevant contents of ICAO standards for B1C and B2a signals.

References 1. Wong, G.: Impact of Nominal Signal Deformations on Satellite Navigation Systems. Stanford University, California (2014) 2. RTCA, DO 229E - Minimum Operational Performance Standards (MOPS) for GPS/WAAS Airborne Equipment (2016) 3. EUROCAE, ED-259A v0.5 - MOPS for Airborne Galileo GPS SBAS Satellite Receiving Equipment (2020) 4. Phelts, R.E., Walter, T., Enge, P., Wong, G.: Signal deformation monitoring for dual- frequency WAAS. In: Proceedings of ION ITM, San Diego, California, pp. 93–106 (2013) 5. Mitelman, A.M.: Signal Quality Monitoring for GPS Augmentation Systems. Stanford University, California (2004)

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6. Pagot, J.B.: Modelling and monitoring of new GNSS signal distortions in the context of civil aviation. Signal and Image processing, Institute National Polytechnique de Toulouse (INPT), Toulouse (2016) 7. Selmi, I., Thevenon, P., Macabiau, C., Julien, O., Mabilleau, M., et al.: Test of the filter design effect on Evil Waveform monitoring in SBAS for Galileo E1 and E5a signals. In: Proceedings of ION GNSS+ 2020, Virtual event, United States (2020) 8. China Satellite Navigation Office. BDS-SIS-ICD B1C-1.0 BeiDou Navigation Satellite System Signal In Space Interface Control Document Open Service Signal B1C (Version 1.0). China Satellite Navigation Office, Beijing (2017) 9. Yao, Z., Lu, M., Feng, Z.M.: Quadrature multiplexed BOC modulation for interoperable GNSS signals. Electron. Lett. 46(17), 1234 (2010) 10. China Satellite Navigation Office. BDS-SIS-ICD B2a-1.0 BeiDou Navigation Satellite System Signal In Space Interface Control Document Open Service Signal B2a (Version 1.0). China Satellite Navigation Office, Beijing (2017) 11. International Civil Aviation Organization. ISBN 978-92-9258-504-4. ICAO International Standards and Recommended Practices. Annex 10 to the Convention on International Civil Aviation. Volume I Radio Navigation Aids Seventh Edition. International Civil Aviation Organization, Canada (2018) 12. Selmi, I., Thevenon, P., Macabiau, C., et al.: Signal quality monitoring algorithm applied to galileo signals for large evil waveform threat space. In: Proceedings of 2020 International Technical Meeting of The Institute of Navigation. San Diego, California, 21–24 January 2020, pp. 352–365 (2020) 13. Shao, B., Ding, Q., Wu, X.: Estimation method of SBAS dual-frequency range error integrity parameter. Satell. Navig. 1(1), 1–8 (2020). https://doi.org/10.1186/s43020-020-00011-1 14. Lu, J., Guo, X., Su, C.: Global capabilities of BeiDou navigation satellite system. Satell. Navig. 1(1), 1–5 (2020). https://doi.org/10.1186/s43020-020-00025-9

Weakening Test of Pseudo-range Bias Based on Parameters-Constrained of BDS Monitoring Receiver Xiaochao Feng(B) , Lei Gong, Kuixing Liu, Qian Ma, Shuai Gao, and Xin Qi Beijing Satellite Navigation Center, Beijing 100094, China [email protected]

Abstract. Due to the influence of many factors, such as the difference of satellite navigation load device characteristics, space transmission, ground multipath and so on, the navigation signal arriving at the ground presents non-ideal characteristics and the difference between satellites, which results in the pseudo range bias of different satellites by the monitoring receiver. Moreover, the difference of technology status further results in the in conformity of pseudo-range bias of the same satellite by the monitoring receiver, the processing errors of precise orbit determination, satellite clock error correction and other services become larger, which affects the improvement of system spatial signal accuracy and the implementation effect of satellite based Augmentation services (SBAS). First this paper analyzes the effect to the pseudo-range bias due to the receiver’s parameters. The result of analysis shows that the receiver’s parameters more effects pseudo-range bias of navigation signals with low code rate such as 1 Mcps, 2 Mcps than with high code rate such as 8 Mcps, 10 Mcps, which can be neglected. Afterwards, the paper gives weakening test of pseudo-range bias with 3 BeiDou monitoring receivers from different manufacturers, different hardware architectures and different technology status by observing the space navigation signal. The test results show that the value of pseudo-range bias of BeiDou’s B1C, B2a can be reduced from about 2 ns to within 1 ns and about 0.5 ns to within 0.4 ns by constraining and readjusting the filter bandwidth and loop correlator spacing of the monitoring receiver. Keywords: BeiDou · Monitoring receiver · Parameters-constrained · Pseudo-range bias

1 Introduction The so-called pseudo-range bias refers to the phenomenon that the mutual difference of pseudo-range residuals from different satellites obtained by the receiver after deducting the corresponding theoretical distance between satellite and ground, clock error between satellite and ground, space propagation error, etc. Under ideal conditions, the correlation function of navigation signals transmitted by different satellites is completely symmetrical, and the pseudo-range residuals of each satellite in the satellite navigation system © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 66–74, 2021. https://doi.org/10.1007/978-981-16-3142-9_7

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by the ground receiver are completely consistent, so there will be no pseudo-range bias between satellites. However, due to the different channel characteristics of satellite navigation payload devices, the influence of space troposphere and ionosphere, ground multipath effect and other factors, the navigation signals arriving at the ground will be distorted because of the non-ideal characteristics and the difference of each satellite’s signal, the receiver’s pseudo-range measurements of different satellites have large bias [2–4]. Whether in the precise orbit determination, satellite clock monitoring, ionospheric monitoring and other service processing of the ground operation and control system, or in the positioning, navigating and timing (PNT) service solution of the user equipment, it is usually assumed that the pseudo-range residuals between satellites are consistent. This assumption of ignoring the pseudo-range bias between satellites will affect the further improvement of the service processing accuracy and PNT service accuracy of the satellite navigation system. The navigation satellites and ground monitoring receiver of BeiDou system (BDS) come from many providers with different technical status, which results in relatively large pseudo-range bias of the system and brings difficulties to the improvement of system service processing accuracy, especially the service accuracy of basic navigation service and satellite based augmentation service. The phenomenon of pseudo-range bias also exists in GPS system. Many scholars have studied this problem for a long time, and through experimental analysis, the main factors causing pseudo-range bias are given, including three aspects: One is the distortion of space navigation signal caused by satellite navigation processing unit, RF analog circuit, space propagation and other factors. The other is the distortion of space navigation signal caused by different characteristics of each satellite load device, there are differences in the navigation signals arriving to the ground from satellites. Third, the differences in the design and processing of receivers will also cause differences in the measurement of different satellite navigation signals. At the same time, the conclusion is given through the experiment. By unifying the constraints and setting the filter bandwidth parameters and loop correlator spacing parameters of the receiver, the negative impact of pseudorange bias on user positioning accuracy can be avoided to a certain extent. For example, Andre and other scholars have given the relationship between the pseudo-range bias of different satellite GPS L1 and the receiver’s correlator spacing through calculation simulation and satellite receiving test, and the difference the pseudo-range bias between 1 chip and 0.1 chip of correlator spacing can reach 0.5 m. At the same time, the suggestions on the filtering bandwidth and correlator spacing of WAAS receiver L1 and L5 signals are given [1, 5–7]. In this paper, the influence on pseudo-range bias from receiver parameters is analyzed theoretically, and then the adjustment test of receiver parameters constraint specification is carried out based on the BDS monitoring receiver to analyze the pseudo-range bias.

2 The Influence on Pseudo-range Bias from Receiver Parameters Filter bandwidth and tracking loop parameters are the main factors that affect the precision of receiver’s pseudo-range. The main function of the filter is to selectively transmit the navigation signal within the specified frequency range, and filter out the noise and interference signal outside the

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signal frequency range. The choice of filter bandwidth will affect the effective reception of navigation signal and the isolation and filtering of interference signal, and then affect the measurement accuracy of the receiver. The measurement accuracy of PN code mainly depends on the tracking accuracy of code tracking loop. In the code tracking loop, the tracking error is mainly caused by thermal noise and dynamic stress. The tracking error caused by thermal noise is as follows [8]:  2d 2 2d Bn [2(1 − d ) + ] (1) σDLL = λc C/N0 TC/N0 Among them, d represents the correlator spacing (chip) of lead and lag codes relative to real-time codes, Bn the closed-loop noise bandwidth (Hz) of code loop, C/N0 is the power density ratio of carrier to noise (dB/Hz), T is the pre detection integration time (s), and λc is the base code wavelength. For the receiver with high-order phase-locked loop, the steady-state tracking error caused by satellite motion in static state can be ignored. Therefore, the tracking error is mainly caused by thermal noise. From the tracking error formula, we can see that the tracking error of code loop mainly depends on C/N0 , d , Bn , T and so on. According to Eq. (1), the pseudo-range measurement accuracy of ideal receiver caused by thermal noise is calculated theoretically. Assuming that the carrier to noise ratio (C/N0 ) and predetection integration time (T ) of receiver are 40 dBHz and 2 ms fixed values respectively, the variation trend of code loop tracking error of 1 Mcps, 2 Mcps and 8 Mcps, 10 Mcps code rate with correlator spacing d and closed-loop noise bandwidth Bn is shown in Fig. 1 and Fig. 2.

Fig. 1. Variation trend of loop tracking error of 1 Mcps and 2 Mcps code rates with Bn and d

It can be seen from Fig. 1 and Fig. 2 that the pseudo-range of receivers under different loop parameters are different, and there are certain bias between them. For 1 Mcps navigation signal, under the condition of narrow correlation processing technology, the maximum pseudo-range bias between 0.025 chip and 0.2 chip of the correlator spacing is more than 1 ns; for 10 Mcps navigation signal, the maximum pseudo-range bias between 0.1 chip and 0.5 chip is less than 0.1 ns. Similarly, for the same correlation

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Fig. 2. Variation trend of loop tracking error of 8 Mcps and 10 Mcps code rates with Bn and d

spacing, the pseudo-range difference of 1 Mcps code rate signal under different predetection integration time conditions will be more than 1 ns, while the pseudo-range bias of 10 Mcps code rate signal under different pre-detection integration time conditions will be less than 0.1 ns. It can be seen that the pseudo-range of 8 Mcps and 10 Mcps signal relative to 1 Mcps and 2 Mcps rates navigation signals vary with the loop parameters of the receiver, which leads to relatively small changes in the pseudo-range and can be ignored. Therefore, we need to focus on the pseudo-range bias of low code rate navigation signal to eliminate its impact on the quality of observation and the precision of service processing.

3 Constraint Adjustment Test Based on Receiver Parameter The main task of BDS monitoring receiver is to receive the satellite navigation signals in orbit, obtain the observation data such as pseudo-range, carrier-phase, doppler, carrier to noise ratio (CNR) and navigation message, and provide the observation data for the key service of BDS, such as precise orbit determination, correction of satellite clock error, calculation of ionospheric and troposphere, integrity monitoring and so on. Therefore, the quality of observation data obtaining by the monitoring receiver will affect the service accuracy of basic navigation service, satellite based augmentation service (SBAS) and precise point positioning (PPP) service of the BDS. Three BDS monitoring receivers from different manufacturers, with different hardware platforms and different technical states are used to carry out the weakening test of pseudo-range bias in Beijing. Firstly, the constraint conditions of filter bandwidth and correlator spacing parameters of the receiver are given, and the adaptive adjustment settings are made according to the technical states of the three receivers. The changes of pseudo-range bias before and after parameter adjustment are compared and analyzed, in order to verify the weakening effect of pseudo-range bias of BeiDou monitoring receiver with different technical states after parameter constraint specification. As shown in Fig. 3, the zero baseline method is adopted in the test. The three monitoring receivers work with the same rubidium clock as the frequency source reference, and receive the space navigation signals broadcasted by the BeiDou navigation satellites on orbit through the same choke antenna with multi-frequency and high stable phase.

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Power divider RNSS signal

RNSS signal

RNSS signal

2# Receiver 10MHz

1# Receiver

10MHz

3# Receiver

10MHz

Rubidium clock Fig. 3. Block diagram of equipment used in parameter adjustment test

The working environment of the three monitoring receivers is consistent. Under the condition, the 2# and 3# monitoring receivers take the 1# monitoring receiver as the benchmark to process the zero baseline double difference of pseudo-range observation, eliminate the orbit error, clock error, ionosphere error, troposphere error, and compare the pseudo-range bias between the receivers before and after adjustment. Firstly, the pseudo-range observation equation is defined as follows P = ρ + δρ + δtr − δts + δtion + δttrop + ε

(2)

P is the pseudo-range observation, ρ is the real distance between the satellite and the receiver, δρ is the ranging error, δtr , δts , δtion , δttrop , ε is the receiver clock error, the satellite clock error, the ionospheric delay error and the tropospheric delay error, and other noise errors such as multipath. According to the definition of observation equation in formula (2), the double difference equation of pseudo-range observation can be obtained by subtracting 1# receiver from 2# receiver, 3# receiver and inter satellite J and K respectively jk

jk

jk

∇P12 = ∇δρ12 + ∇ε12 jk

(3)

Over a long-term of time, the mean value of ∇ε12 is close to 0. The double difference processing takes the pseudo-range of a certain satellite as reference, and the mean value of the double difference results reflects the difference of the pseudo-range bias of two receivers from the same satellite to the reference satellite. In order to verify the pseudo-range bias between the three monitoring receivers, the filter bandwidth and the correlator spacing parameters of each monitoring receiver

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are optimized and adjusted according to the predetermined parameter constraint conditions. Taking the receiving measurement of B1C and B2a signals as the test object, the filter bandwidth and loop parameters of the receiver are adjusted. Table 1 shows the filter bandwidth and correlator spacing parameters before and after the adjustment of B1C by three monitoring receivers, and Table 2 shows the parameters before and after the adjustment of B2a by three monitoring receivers. Table 1. Comparison of parameters before and after adjustment of B1C Filer bandth/MHz

Correlator spacing/chip

1#

2#

3#

1#

2#

3#

Before adjusting

20

26

34

0.1

0.125

0.2

After adjusting

24

24

24

0.1

0.093

0.1

Table 2. Comparison of parameters before and after adjustment of B2a Filer bandth/MHz

Correlator spacing/chip

1#

2#

3#

1#

2#

3#

Before adjusting

37

26

34

0.4

0.125

0.5

After adjusting

24

24

24

1

1

1

After the adjusting, three BeiDou monitoring receivers continuously observe and collect 24-h BDS-3 space navigation signals at the same time. Taking PRN61 satellite as the benchmark, the statistical results of B1C and B2a signal pseudo-range bias before and after the adjustment of filter bandwidth and correlator spacing parameters are analyzed. Table 3 and Table 4 show the statistical results of B1C-d, B1C-p, B2a-d, B2a-p signal pseudo-range bias of 2# and 3# receivers relative to 1# receiver before and after parameter adjustment, respectively; Fig. 4 and Fig. 5 show the comparison chart of B1Cd, B2a-d signal pseudo-range bias of 2# receivers relative to 1# receivers before and after parameter adjustment, respectively. Table 3. Comparison of pseudo-range bias of 2#-1# receiver before and after adjusting (ns) B1C-d B1C-p B2a-d B2a-p Before adjusting 1.83

1.10

0.43

0.37

After adjusting

0.93

0.30

0.23

1.00

From the test results, by adjusting the filter bandwidth and loop correlator spacing of three BeiDou monitoring receivers from different manufacturers, with different hardware

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Table 4. Comparison of pseudo-range bias of 3#-1# receiver before and after adjusting (ns) B1C-d B1C-p B2a-d B2a-p Before adjusting 2.97

1.20

0.53

0.47

After adjusting

1.03

0.37

0.40

1.12

Fig. 4. Comparison of B1C-d pseudo-range bias from 2#-1# receivers before and after adjusting

Fig. 5. Comparison of B2a-d pseudo-range bias from 2#-1# receivers before and after adjusting

platforms and different technical states, the pseudo-range bias of B1C signal can be reduced from about 2 ns to 1 ns, and the pseudo-range bias of B2a signal can be reduced from about 0.5 ns to 0.4 ns.

4 Conclusion Satellite signal is not ideal, which is the main cause of receiver pseudo-range bias. Filter bandwidth, loop parameters and other factors will affect the pseudo-range bias. The pseudo-range bias of low-code rate navigation signal is relatively large, which will affect the accuracy of key service processing or PNT service, and needs to be focused

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on; the pseudo-range of high-code rate navigation signal is relatively small, which can be ignored. In the aspect of BDS operation and control, for navigation satellites in the space segment, the first step is to continuously optimize the payload design of navigation satellites, strengthen the quality control in the navigation satellites manufacturing, and ensure the consistency of navigation signals of all in-orbit satellites while improving the quality of navigation signals transmitted by each satellite.For operation and control system equipment in the ground segment, on the one hand of monitoring receiver signal receiving and observation, for different research & development unit and different technical states of BDS monitoring receivers, on the basis of ensuring the quality of observation, it is necessary to unify and standardize the filter bandwidth, correlation spacing and other key design parameters of the receiver, so as to weaken the influence of pseudo-range bias on the quality of observation. At present, the online BDS monitoring receivers have realized the unified specification of parameters. On the other hand of the service processing level of the BDS operation and control system, according to the pseudo-range bias characteristics of different satellites, different navigation signal and different types of monitoring receivers, it is necessary to construct the satellite precise orbit determination, clock error calculation and satellite based augmentation correction calculation and other navigation service processing methods considering the pseudo-range bias, so as to eliminate the influence on the precision of the BDS service processing from pseudo-range bias, for ensuring position, navigation and timing (PNT) services. In the aspect of BDS application and promotion, it is necessary to take the filter bandwidth and loop parameters based on the online monitoring receiver of the ground operation and control system as the reference, and provide the channel parameter design constraint reference specification for the user receiving terminal, so as to weaken the pseudo-range bias caused by the parameter inconsistency between the user terminal equipment and the system monitoring receiver, so as to ensure that the user can obtain the high precision navigation, positioning and timing service from BDS.

References 1. Hauschild, A., Montenbruck, O.: A study on the dependency of GNSS pseudorange biases on correlator spacing. GPS Solutions 20(2), 159–171 (2014). https://doi.org/10.1007/s10291014-0426-0 2. He, C., Xiaochun, L., Guo, J., Chengeng, S., Wang, W., Wang, M.: Initial analysis for characterizing and mitigating the pseudorange biases of BeiDou Navigation Satellite System. Satell. Navig. 1(1), 3 (2020). https://doi.org/10.1186/s43020-019-0003-3 3. Feng, X., Chu, H.L., Liu, J.C., Liu, K.X., Gao, H.: Analysis on pseudorange biases between GNSS navigation satellites. In: China Satellite Navigation Conference (CSNC) 2016 Proceedings: Volume I. Lecture Notes in Electrical Engineering, vol. 340, pp. P517–P527 (2016) 4. He, C., Guo, J., Lu, X., et al.: Researches on pseudo-range biases of BeiDou navigation satellite system B1 signals. J. Electron. Inf. Technol. 40(11), P.2698-P.2704 (2018) 5. Wang, Y., Zhan, L., Gao, Y., Chen, S.: Research on dependency of GNSS pseudorange biases on correlator spacing and tracking. In: 2018 Proceedings of the China Satellite Navigation Conference (CSNC) (2018)

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6. Hauschild, A., Montenbruck, O.: A study on the dependency of GNSS pseudo-range biases on correlator spacing. GPS Solutions 20(2), 159–171 (2016). https://doi.org/10.1007/s10291014-0426-0.1 7. Jefferson, D.C., Hefion, M.B., Muellerschoenr, J.: Examining the C1-P1 pseudo-range bias. GPS Solutions 4(4), 25–30 (2001) 8. Kaplan, E.D., Hegarty, C.J.: Understanding GPS: Principle and Application, 2nd edn. Publishing House of Electronics Industry

Signal Quality Monitoring Algorithms of DFMC SBAS for Dual-Frequency Civil Signals of BDS Xiang Wang1 , Xiaowei Cui1(B) , Kefan Wei3 , Gang Liu1 , Yang Gao4 , and Mingquan Lu2 1 Department of Electronic Engineering, Tsinghua University, Beijing 100084, China

[email protected]

2 Beijing National Research Center for Information Science and Technology, Tsinghua

University, Beijing 100084, China 3 North Information Control Research, Academy Group Co. Ltd., Nanjing 211153, China 4 Beijing Satellite Navigation Center, Beijing 100094, China

Abstract. The integrity of GNSS characterizes the ability to alert users in time when reliable services could not be provided as expected. BeiDou SatelliteBased Augmentation System (BDSBAS) is an important component of the generalized BeiDou Navigation Satellite System (BDS), and would provide DualFrequency Multi-Constellation (DFMC) augmented services for life-safety applications. Thus, users could be better protected against integrity risks with the firstorder ionospheric error, which is the largest ranging uncertainty, removed and observation redundancy provided. The potential evil waveform (EWF) existing in iono-free combined signals is an important threat affecting the integrity performance. It is urgent to particularly and systematically design the signal quality monitors for DFMC SBAS to monitor the potential imperfections or failures on navigation signals. For BDSBAS, a hybrid Signal Quality Monitoring (SQM) algorithm based on both chip domain observables (CDO) and multi-correlator observables (MCO) is proposed in this paper on the basis of modulation characteristics of B1C and B2a signals, thus improves detection performances without significantly raising complexity in implementation. Configurations and procedures of the proposed hybrid SQM algorithm are expounded and detailed evaluation schemes are designed in this paper. In addition, the proposed algorithms are simulated and evaluated by applying the Threat Model and Threat Spaces of both signals lately adopted by ICAO. The results show that the DF civil signals of BDS could be well guaranteed to meet the integrity monitoring requirements of DFMC SBAS by this hybrid SQM algorithm. Keywords: DFMC SBAS · Signal Quality Monitoring · BeiDou navigation satellite system · Chip domain observable · Multi-correlator

1 Introduction Satellite-Based Augmentation System (SBAS), as is an important addition to Global Navigation Satellite System (GNSS), broadcasts differential corrections to improve © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 75–91, 2021. https://doi.org/10.1007/978-981-16-3142-9_8

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precision of positioning, while at the same time, monitors metrics such as clock and ephemeris error, ionospheric delay, signal distortion, code-carrier divergence and so on by utilizing a series of monitors to protect users against Hazardous Misleading Information (HMI). Early SBAS’s, including Wide Area Augmentation System (WAAS) in North America and European Geostationary Navigation Overlay Service, provided integrity monitoring on GPS L1 C/A signal only. While with the development of GNSS’s, the next generation of SBAS would apply technology of Dual-Frequency Multi-Constellation (DFMC) to mitigate integrity risks for users, by eliminating the first-order ionospheric error, which is the largest ranging uncertainty, and providing observation redundancy [19, 23]. With the removal of ionospheric error, impacts on ranging accuracy of other anomalies or errors, including signal distortions, would become relatively significant. Signal distortion, or called Evil Waveform (EWF), is caused by the signal generating hardware on board a navigation satellite with imperfections or failures [15]. Owing to the fact that an EWF could be neither detected from observables nor eliminated by differential process, in addition, different characteristics of an EWF are exhibited on and different effects are caused on different signals, a series of techniques called Signal Quality Monitoring (SQM) have been developed, to monitor the potential EWFs in real time. The third generation of BeiDou Navigation Satellite System (BDS-III) has been officially declared to provide global services, with B1C and B2a signals provided for civil aviation. BeiDou Satellite-Based Augmentation System (BDSBAS), as is an important component of BDS, is under development and will provide DFMC integrity augmentation services on B1/B2 frequencies for life-safety applications [3, 9, 11]. Therefore, a particularly and systematically design of SQM technique adaptive to BDSBAS is needed. In order to meet the integrity monitoring requirement in DFMC service of BDSBAS, a hybrid SQM algorithm based on both chip domain observables (CDO) and multi-correlator observables (MCO) is proposed in this paper on the basis of modulation characteristics of B1C and B2a signals, thus improves detection performances without significantly raising complexity in implementation. Considering the lower chip rate and higher ranging accuracy requirement for B1C signal (BOC(1,1) modulated), an SQM algorithm based on CDOs is suggested. While for B2a signal (BPSK(10) modulated), an SQM algorithm based on MCOs is suggested because of the higher chip rate and lower inflation factor on errors. In addition, the proposed algorithms are simulated and evaluated by applying the Threat Model and Threat Spaces of both signals lately adopted by International Civil Aviation Organization (ICAO). The results show that the DF civil signals of BDS could be well guaranteed to meet the integrity monitoring requirements of DFMC SBAS by this hybrid SQM algorithm.

2 BDS Signals for Civil Aviation and Threat Models 2.1 B1C and B2a Signals B1C and B2a signals are both composed of data and pilot components, as listed in Table 1 [1, 2].

pilot

B2a

sB1C_ pilot_ a (t)

data

B1C

sB2a_ data (t)

sB2a_ pilot (t)

data

pilot

sB1C_ pilot_ b (t)

sB1C_ data (t)

Signal components

Signal

1176.45

1575.42

Carrier frequency (MHz)

BPSK(10)

BPSK(10)

QMBOC(6,1,4/33)

BOC(1,1)

Modulation

BOC(6,1)

BOC(1,1)

Table 1. Structures of B1C and B2a signals

90

0

0

90

0

Phase

1/2

1/2

4/44

29/44

11/44

Power ratio

0

200

0

100

Symbol rate (sps)

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The pilot component of B1C signal could be expressed as the product of code and sub-carrier [1]: √ 3 CB1C_ pilot (t) · scB1C_ pilot (t) sB1C_ pilot (t) = (1) 2 Where, the sub-carrier is combined with orthogonal BOC(1,1) and BOC(6,1) subcarriers, the power ratio between whom is 29 to 4. According to specifications of ICAO, ranging observations on airborne receivers are obtained only from pilot_a component modulated by BOC(1,1) sub-carrier. The pilot component of B2a signal only contains code [2]: sB2a _

pilot (t)

1 = √ CB2a_ pilot (t) 2

(2)

According to specifications of ICAO, ranging observations on airborne receivers are obtained from the pilot component (BPSK(10) modulated). 2.2 Threat Models The threat model of a navigation signal characterizes the modeled approximations of EWFs it would be able to produce. Since GPS SVN-19 Event in 1993, the first observed EWF occurrence [15], several threat models on EWFs were proposed to precisely describe the anomalies in SVN-19 Event. In 2000, ICAO adopted 2nd-Order Step Threat Model (2OS-TM) into Standards and Recommended Practices (SARPs), and specified corresponding threat spaces for GPS and GLONASS [8]. The systems of Galileo and BDS are developing and researches on the applicability of 2OS-TM to new signals have been carried out. The threat spaces of both systems, having been submitted to ICAO [4, 18], would also be adopted into SARPs, indicating that the DF signals of both systems could meet the requirements of life-safety and be able to provide integrity augmentation services globally. EWF threats are categorized into threat modes by 2OS-TM, described by: (1) Digital Deformation Mode (TM-A): indicates the occurrence of failures on digital components of signal generating hardware. One parameter,  in length of chip (TC ), is used corresponding to the ratio of a lead or lag amount to a nominal chip on each falling edge of ideal code sequence which has been modulated by nominal sub-carrier BOC(1,1). (2) Analog Deformation Mode (TM-B): represents the existence of failures on analog components. Two parameters used are fd in Megahertz (MHz), corresponding to the damped frequency of oscillation on each transition of ideal code sequence, and σ in Meganeper per second (MNp/s), corresponding to the damping factor, respectively. (3) Combination Mode (TM-C): means a combination of digital and analog failure, and uses all the three parameters above. To date, although there is not any EWFs observed on either B1C or B2a signal, relevant researches have been moved on domestically. To guarantee applications with

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high accuracies and high integrities, it is necessary for DFMC SBAS to apply a set of threat model with proper threat space to describe potential EWFs in signals. Reference [4] suggested that the analyses and selections of Threat Model frames and corresponding Threat Spaces of BDS B1C and B2a signals, should be based on thorough considerations about factors of characteristics of signal generating hardware onboard, abilities on distortion detections on board, ranging biases and differential errors induced by distortions, etc. The Threat Model frames are also suggested to be aligned with ICAO Threat Model, basing on the facts that the signal generating hardware on board BDS satellites is similarly consist of digital and analog components with GPS and GLONASS satellites, and it would be reasonable and feasible to apply a mature, simple and widely used model for an emerging signal. The related further simulations were carried out in Reference [5]. Reference [20] clarified digital failures into three categories for BOC signals, namely PRN code failure, subcarrier failure and combination digital failure. Reference [25] proved that distortions on pilot_b signal could not affect code tracking, thus TM-A of BDS B1C signal was defined as a lead/lag on the falling edge of BOC(1,1) sub-carrier. In conclusion, the Threat Model and Space for BDS B1C and B2a signals applied in this paper are based on the work of Reference [4]. Digital, analog and combined distortions are modeled by TM-A(), TM-B(fd , σ ) and TM-C(, fd , σ ), respectively. The Threat Models and Threat Spaces are listed in Table 2. Table 2. Threat models and spaces for B1C and B2a signals Signal

TM-A

TM-B

TM-C

B1C

−0.05 ≤ B1C ≤ +0.05

1.5 ≤ fdB1C ≤ 18 0.1 ≤ σ B1C ≤ 20

−0.05 ≤ B1C ≤ +0.05 1.5 ≤ fdB1C ≤ 18 0.1 ≤ σ B1C ≤ 20

B2a

−0.5 ≤ B2a ≤ +0.5

4 ≤ fdB2a ≤ 18

−0.5 ≤ B2a ≤ +0.5

0.1 ≤ σ B2a ≤ 18

4 ≤ fdB2a ≤ 18 0.1 ≤ σ B2a ≤ 18

Figure 1 shows distorted chip shapes and correlation peaks (red curves) of B1C signal under TM-C (0.05TC , 7.5MHz, 2.5MNp/s) and B2a signal under TM-C (0.5TC , 7.5MHz, 2.5MNp/s), comparing to those of ideal signals (dash curves).

3 Progress of Signal Quality Monitoring Techniques The basic concept of SQM is to obtain observations from the monitored signal and then form a set of detection metrics. While at least one bias between a pair of real-time and nominal metrics exceeds corresponding threshold, EWF would be judged to exist in the monitored signal. In terms of observables, there are mainly 3 types of SQM techniques, namely based on pseudo-range observables, MCOs and CDOs.

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(a) Deformation of B1C Signal (PRN-5)

(b) Deformation of B2a Signal (PRN-5)

Fig. 1. EWF Manifestations on Codes and Correlation Peaks

3.1 SQM Techniques Based on Pseudo-Range Observables The acquisition and tracking of GNSS signal receivers are conventionally achieved by utilizing the good auto-correlation characteristics of Pseudo Random Noise (PRN) codes. EWFs might make correlation functions deformed, causing different pseudorange values obtained from different receivers with different tracking correlator spacings, from which larger differential pseudo-range errors might be induced. As a result, early methodology of SQM tended to judge the existence of EWFs by checking the relative biases among all the measured pseudo-ranges from different tracking correlator spacings. However, one receiver channel conventionally has only one code tracking loop. It is hardware and budget consuming to locate large amount of receivers ergodic toward the whole user receiver configuration space with different correlator spacings and different pre-correlation bandwidths. Therefore, it is implausible to implement SQM based on pseudo-range observables [15]. 3.2 SQM Techniques Based on Multi-Correlator Observables The restriction of implementation complexity on multiple pseudo-range observables could be mitigated by putting the observation source forward to correlation function. Therefrom it becomes mainstream for SQM to be implemented on monitoring receivers with multiple correlator pairs. To implement SQM techniques based on MCOs, several pairs of Early (E) and Late (L) correlators are set symmetric about the Prompt (P) correlator to consecutively

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obtain multiple correlator values to form a series of detection metrics, which are used to measure slopes and symmetries of various parts of or the overall shape of correlation peak. Although a bit of hardware complexity is induced by multiple correlators, this SQM technique was widely used by early SBAS’s because of its simple design. SQM techniques based on MCOs can be mainly divided into two categories in terms of metric forms. The first one uses particular correlator values to form local metrics, e.g. -test and ratio-test, which are applied by SQM2b monitor receivers on current EGNOS reference stations [14]. The second one uses all the correlator values to form overall metrics, e.g. α-metric once applied by NovAtel G-II monitor receivers on WAAS reference stations [16, 17]. SQM techniques based on MCOs have been used in WAAS and EGNOS for decades, which however reached pure performances not that satisfactory [21]. A lower performance bound of this type of SQM is indicated mainly on the fact that some local EWFs might be averaged down by correlation process, making it hard to detect. While toward SQM in DFMC SBAS, problems come from two aspects. On one hand, Binary Offset Carrier (BOC) modulation is applied on most emerging and modernized GNSS signals, of which the shapes of correlation functions are quite different from traditional Binary Phase Shift Keying (BPSK) modulated signals, changing manifestations of EWFs on correlation functions. On the other hand, any biases on each single-frequency observables of iono-free combination measurements should be inflated, e.g. B1/B2 combination, by 2.26 and 1.26 times respectively [20], strongly challenging the detection performance of existing techniques. 3.3 SQM Techniques Based on Chip Domain Observables In order to overcome the problems of modulation applicability and low performance of detections on correlation peak, the observation source of SQM should be further advanced to chip-shape. Mitigation on the attenuation of local EWFs by correlation process and the restriction of applicability by modulations could be achieved by measuring several CDOs from code waveform to form detection metrics. Furthermore, Maximum Undetected Differential Error (MUDE) would be reduced to meet requirement of ranging accuracy based on the raised detection sensitivity [13, 17]. The concept of CDO was first introduced by NovAtel Inc. for development of Vision Correlator [7], aiming at providing effective mitigation of multipath. Reference [16] compared the performances of SQM based on both technical paths before NovAtel GIII receivers were equipped at WAAS reference stations, on which Vision Correlators are applied. Further, Reference [22] derived the computation of CDOs and tested on some scenarios for GPS L1 C/A signal, applying a parabolic dish and omnidirectional antennas. Basing on this, Reference [12] gave a comparison between the visualizations of nominal distortion in both correlation and chip-shape domains on GPS L1 C/A signal with parabolic dishes. Also with a high-gain antenna, Reference [10] presented a method for assessment of signal quality using chip measurement. The hardware complexity of SQM techniques based on CDOs is raised by introducing Vision Correlator technology. In summary, the general trend of observation source for SQM is forward with the development of hardware and software technology, being able to avoid the limitations on the original information of signals by follow-up processing, to achieve better detection

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performance. However, the more front the observation source is put, the more original and sufficient could the information obtained be, and the higher implementing complexity would be needed for an individual receiver. Each type of SQM technique has its own types of applicable signals because of the particular compromise between processing characteristics and implementing complexity. As a result, a hybrid SQM algorithm based on both CDOs and MCOs is proposed in this paper on the basis of characteristics of B1C and B2a signals.

4 Hybrid SQM Algorithm and Evaluation 4.1 Hybrid SQM Algorithm A detailed hybrid SQM algorithm of BDS DF civil signals for DFMC SBAS is introduced in this section, where a chip-shape detection algorithm based on CDOs is applied to B1C signal, and a correlation-shape detection algorithm based on MCOs is applied to B2a signal. Configurations of the proposed algorithms are listed in Table 3. Table 3. Configurations for the proposed hybrid SQM algorithm Items

Configurations

Name

SCSQM8r

SRPQM3

B1C

B2a

Signal Correlators

Observable

CDO

MCO

Quantity

8

7

Locations

± 0.0875, ± 0.0625, ± 0.0375, ± 0.0125

± 1.0, ± 0.5, ± 0.1, 0

Integration (seconds) Detection metrics

1 Quantity

8

Smoothing (seconds)

100

12 ——

Stations for smoothing

2

Probability of false alert

1.5 × 10−7 per test

Probability of miss detection

1 × 10−3 per test

Minimum C/N0 (dB-Hz)

35.5

37.3

MERR (meters)

1.61

2.89

——

The SQM algorithm for B1C signal on monitoring receivers of DFMC SBAS reference stations is called Signal Chip-Shape Quality Monitoring toward 8-CDO risingedges Algorithm, taking SCSQM8r as the abbreviation [24]. Algorithm configurations refer to the typical distribution of multi-correlator in ICAO SARPs [8] for device versatility and concept acceptability. The distribution of 8 CDOs on code waveforms is shown in Fig. 2.

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Fig. 2. Illustration of CDOs on a rising edge

The detection metrics of SCSQM8r algorithm are directly defined as the CDOs from one period of integration that are normalized by the original estimated signal amplitude, given by: metrici = CDOi,nml , 1 ≤ i < 8

(3)

The SQM algorithm for B2a signal on monitoring receivers of DFMC SBAS reference stations is called Signal corRelation-Peak Quality Monitoring with 3-MCO pairs Algorithm, taking SRPQM3 as the abbreviation. The distribution of P-correlator and 3 pairs of E-L correlators is shown in Fig. 3.

Fig. 3. Distribution of multi-correlators for B2a SQM

Twelve detection metrics of SRPQM3 algorithm, including 6 simple-ratio, 3 symmetric diff-ratio and 3 symmetric sum-ratio metrics, are formed from 7 correlator values, given by:  ⎧ x M ≡ Ix IP ⎪ ⎨  M [−x]−[x] ≡ (I−x − Ix ) IP (4) ⎪  ⎩ [−x]+[x] M ≡ (I−x + Ix ) IP Where, Ix is the E/L correlator value x times of chip length far from P correlator, and IP is P correlator value. Reference [14] proved that the approximately best performance of SQM algorithm based on MCOs could be reached by applying this formation scheme of metrics.

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Thresholds of the algorithms are functions of corresponding nominal standard deviations of detection metrics, σtest , given by: Threshold = Kffd · σtest

(5)

Where, Kffd = 5.26 is calculated from the probability of fault-free detection requirement of Category I precision approach (CAT-I) in Table 3, and σtest is calculated from the minimum Carrier-to-Noise ratios (C/N0 ) on ground [5]. The procedure of proposed hybrid SQM algorithm is as follows: (1) Monitoring receiver on reference station outputs a set of real-time measured CDOs/MCOs from the monitored B1C/B2a signal per 1-s integration to form real-time measured metrics respectively; (2) By long-time observing nominal B1C/B2a signal to obtain nominal metrics and corresponding thresholds respectively in the same way, which should be pre-stored for SQM; (3) Detection execution: for each signal, get differences between each pair of realtime measured and nominal metrics and then compare them against corresponding thresholds. The several ratios obtained are called Figures of Merit (FoM). The Figure of Detection (FoD), defined as the maximum one of FoMs, represents the result of this detection, given by:   metricEWF − metricnom  i i (6) T EWF = max i Thresholdi (4) Judgement: as long as T EWF ≥ 1, the monitored signal should be considered containing EWFs. The deformed correlation peak caused by distorted B1C signal might have greater impact on ranging accuracy because of the low chip rate. Concurrently, the inflation factor to biases on B1C signal induced by DF iono-free combination measurements is high as 2.26. Therefore, by detecting deformations on chip rising edges to raise detection sensitivity and equivalently reduce MUDE, it is proper to apply SQM algorithm based on CDOs, e.g. SCSQM8r, on B1C signal under simpler smoothing conditions, i.e. shorter time for metric-smoothing and/or fewer stations for reference-smoothing, to meet DFMC SBAS performance requirement. For B2a signal, SQM algorithm based on MCOs is enough to meet requirements because of the fact that distorted signals have weaker impact on ranging accuracy for the high chip rate, and the DF inflation factor is merely 1.26. Meanwhile, the rising edge density of B2a signal is much higher than that of B1C signal, resulting in much limited effective length of chip for CDO obtention. On the other hand, situations of longer, e.g. at least 5, continuous positive chips are rare, which limits Signal-to-Noise Ratios (SNR) of CDO and performance of algorithm. In other word, the needed smoothing conditions or hardware complexity should be significantly raised if we apply an SQM algorithm based on CDOs to B2a signal and want to reach a performance as good as to B1C signal. Therefore, it is proper to apply SQM algorithm based on MCOs, e.g. SRPQM3, on B2a signal.

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4.2 Evaluation on Hybrid SQM Algorithm Two rounds of examinations should be included in evaluation on performance of an SQM algorithm, which needs to be carried out within specified threat model and threat space of the monitored signal. The first examination is the detections on the monitored signal of the SQM algorithm itself. The more EWFs within the threat space could be detected, the more robust the algorithm would be, and the better users should be protected against integrity risks. The detections run as Eq. (6), of whom the thresholds are set as the Minimum Detectable Errors (MDE). An MDE is also a function of the standard deviation of nominal noise on corresponding detection metric, σtest , given by: MDE = (Kffd + Kmd ) · σtest

(7)

Where, Kmd = 3.09 is calculated from the probability of miss detection requirement of CAT-I in Table 3. The second examination is determined by requirements of DFMC SBAS with judgement of whether the MUDE resulted from the first examination exceeds Maximum Error Range Residual (MERR), in order to make sure whether the signals potentially with undetected EWFs are safe to users. MERR is such a value of Maximum Differential Pseudo-Range Error (maxPRE) that is obtained with the worst satellite geometries but without resulting an HMI to the user. Any biases present on each single frequency signal of an iono-free combination measurement would be amplified by a pair of inflation factors decided by the combined carrier frequencies. Taking MERRDF = 3.64 meters as the maximum allowable ranging error of DFMC SBAS, MERRs for both signals are listed in Table 3. The evaluation on an SQM algorithm is essentially an examination on the detection ability toward the whole threat space, which hence needs to be properly discretized. Table 4 lists the discretized threat spaces of B1C and B2a signals, which are enlarged beyond the ranges in Table 2 for conservativeness. Note that threat space of TM-C could be divided into two sub-spaces corresponding to positive or negative values of parameter , and each pair of symmetric EWF points from the two sub-spaces respectively would make symmetric deformation effects on correlation peak. Thus, the positive sub-space of TM-C is selected for B2a signal simulations. However in chip domain, the deformation effects on code waveform caused by the pair of EWF points could not be considered symmetric, because a rising edge on code waveform is not centrosymmetric about the prompt point. As a result, both sub-spaces are needed for B1C signal simulations. The whole procedure of the evaluations on the proposed hybrid SQM algorithm in this paper is shown in Fig. 4 and listed as follows: a. Select an EWF point within the discretized threat space of B1C/B2a signal, and insert the signal with the selected EWF parameters into pre-correlation filter of reference station;

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B2a

B1C (TC )

0.12: 0.01: -0.01, 0.01: 0.01: 0.12

fdB1C (MHz) σ B1C (MNp/s)

1: 1: 20

B2a (TC ) fdB2a (MHz) σ B2a (MNp/s)

0.1, 1: 1: 25 0.1: 0.1: 0.9 2: 1: 20 0.1, 1: 1: 20

Fig. 4. General processing chart of performance evaluation of the proposed hybrid SQM algorithm

b. Obtain 8 CDOs/7 MCOs from the filtered code waveform/correlation function, and form 8/12 detection metrics of the monitored signal. Reference pseudo-range is measured concurrently; c. Execute detections to the 8/12 real-time metrics after loading the 8/12 pre-stored nominal metrics and 8/12 corresponding MDEs, and the FoD is calculated, which is then non-linearly mapped to the output equivalent C/N0 ; d. Insert the monitored B1C/B2a signal synchronously into a series of user receivers with various configurations to measure a series of user pseudo-ranges. Then, use the reference pseudo-range value to calculate the output maxPRE; e. Select a new EWF point into the loop until all the points within the discretized threat space have been examined.

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5 Simulations and Analyses Table 5. Configurations on reference and user receivers in simulations Signal

BDS B1C

Receiver

Reference

BDS B2a

Tracking

E-L, BOC(1,1) Local Replica

E-L, BPSK(10) Local Replica

Correlator Spacings

0.10 chips

0.08, 0.10, 0.12 chips

1.0 chip

0.9, 1.0, 1.1 chips

Pre-Correlation Bandwidths (double-sided)

24 MHz

12, 14, 16, 18, 20, 22, 24 MHz

24 MHz

12, 14, 16, 18, 20, 22, 24 MHz

Filters

6th-order Butterworth

(1) 6th-order Butterworth (2) mixed Butterworth (3–6) 4 types of resonators

6th-order Butterworth

(1) 6th-order Butterworth (2) mixed Butterworth (3–6) 4 types of resonators

Users

Reference

Users

Simulation results of the proposed hybrid SQM algorithm on BDS DF civil signals are introduced in this section, within which SCSQM8r algorithm is applied to B1C signal and compared to performance of an algorithm based on MCOs, and SRPQM3 algorithm is applied to B2a signal. Receiver configurations of the simulations are listed in Table 5, where correlator spacings and pre-correlation bandwidths are set according to specifications in Reference [6]. The four types of resonator filters are with: 24/30 dB per octave gain roll-off and 0/150 ns differential group delay, respectively. 5.1 Simulations and Analyses on B1C Signal The threat space of B1C signal is discretized to 13,024 EWF points according to Table 4. The red part of Fig. 5 shows the results of SCSQM8r algorithm simulation on B1C signal, indicating an equivalent C/N0 not lower than 40.3 dB-Hz is needed to make sure 1.61-m MERR not exceeded by maxPRE induced by any EWF point within threat space across user receiver design space. Given 35.5 dB-Hz as the minimum C/N0 for ground receivers, at least 4 dB gain obtained from 100-s metric-smoothing process [5], and about 3 dB gain provided by a double-station reference-smoothing process, the result could be written as: 35.5 dB - Hz + 4 dB + 3 dB > 40.3 dB - Hz

(8)

Which shows that the proposed SCSQM8r algorithm based on CDOs may sufficiently guarantee B1C signal for DFMC SBAS performance requirement. The blue part of Fig. 5 shows the simulation results of an SQM algorithm based on MCOs. Advantages of SCSQM8r algorithm are reflected by comparing the red and blue parts and listed as follows:

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Fig. 5. Comparison of detection results of both SQM algorithms on B1C signal with 1-s integration

(1) SCSQM8r algorithm has a higher detection sensitivity, thus provides about 4 dB gain and better performance bounds to support DFMC SBAS protecting integrity for users better; (2) The number of stations of SCSQM8r algorithm needed for reference stations is less than a half of that of traditional method under the same metric-smoothing conditions, indicating the requirement of DFMC SBAS may be met better. To sum up, with the higher detection sensitivity, SCSQM8r algorithm shows high efficiency upon traditional method for steady-state SQM, where in fewer stations needed for reference-smoothing on B1C signals from GEOs, and in faster diagnosis on signals from IGSOs and MEOs. The latter one is particularly beneficial for transient SQM. 5.2 Simulations and Analyses on B2a Signal The threat space of B2a signal is discretized to 3,999 EWF points according to Table 4. Figure 6 shows the results of SRPQM3 algorithm simulation on B2a signal, indicating an equivalent C/N0 only not lower than 30.1 dB-Hz is needed to make sure 2.89 m MERR not exceeded by maxPRE induced by any EWF point within threat space across user receiver design space. Additionally considering 37.3 dB-Hz as the minimum C/N0 for ground receivers, an MERR descending to 2.20 m is also satisfactory. Furthermore, an even low MERR of 1.38 m could be reached by taking at least a 4 dB gain contributed by 100-s metric-smoothing into account. So, B2a signal may be very well guaranteed by the proposed SRPQM3 algorithm based on MCOs for DFMC SBAS performance requirement.

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Fig. 6. Detection result of SRPQM3 algorithm on B2a signal with 1-s integration

6 Conclusions and Future Work The academia and the industry of BDS have carried out in-depth research and made unremitting efforts to promote BDS DF civil signals meeting integrity requirements for life-safety users and being adopted into ICAO SARPs. Basing on existing achievement and the Threat Model and Spaces of both signals lately adopted by ICAO, a hybrid SQM algorithm based on both CDOs and MCOs is proposed in this paper, improving detection performances without significantly raising complexity in implementation. a. An SQM algorithm based on CDOs is suggested for B1C signal. SCSQM8r algorithm proposed in this paper could provide about 4 dB gain in detection sensitivity and better performance bounds compared to traditional SQM method, and incorporate fewer stations in reference-smoothing process to more swiftly meet DFMC SBAS requirement efficiently. b. An SQM algorithm based on MCOs is suggested for B2a signal, comprehensively compromising between algorithm performance and hardware overhead. SRPQM3 algorithm proposed in this paper could sufficiently meet requirement. The hybrid SQM algorithm proposed in this paper could be considered as an effective candidate for DF SQM of the developing BDSBAS and other new generation DFMC SBAS’s, providing better integrity performance for life-safety users such as civil aviation and self-driving vehicles.

References 1. China Satellite Navigation Office: BeiDou Navigation Satellite System Signal in Space Interface Control Document, Open Service Signal B1C (version 1.0) (2017) 2. China Satellite Navigation Office: BeiDou Navigation Satellite System Signal in Space Interface Control Document, Open Service Signal B2a (version 1.0) (2017)

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3. China Satellite Navigation Office: BeiDou Navigation Satellite System Signal in Space Interface Control Document, Satellite Based Augmentation System Service Signal BDSBAS-B1C (version 1.0) (2020) 4. Cui, X.W., Liu, Y.Q., Xu, Q.B.: Threat Model and Threat Space of BDS B1C and B2a Signals. ICAO, GNSS SARPS Working Group, Spectrum Working Group and Validation Working Group Meetings (GSSVWG) (2020) 5. Cui, X.W.: Applicability of DFMC SBAS Receiver Design Constraints for BDS B1C and B2a Signals under Distorted Signal Conditions. ICAO, GNSS SARPS Working Group, Spectrum Working Group and Validation Working Group Meetings (GSSVWG) (2020) 6. DFMC SBAS SARPs Sub Group: DFMC SBAS SARPs – PART B VERSION 2.0. International Civil Aviation Organization, Navigation Systems Panel (2018) 7. Fenton, P.C., Jones, J.: The theory and performance of NovAtel Inc.’s vision correlator. In: Proceedings of the 19th International Technical Meeting of the Satellite Division of the Institute of Navigation, Long Beach, CA, pp. 2178–2186 (2005) 8. International Civil Aviation Organization: International Standards and Recommended Practices, Annex 10 to the Convention on International Civil Aviation, Aeronautical Telecommunications, vol. I, Radio Navigation Aids, 6th edn. (2006) 9. Li, R., Zheng, S.Y., Wang, E.S., et al.: (2020) Advances in BeiDou Navigation Satellite System (BDS) and satellite navigation augmentation technologies. Satell. Navig. 1, 12 (2020). https:// doi.org/10.1186/s43020-020-00010-2 10. Li, R.D., Tang, X.M., Ou, G.: GNSS signal quality analysis technique based on chip measurement. In: 2017 IEEE 3rd Information Technology and Mechatronics Engineering Conference (ITOEC), Chongqing, pp. 470–475 (2017) 11. Lu, J., Guo, X., Su, C.: Global capabilities of BeiDou navigation satellite system. Satell. Navig. 1(1), 1–5 (2020). https://doi.org/10.1186/s43020-020-00025-9 12. Pagot, J.B., Thevenon, P., Julien, O., et al.: Estimation of GNSS signals’ nominal distortions from correlation and chip domain. In: Proceedings of the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, CA, pp. 415–427 (2015) 13. Pagot, J.B.: Modeling and Monitoring of New GNSS Signal Distortions in the Context of Civil Aviation. Ph.D. Thesis, Université de Toulouse (2016) 14. Pagot, J.B., Julien, O., Thevenon, P., et al.: Signal quality monitoring for new GNSS signals. Navigation 65(1), 83–97 (2018) 15. Phelts, R.E.: Multi-correlator Techniques for Robust Mitigation of Threats to GPS Signal Quality. Ph.D. Thesis, Stanford University, CA (2001) 16. Phelts, R.E., Walter, T., Enge, P.: Toward real-time SQM for WAAS: improved detection techniques. In: Proceedings of the 16th International Technical Meeting of the Satellite Division of the Institute of Navigation, Portland, OR (2003) 17. Phelts, R.E., Wong, G., Walter, T., et al.: Signal deformation monitoring for dual-frequency WAAS. In: Proceedings of ION International Technical Meeting 2013, San Diego, CA, pp. 93– 106 (2013) 18. Selmi, I., Thevenon, P., Macabiau, C., et al.: Signal quality monitoring algorithm applied to Galileo signals for large evil waveform threat space. In: Proceedings of ION International Technical Meeting 2020, San Diego, CA, pp. 352–365 (2020) 19. Shao, B., Ding, Q., Wu, X.: Estimation method of SBAS dual-frequency range error integrity parameter. Satell. Navig. 1(1), 1–8 (2020). https://doi.org/10.1186/s43020-020-00011-1 20. Sun, C., Zhao, H.B., Feng, W.Q., et al.: A novel digital threat model and effect analysis on modernized BeiDou signals. In: Proceedings of the 2016 International Technical Meeting of the Institute of Navigation, Monterey, CA, 401–413 (2016) 21. Thevenon, P., Julien, O., Tessier, Q., et al.: Detection performances of evil waveform monitors for the GPS L5 signal. In: Proceedings of the 27th International Technical Meeting of the Satellite Division of the Institute of Navigation, Tampa, Florida, pp. 3312–3322 (2014)

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22. Thevenon, P., Pagot, J.B., Julien, O., et al.: Processing technique and performance of the observation of evil waveform in the chip domain. In ESA Navitech 2014, 7th ESA Workshop on Satellite Navigation Technologies, European Space Agency, Noordwijk, Netherlands (2014) 23. Walter, T., Blanch, J., Phelts, R.E., et al.: Evolving WAAS to serve L1/L5 Users. Navigation 59(4), 317–327 (2012) 24. Wang, X., Gao, Y., Cui, X.W., Liu, G., Lu, M.Q.: A signal quality monitoring algorithm based on chip domain observables for BDS B1C signal. In: Proceedings of the 2021 International Technical Meeting of the Institute of Navigation, San Diego, CA, pp. 149–161 (2021) 25. Wei, K.F., Cui, X.W., Wen, J., Lu, M.Q.: A research on modeling and monitoring of new BDS B1C signal distortions in the context of Beidou satellite BASED augmentation system. In: Proceedings of the 2020 International Technical Meeting of The Institute of Navigation, San Diego, CA, pp. 341–351 (2020)

Optimal Design of LEO Constellation for Communication and Navigation Fusion Based on Genetic Algorithm Jinquan Huang1 , Ying Liu2 , Xiaohui Liu1(B) , Xiaozhou Ye1 , Xiangjun Li1 , Wei Xiao1 , Wenxiang Liu1 , and Yong Zuo1 1 College of Electronic Science and Engineering, National University of Defense Technology,

Changsha 410073, People’s Republic of China [email protected] 2 Beijing Institute of Tracking and Telecommunication Technology, Beijing 100094, China

Abstract. Broadband low earth orbit (LEO) satellite communication systems are increasingly deployed in recent years. The stronger user-renceived signal power of LEO satellites and the rapid changes in constellation geometry have been realized to improve navigation performance. This makes the use of LEO satellites to construct the next-generation global satellite navigation system a hot research topic. In order to solve the problem that the new generation of LEO constellations need to fusion with multiple services of communication and navigation, a hybrid constellations design method with the objective of the minimum number of satellites and the optimal geometric dilution of precision (GDOP) is proposed. Based on the genetic algorithm (GA), comprehensively considering the global user distribution model and the space constraints of the Van Allen radiation belt, the optimal hybrid constellations are designed to fusion communication and navigation using Walker Star and Walker Delta constellation. In our optimized constellations shows that the number of LEO satellites required in the hybrid constellations has been reduced by 6.25% and the global average GDOP has been improved by 41.41%. When the number of LEO satellites increased, 100% allocation was realized in user-intensive areas, and the constellation global average GDOP increased by 25.69%. Keywords: LEO · Hybrid constellations · Communication and navigation fusion · Genetic algorithm

1 Introduction The Global Navigation Satellite System (GNSS) is a navigation system with artificial satellites as the navigation platform. It is considered as one of the key infrastructure that can provide positioning, navigation, and timing (PNT) services [1]. Currently, the established GNSS include GPS, BDS, Galileo, and GLONASS. The medium earth orbit (MEO) satellites in these systems run on an orbit at about 20,000 km altitude, and the power of the satellites signal arriving on earth is weak. So it is easy to be influenced by jamming in complex environments such as urban canyons and indoors. In recent years, © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 92–103, 2021. https://doi.org/10.1007/978-981-16-3142-9_9

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megascale LEO broadband Internet constellations such as Starlink, OneWeb and Kuiper, etc. have made it possible to deploy LEO navigation systems [2]. The narrowband LEO satellite communication system Iridium-Next has add satellite time and location (STL) signal to realize navigation and timing, and the signal gain is 30dB stronger than that of GPS, which improves the anti-jamming capabilities [3]. The Luojia-1A of Wuhan University realizes navigation enhancement by co-locating with BDS/GPS signals [4]. While first experimental satellite of Hongyan system provides users with communication services, while the integration of GNSS signal moreover information augmentation was considered [5]. Thus, the fusion of communication and navigation is expected to make a considerable a critical development direction for LEO satellite systems. Constellation design is the primary task of building a communication and navigation fusion system. It is to determination of the geometric configuration parameters of the constellation, and which is the prerequisite for the deployment and operation of the satellite system. Some traditional constellation diagrams are designed and optimized by geometric analysis [6, 7]. The global coverage of the LEO constellation requires a large number of satellites to run in formation, and the integration of multiple services such as communication and navigation also increases the complexity of constellation design and optimization. Genetic algorithm (GA) is an effective method to solve complex constellation design [8]. LEO satellite constellation designed with a single Walker Star constellation will have the phenomenon of more visible satellites in the polar region and fewer low latitudes, and it’s hard to get global coverage [9]. In addition, the benefits of LEO hybrid constellations in communication and navigation have been verified by geometric analysis methods [10]. The hybrid configuration LEO navigation enhancement constellation is designed by the combination of geometric analysis method and GA, which proves that the hybrid constellations can increase the number of LEO visible satellites at low latitudes [11]. The participation of geometric analysis method may cause the optimal configuration of LEO constellation to be suboptimal, and different LEO constellation configurations may bring about differences in system service performance. In order to realize the rapid design and optimization of the communication and navigation fusion LEO constellation, a hybrid constellation design and optimization method combined with the user distribution model is proposed. Then, the LEO constellation with a hybrid of Walker Star/Walker Delta is designed from the aspects of communication and navigation.

2 Constellation Design 2.1 Constellation Configuration Selection Walker Star and Walker Delta constellation were proposed by Walker, and they are composed of near-polar circle orbits and inclined circle orbits of the same altitude and inclination, respectively [12]. The Walker Star constellation can achieve global coverage, especially in polar regions, while the symmetrical constellation Walker Delta can flexibly adapt to orbital inclination range and improve the coverage in low-latitude areas. Symmetrical constellations have similar effects on the perturbation of satellites during the constellation regression period, which is beneficial for megascale constellations to achieve long-term constellation configuration maintenance and accurate orbit prediction.

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Walker Star constellation has adjacent co-rotating and counter-rotating motion ways orbits. The right ascension of ascending node (RAAN) of each co-rotating orbit is evenly distributed between 0-π on the equatorial reference plane. The RAAN Ω wsj on the j-th orbital plane and the mean anomaly M wsjk of the k-th satellite on the j-th orbital plane can be expressed as π · (j − 1) Pws

wsj = ws0 + Mwsjk =

2π · (j − 1)+M · (k − 1) Sws

(1) (2)

where Ω ws0 is the RAAN of the first orbital plane, and Pws is the orbital plane number of the constellation. M is the phase interval of the satellites corresponding to adjacent orbital planes. In order to obtain the best coverage of the Walker star constellation M is given as M =

π Sws

(3)

The RAAN of each orbital plane of the Walker Delta constellation is evenly distributed between 0-2π on the equatorial reference plane, and can be represented by Pwd /S wd / F wd , where Pwd is the number of orbital plane, S wd is the number of satellites per orbital plane and F wd denotes the phase difference between satellites in adjacent planes. F wd is an integer between 0-Pwd . The RAAN Ω wdj on the j-th orbital plane and the mean anomaly M wdjk of the k-th satellite on the j-th orbital plane is given as 2π · (j − 1) Pwd

(4)

2π 2π · Fwd · (j − 1) + · (k − 1) Nwd Swd

(5)

wdjk = wd 0 + Mwdjk = Mwd 0 +

where Ω wd0 is the RAAN of the first orbital plane, and Pwd is the orbital plane number of the constellation. N wd = Pwd S wd denotes the total number of Walker Delta constellation. 2.2 Orbital Altitude Determination The determination of orbital altitude is extremely crucial to the LEO constellation design, which is restricted by the orbital resources and space environment, etc. The Van Allen radiation inner belt located at 1500–5000 km may affect the normal operation of the satellite, so the LEO orbital altitude is usually below 1500 km [13]. The distinctive characteristic of satellites running in regressive orbit is that they can achieve sub-satellite point repetition within a certain period of time, which is convenient for orbit prediction, control station selection and communication delay prediction. Assuming that the satellite’s orbital period is T s , if there is a positive integer D and Q satisfy Ts =

D Te Q

(6)

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where Te = 86,164 s is the period of the earth’s rotation. It means that the trajectory of the sub-satellite point begins to repeat after the satellite passes through the D day with Q circle. According to Kepler’s third law, the orbital altitude can be obtained after the regression period is determined by  TS 3 (7) h = GM ( )2 − Re 2π where Re = 6,378.14 km is radius of the earth and GM = 398,600.4418 km3 /s2 is the gravitational coefficient of the earth. Constellation regression periods of the orbital altitude of D = 1 and D = 2 in Table 1 correspond to 1 or 2 sidereal days, respectively. For the ease of meeting easier global coverage and achieve stronger user-received signal power and greater broadband capacity in user-intensive areas at low latitudes, the orbital altitude of the Walker Star and Walker Delta constellation are set to 896 km and 1248 km, respectively. Table 1. Regression period and orbital altitude D Q

Altitude

1 13,14

1248 km, 896 km

2 25, 27, 29 1461 km, 1070 km, 725 km

3 Optimization Method 3.1 Constellation Configuration Selection Decision variables are parameters to be optimized in GA, and the decision variables in the hybrid constellations are given as X = {Pws , Sws , Iws , Pwd , Swd , Fwd , Iwd }

(8)

where I ws and I wd represent the orbital inclination of the Waker Star and Walker Delta constellation, respectively. The range of decision variable should avoid too much search space to reduce the amount of calculation, and also not excluding the optimal solution. Table 2 is the range of parameter optimization (Fig. 1). Table 2. Optimization range of decision variables Pws

S ws

I ws

Pwd

S wd

F wd

I wd

2–30 2–30 80°–100° 2–30 2–30 0–29 40°–65°

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Fig. 1. Gridded population of the world and the top 100 ports in 2020

Fig. 2. Global population distribution and the top 100 ports throughput in 2020

In order to make the allocation of LEO satellites in the constellation more reasonable, we have established a world user distribution model.The user distribution model was generated as follows. A population distribution model according to latitude was established, using the Gridded Population of the World v4 dataset [14]. The distribution of maritime users is represented by the top 100 ports in the world in terms of throughput in 2020, as published by Lloyd’s List [15]. Table 3. Population data weighting by latitude Lat 0°

6°

12°

18°

24°

30°

36°

42°

48°

54°

60°

66°

72° 78° 84° 90°

wp 0.1 0.06 0.04 0.05 0.02 0.03 0.04 0.07 0.14 0.18 0.18 0.09 0

0

0

0

In areas where the population is concentrated, the construction of ground-based networks is relatively complete, while sparsely populated areas have more demand for satellite networks. Therefore, the population data is weighted in Table 3 in the design. The highest latitude of the top 100 ports for throughput is 59°N, so we set the port demand in the range of 0°N to 66°N as the average throughput of 92 ports in the northern hemisphere. The land is densely populated, so user distribution is more concentrated. The user demand model is obtained as dcurv = 0.7 · pop · wp + 0.3 · port

(9)

where pop is the population number by latitude, wp is the corresponding weighted value, and p is the port data. Finally, the normalized population curve distribution map shown in Fig. 2 is obtained. 3.2 Calculation Method The earth was first separated into an evenly spaced grid of representative user locations, in order to calculate the number of visible satellites and the GDOP on global, of which with a resolution of 6 × 6° latitude and longitude on the earth’s surface. The simulation

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time is a regression period of the constellation, which ensures that all satellites in the constellation realize the repetition of the sub-satellite point trajectory and can traverse all the geometric configuration changes of the constellation. The grid points visible satellite formula is given by GPq = min GP(q, t) t ∈ ST

(10)

where GPq is the q-th grid point on the ground, GP(q,t) represents the number of visible satellites of the LEO satellite in the simulation time (ST) at the q-th grid point established on the earth’s surface, and the 95-th percentile is taken. The average of the maximum GDOP value of each grid point can be defined as ϕq 

GDOPmax =

GDOPmax (q, t)

q=1

q

t ∈ ST

(11)

where GDOPmax (q,t) is the maximum value of the 95th percentile of GDOP at the ST of the grid point. 3.3 Optimize Objective Function Design The objective function can realize the evaluation of the performance of the constellation. The smaller the value of the objective function, the better the matching with the design objective. For LEO satellite constellation quickly designed with communication and navigation. The objective function is given as min(g(X )) = min(w1 · (|cov(X ) − ξ1 | + |covws>60 (X ) − ξ2 |) x∈X

+ w2 · |1/ρ(X )| + w3 · f (N ) + w4 · GDOPmax )

(12)

where w1 , w2 , w3 , w4 is weighting factors, different combinations mean the trade-offs of different indicators in optimization. cov(X) is the minimum number of visible satellites in global area, |cov(X ) − ξ1 | means the object value of cov(X) is ξ 1 . cov>60 (X) is the minimum number of visible satellites of Walker Star constellation while the latitude is greater than 60°N, |covws>60 (X ) − ξ2 | means the object value of cov>60 (X) is ξ 2 , to ensure the navigation performance in the polar regions, ξ 2 will be set to 4. ρ(X ) is the Pearson linear correlation coefficient obtained by the number of visible satellites in each latitude of the Walker Delta constellation and the user distribution model d curve . f(N) is a simplified satellite cost constraint model. A large number of satellite formations are required to achieve global coverage of high-speed broadband connections and highprecision positioning and navigation. The cost is a factor that cannot be ignored in the LEO constellation, so the establishment of a simple constraint model is expressed as  (0.001∗N +1) N < ThN e (13) f (N ) = 0.007∗N 0.007∗ThN (0.001∗ThN +1) − (e −e ) N ≥ ThN e

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where N is the total number of satellites in the hybrid configuration, and ThN is the bound threshold. The remaining optimization parameter constraints of the objective function are given by ⎧ ⎪ cov(X ) ∈ GPq ⎪ ⎪ ⎪ ⎪ cov ⎪ ws>60 (X ) ∈ GPq ⎪ ⎪ ⎪ ⎨ Pws , Pwd ∈ Z (14) Sws , Swd ∈ Z ⎪ ⎪ ⎪ Fws = Pwd − 1 ⎪ ⎪ ⎪ ⎪ 0 ≤ ρ(X ) ≤ 1 ⎪ ⎪ ⎩ N =P S +P S ws ws wd wd

3.4 Optimization Algorithm GA is an evolutionary algorithm. The core of the algorithm is based on the theory of biological evolution and genetic variation. It simulates the phenomena of replication, crossover, and mutation that occur in natural selection and genetics, and obtains the individuals in the group that are most suitable for the environment [16]. Because of its excellent multi-objective search ability, it is widely used in constellation design [16]. The optimization process of the LEO hybrid constellations is shown in Fig. 3.

Start

Parameter settings

Calculating hybrid configuration constellation epoch

Calculating for grid point.

Genarating initial constellation population, M=0

Calculating objective function

Calculating optimized coverage, GDOP

Selecting, crossover, and mutation, generating next population

Yes

Gen TWMD , it will be proved that there is a faulty satellite at that moment, and the faulty satellite needs to be identified and excluded. If TWMS < TWMD , it will be proved that there is no fault satellite at that moment.

3 Experimental Verification and Result Analysis In order to compare and analyze the improved M-estimation algorithm with the Mestimation algorithm and the least squares algorithm. The BDS data is collected on June 6, 2020. The observation station is JFNG. The time starts from 2020.6.6.00:00:00,

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which lasts 27000 s and 900 simulations epochs are taken. The receiver coordinates are [−2279828.6768, 5004705.5635, 3219777.3655], and the false alarm rate is set up 0.002/h. In order to verify that the improved M-estimation algorithm can detect satellite fault, we collect 900 simulation epochs. The number of visible satellites and the GDOP (Geometric Dilution of Precision) are shown in Fig. 1.

Fig. 1. Number of visible satellites and GDOP

It can be seen from Fig. 1 that the number of visible satellites is relatively stable. The number satellites remain between 13 and 16. The GDOP decreases as the number of visible satellites increasing. Figure 2 shows the fault detection effects of the three algorithms with no pseudorange error between 0 and 900 epochs. In Fig. 2, the three algorithms are all less than the detection threshold with no fault. It can be indicated that the detection effects of the three algorithms are effective with no fault satellites. Figure 3 is the fault detection results with pseudo-range error on C03 satellite. Adding 2 m/epoch pseudo-range error between 200 epochs and 400 epochs; the step length is 5 epochs. The fault detection results are shown in Fig. 3. In Fig. 3, the three algorithms are all more than the detection threshold between 200 epochs and 400 epochs. It means that all faults can be detected within these epochs. However, the detection statistics are all lower than the detection threshold in other time periods. It means that there is no fault satellite in this period. In Fig. 2 and Fig. 3, the three detection algorithms are all effective both no fault and fault satellites. In addition, the M-estimation algorithm has a good impact on the resisting outliers. Therefore, a random satellite is selected and a pseudo-range of 20 m is added between 0 and 900 epochs. The position calculations of the three algorithms are shown in Fig. 4, Fig. 5, and Fig. 6.

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Fig. 2. Detection results with no fault for three algorithms

Fig. 3. Detection results with fault for three algorithms

It can be seen from Fig. 4, Fig. 5 and Fig. 6 that when 20 m error is added to the satellite at a certain moment and the position is directly calculated with fault satellites. M-estimation and the improved M-estimation algorithm are good at resisting outliers. It can be seen from the above three figures, the position error value calculation with the pseudo-rang error is better than the position error of the LS algorithm. In order to test the performance of the improved algorithm in terms of fault detection rate and fault identification rate, a fault error of 1–120 m is added to the satellite C03, the simulation time is 900 epochs. Figure 7 shows the fault detection rate comparison of three algorithms. It can be seen from Fig. 7 that the improved M-estimation algorithm can quickly detect satellite faults. The improved M-algorithm can detect the faulty satellites at a

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Fig. 4. Position error of the improved M-estimation algorithm

Fig. 5. M-estimation position error

Fig. 6. LS estimation position error

Fig. 7. Fault detection rate comparison of three different algorithms

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pseudo-range error of 19 m. Meanwhile, the fault detection rate is 0.00697. The fault detection rate of M-estimation and the LS algorithm are 0, too. The M-estimation algorithm fault detection rate is 0.0056 and the improved M-estimation fault is 0.2067 at 23 m. When the pseudo-range error exceeds 31 m, the fault detection rate of the Mestimation algorithm and the improved M-estimation algorithm reach 100%. When the pseudo-range error exceeds 48 m, the detection rates of the three algorithms all reach 100%. Under the same error, it can be seen that the improved M-estimation detection rate is better than the M-estimation and is far better than the LS algorithm. The improved M-estimation algorithm is more robust in the initial value than the LS algorithm and is less affected by outliers. The initial value is not easy to deviate from the true position, improves the RAIM availability, and improves the fault detection rate of the algorithm. As Fig. 7 shows that it is necessary to perform fault identification on all satellites when a fault satellite is detected under the epoch. Figure 8 shows the fault identification rate comparison of three algorithms.

Fig. 8. Fault identification rate comparison of three different algorithms

Figure 8 shows the improved M-estimation algorithm, M-estimation algorithm, and the LS algorithm fault identification rate. It can be seen that the fault identification rate of the improved M-estimation algorithm is bigger than that of the M-estimation, which is much bigger than that of the LS algorithm. Under the pseudo-range error of 19 m, the improved M-estimation fault identification rate is 0.00697, while the Mestimation and the LS algorithm fault identification rate are 0. When the pseudo-range error is 23 m, M-estimation can identify the faulty satellite, the identification rate is 0.0056, the identification rate of the improved M-estimation algorithm is 0.2067, and the identification rate of the least square algorithm is 0. When the pseudo-range error is 26 m, the fault identification rate of the improved M-estimation algorithm is 0.9633, which is much higher than that of the M-estimation algorithm; and the fault identification

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rate of the least squares algorithm is 0. When the pseudo-range error is 31 m, the Mestimation algorithm is improved, and the fault identification rate of the M-estimation algorithm is 100%. When the pseudo-range error is greater than 48 m, the three detection algorithms can identify the faulty satellite, and the fault identification rate reaches 100%. It can be seen that the improved M-estimation RAIM algorithm is more sensitive to faulty satellites and has better fault identification ability than the M-estimation algorithm and the LS algorithm.

4 Conclusion In the paper, the improved RAIM algorithm based on M-estimation is proposed. The improved M-estimation algorithm is derived.Through BDS raw data, the algorithm is verified and compared with the LS algorithm and M-estimation algorithm. The results show that the performance of the improved M-estimation algorithm is better than the M-estimation algorithm and the LS algorithm under resisting fault. In addition, the improved M-estimation algorithm can improve the fault detection and identification rate by comparing M-estimation and LS algorithm. Acknowledgment. This study was supported by the National Natural Science Foundation of China (61571309), the Talent Project of Revitalization Liaoning (XLYC1907022), the Key R & D projects of Liaoning Province (2020JH2/10100045), the Capacity Building of Civil Aviation Safety (TMSA1614), the Natural Science Foundation of Liaoning Province (2019-MS-251), the Scientific Research Project of Liaoning Provincial Department of Education (JYT2020142), the High-Level Innovation Talent Project of Shenyang (RC190030).

References 1. Li, R., Zheng, S.Y., Wang, E.S., et al.: Advances in BeiDou Navigation Satellite System (BDS) and satellite navigation augmentation technologies. Satell. Navig. 1, 12 (2020). https://doi. org/10.1186/s43020-020-00010-2 2. Guang, H.S., Cheng, D.: An enhanced least squares residual RAIM algorithm based on optimal decentralized factor. Chin. J. Aeronaut. 33(10), 2757–2769 (2020) 3. Du, Y.J., Wang, J.L., Rizos, C., et al.: Vulnerabilities and integrity of precise point positioning for intelligent transport systems: overview and analysis. Satell. Navig. 2, 3 (2021). https:// doi.org/10.1186/s43020-020-00034-8 4. Wang, W.B., Xu, Y.: REKF RAIM algorithm based on robust MM-estimation. Syst. Eng. Electron. 43(1), 216–222 (2021) 5. Yu, S.Q., Zhang, X.H., Guo, F., et al.: Recent advances in precision approach based on GNSS. Acta Aeronautica et Astronautica sinica 40(3), 1–21 (2019) 6. Sturza, M.A.: Navigation system integrity monitoring using redundant measurements. J. Inst. Navig. 35(4), 483–501 (1988) 7. Parkinson, B.W., Axelrad, P.: Autonomous GPS integrity monitoring using the pseudorange residual. Navigation 35(2), 255–274 (1988) 8. Joerger, M., Chan, F.C., Langel, S., et al.: RAIM detector and estimator design to minimize the integrity risk. In: Proceedings of International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2012), Nashville TN, United states, pp. 2785–2807 (2012)

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9. Yang, Y.X., Xu, J.Y.: GNSS receiver autonomous integrity monitoring (RAIM) algorithm based on robust estimation. Geodesy Geodyn. 7(2), 117–123 (2016) 10. Clements, K.A., Davis, P.W., Frey, K.D.: An efficient algorithm for computing the weighted least absolute value estimate in power system static state estimation. Electr. Power Syst. Res. 9(22), 371–375 (1989) 11. Wang, E.S., Yang, F.S., Pang, T.: GNSS receiver autonomous integrity monitoring algorithm based on least squared method. In: 2017 12th IEEE Conference on Industrial Electronics and Applications (ICIEA), Siem Reap, Cambodia, 2017–2021 (2017) 12. Wang, E.S., Yang, D., Wang, C.Y., et al.: Optimized fault detection algorithm aided by BDS baseband signal for train positioning. Chin. J. Electron. 29(1), 34–40 (2020) 13. Xie, J.S., Xin, J., Guo, R., et al.: Design and realization of RAIM algorithms for BDS. J. Navig. Positioning 6(1), 54–59 (2018) 14. Wang, G., Ye, L., Hao, C.X., et al.: Analysis of different weight functions based on robust estimation. J. North China Univ. 42(3), 14–22 (2020) 15. Zhang, P.F., Chen, P.Y., et al.: A RAIM method based on M-estimation for single fault of multi-constellation. In: China Satellite Navigation Conference (CSNC), Shang Hai, China, pp. 49–54 (2017) 16. Wang, E.S., Yang, F.X., Jia, C.Y., et al.: Research on RAIM algorithm based on weighted least-square method. Electron. Opt. Control 24(11), 7–10 (2017)

Analysis of the BDS-3 Complete System on Positioning Performance in Polar Region Shunxi Fan1(B) , Yi Fan1 , Xianbing Wu2 , Kang Zheng1 , Deyan Xu1 , Yue Mao3 , and Xiaolin Jia3 1 Xi’an Aerors Data Technology Co., Ltd., Xi’an 710100, China 2 The 20th Research Institute of CETC, Xi’an 710068, China 3 Xi’an Research Institute of Surveying and Mapping, Xi’an 710054, China

Abstract. The BDS-3 complete system was officially put into operation on July 31, 2020. This article uses the measured data of international GNSS Monitoring and Assessment System (iGMAS) stations to analyze the basic positioning performance of the BDS-3 complete system in the polar region. It includes multiple evaluation contents such as coverage performance, data quality, user equivalent ranging error (UERE), and positioning performance. Through experimental analysis, it can be seen that the BDS-3 complete system has more than 10 visible satellites in polar region. PDOP value is less than 1.6, and PDOP availability is 100%; BDS-3 data quality is better than BDS-2. The accuracy of BDS-3 B1C uere in polar region is only 0.47 m, and the positioning accuracy of BDS-3 at various frequency in polar region meets the service performance specifications, and the positioning accuracy is better than GPS. Compared with BDS-2, BDS-3 has significantly improved in coverage capability, UERE and positioning accuracy. Keywords: BDS-3 · iGMAS · Coverage performance · Data quality · Positioning performance

1 Introduction The polar region is the general term for the Antarctic and Arctic regions. It is located at the north and south ends of the earth. It is covered by snow and ice all year round and has harsh natural conditions. The polar region are rich in natural resources and important scientific value, as well as very important strategic values [1]. They are hotspots for scientific investigations and research around the world; However, there are very few landmarks in the polar region that can be used to determine the orientation. Position perception is not clear, and it is easy to get lost. Therefore, the support of the navigation system is indispensable for various activities in the polar region. The shrinking longitude and latitude lines, harsh climate, complex electromagnetic environment and polar daylight phenomena in the polar region have seriously affected the application of inertial navigation, celestial navigation, and geomagnetic navigation in the polar region. Therefore, GNSS has stronger applicability in the polar region.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 174–186, 2021. https://doi.org/10.1007/978-981-16-3142-9_16

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The research on the performance of GPS in the polar region has been relatively complete. However, there are few studies on BDS positioning performance in the polar region, but mainly for simulation tests or for the BDS-2. Literature [2, 3] analyzes the availability of BDS current constellations and future global constellations for navigation and positioning services in polar region through simulation; Literature [4] demonstrates the feasibility of using BDS to enhance GPS positioning performance in Antarctica through simulation; Literature [5, 6] analyzes the positioning performance of BDS-2 in ocean and Antarctic regions. It is found that the positioning accuracy of BDS-2 in high latitude areas is poor. Literature [7] analyzes that the addition of the. New BDS-3 satellite improves the accuracy of pseudo-range single-point positioning in polar region. On July 31st, General Secretary Xi Jinping announced to the world that BDS-3 was formally put into practice commissioned, and which stands for a new era for BDS to serve the world and benefit mankind. BDS-3 will play an increasingly important role in global navigation and positioning services. It will further enhance the safety and reliability of our country’s investigations in polar region. Many scholars [8, 9] have confirmed that the BDS-2 positioning accuracy in low and mid-latitudes meets the design requirements, but the service performance in the Antarctic region is poor. Some scholars have described the service capabilities of BDS-3 [10–13], including the constellation design, service type, navigation signal system, etc. At present, the BDS-3 complete system has officially provided services, covering all over the world, However, there are still kinds of questions that need further verification and analysis, such as whether the performance of the BDS3 meets the design requirements, how much performance is improved compared with BDS-2, and how is the performance of the new frequency signals of BDS-3, whether it is possible to provide navigation and positioning services in the polar region.

2 Data Sources and Processing Strategies The measured data is mainly obtained from the iGMAS observation network. Up to now, iGMAS has been built 29 stations around the world. Although this article focuses on Table 1. Station distribution Station Location

Longitude Latitude

bjf1

Beijing

115.892

39.608

kndy

SriLanka

80.726

7.276

lha1

Lhasa

91.104

29.657

sha1

Shanghai

121.200

31.100

icuk

London

−0.175

51.500

taht

Tahiti

cnyr

YellowRiver Station

gwbd

GreatWall Station

zhon

Zhongshan Station

−149.606 −17.577 11.936

78.923

−58.963 −62.216 76.363 −69.370

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the BDS-3 positioning performance in polar region, but in order to fully compare and analyze service performance in different regions, we select the representative 9 stations from iGMAS. The selected sites are covering all over the world and the receivers of the sites are also from different manufacturers, the distribution and specific conditions are as follows (Table 1): The measured data comes from August 1 to August 31, 2020, and the algorithm used in this article comes from National Standard--Monitoring and Assessment Parameters of international GNSS Monitoring and Assessment System, and focuses on the coverage and basic positioning performance of the BDS-3 complete system with B1I, B3I, B1C and B2a signals. Starting from coverage performance, data quality, user equivalent ranging error and pseudo-range single-point positioning. It will provide a certain reference for the future research on BDS positioning performance in polar region.

3 Coverage Performance Analysis With the addition of BDS-3 satellites, the number of BDS visible satellites in the polar region will increase, and the spatial distribution structure of the BDS satellites in the polar region will be improved. This article uses the actual BDS broadcast ephemeris for 7 days from August 1 to August 7, 2020. The scope of latitudes from −87° to 87° and longitudes from −180° to 180° are divided into 5° × 5° grid points. This article analyzes the constellation coverage performance of BDS-2, BDS-3, and the combination of BDS2 and BDS-3 (referred to as BDS-2 + BDS-3 in the following) from three aspects of the number of visible satellites, DOP value and PDOP availability. The sampling interval is 5 min, and the Cut-off height angle is 5°. 3.1 Number of Visible Satellites The primary condition for GNSS to achieve positioning and navigation is that the number of visible satellites at the positioning point at the same time is more than 4. In certain conditions, the greater the number of visible satellites is, the higher the positioning accuracy is, but the number of visible satellites will continue to change over time. It is necessary to analyze the number of visible satellites. Figure 1 shows the number of satellites that BDS-2 and BDS-3 can be seen at different grid points around the world, with different colors representing different values (see the legend for the correspondence between colors and values). It can be seen from Fig. 1 that BDS-3 satellites effectively compensated for the BDS-2. At present, at least 8 satellites can be seen at any grid point in the world. The minimum number of visible satellites in BDS has increased from 3 to 13, and the number of visible satellites has increased significantly, which will effectively improve the coverage and service performance of polar region. Table 2 lists the statistical results of different regions. 3.2 DOP Value DOP value reflects the influence of geometric distribution of satellites on the positioning accuracy of GNSS, and is one of the important factors to assess performance of

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b)BDS-3

Fig. 1. Number of visible satellites

Table 2. Statistics of the visible BDS satellites number in different regions Regions

Statistic type

Number of visible satellites BDS-3

BDS-2 + BDS-3

Polar

Min

3

10

13

Max

6

10

16

BDS-2

Key

Global

95%

5

10

15

Min

8

12

20

Max

13

14

27

95%

13

14

27

Min

1

8

8

Max

13

14

27

95%

12

13

24

the constellation configuration. DOP values include GDOP, PDOP, HDOP, VDOP and TDOP. PDOP is one of the important indicators to measure the performance of constellation. PDOP value is a parameter that characterizes the strength of the relative position relationship between the satellite and the user. The accuracy can be simply expressed as PDOP*UERE. In the case of a certain user ranging error, the larger the PDOP is, the worse the positioning accuracy is, and the smaller the PDOP, the higher the positioning accuracy. Figure 2 show the PDOP distribution of BDS-2, BDS-3 and BDS-2 + BDS-3 at any location in the world. The darker the color is, the smaller the PDOP value is. It means that better navigation and positioning services can be used here. It can be seen that BDS-2 PDOP value of the Asia-Pacific area is relatively good, basically between 1–3. While outside the BDS-2 service area, PDOP value is poor, (when PDOP value exceeds 20.0, it is expressed as 21.0), which means that BDS-2 can hardly provide services in polar region. With the addition of BDS-3 satellites, coverage area has gradually increased. In the condition of a single BDS-3, PDOP performance in the BDS-2 service area is the

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a)BDS-2

c)BDS-2+BDS-3

b)BDS-3

Fig. 2. BDS-2/BDS-3/BDS-2 + BDS-3 PDOP distribution

best, and the polar region are slightly better than the global average; PDOP performance has been greatly improved in BDS-2 + BDS-3. The maximum PDOP value in key area is only 1.18, and PDOP value in polar region has also been reduced from 21.0 to 1.71. If the user’s ranging error is constant, positioning accuracy will be greatly improved. The statistical results of BDS PDOP value in different areas are shown in Table 3. Table 3. Statistics of the visible BDS PDOP value in different regions Regions

Statistic type

PDOP BDS-2

Polar

Key

Global

BDS-3

BDS-2 + BDS-3

Min

2.77

1.67

1.33

Max

21.00

1.94

1.71

95%

14.21

1.92

1.69

Min

1.80

1.26

0.93

Max

3.06

1.53

1.18

95%

2.85

1.52

1.14

Min

1.80

1.26

0.93

Max

19.68

1.98

1.88

95%

13.76

1.95

1.81

3.3 PDOP Availability PDOP availability is the percentage of time that GNSS can provide the promised better PODP in the service area. The PDOP value is usually 6 as the limit value, and PDOP value on the global grid point during the evaluation period is calculated (The Cut-off height angle is generally set to 5°), and the probability that the PDOP value of the grid point is less than the PDOP limit is calculated. Figure 3 respectively show the PDOP availability distribution of BDS-2 and BDS-3 at any location in the world from August 1 to August 7, 2020. The corresponding situation of colors and values is shown in the legend at the bottom of the picture. The darker the color is, the better the accuracy is.

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a)BDS-2

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b)BDS-3

Fig. 3. BDS-2/BDS-3 PDOP Availability

In the case of single BDS-2, PDOP availability is poor in polar region, with only 20.27% at the minimum and 73.76% at the maximum. Compared with the BDS-2, BDS-3 and BDS-2 + BDS-3 has improved significantly, with a maximum performance improvement of 79.73%. Both the maximum and minimum values are 100%, This means that the BDS-3 complete system can provide navigation and positioning services in polar region now. The statistical results of PDOP availability in different areas are shown in Table 4. Table 4. Statistics of the visible BDS PDOP availability in different regions Regions Polar

Key

Global

Statistic type

PDOP availability (%) BDS-2

BDS-3

BDS-2 + BDS-3

Min

20.27

100.00

100.00

Max

73.76

100.00

100.00

95%

69.44

100.00

100.00

Min

100.00

100.00

100.00

Max

100.00

100.00

100.00

95%

100.00

100.00

100.00

Min

0.00

100.00

100.00

Max

100.00

100.00

100.00

95%

100.00

100.00

100.00

4 Data Quality Analysis The data quality of GNSS observation data directly affects the availability and service accuracy of positioning services. High data quality is a prerequisite for obtaining reliable positioning results and directly affects the service availability of GNSS. It is necessary

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to analyze the data quality first to obtain the relevant results of the BDS data quality of the selected stations before analyzing the performance of BDS navigation services in the polar region. 4.1 Signal-To-Noise Ratio The signal-to-noise ratio (SNR) directly indicates the signal strength. The larger the value is, the stronger the signal’s anti-interference ability is and the better the signal quality is (Table 5). Table 5. Statistics of the SNR in different stations Site

BDS-2 B1I

BDS-3 B3I B1I

B3I B1C B2a

bjf1

43.8

44.8 46.5

47.4 46.6 47.0

lha1

44.0

44.8 47.4

47.7 47.5 46.6

icuk

41.4

40.4 47.0

45.9 46.6 46.0

taht

43.6

45.1 49.9

51.1 40.9 47.5

gwbd 42.4

42.5 47.4

47.2 46.8 45.8

zhon 43.0

42.9 47.0

46.9 46.9 46.8

cnyr

42.7 47.5

46.1 44.7 46.1

43.2

It can be seen from Fig. 4 that The signal-to-noise ratio of B1I/B3I is equivalent, but the average SNR values of BDS-3 is 3–5 dB/Hz higher than BDS-2. The average of B1C/B2a SNR is 1–2 dB/Hz lower than BDS-3 B1I/B3I. Taking the cnyr station as an example, the statistics of the signal-to-noise ratio of the BDS-2 and BDS-3 satellites at different frequencies are given. It can be seen from Fig. 4 below that the statistical result of BDS-3 SNR is larger than that of BDS-2. 60

B1I B3I B1C B2a

50

40

40

30

30

SNR

SNR

60

B1I B3I

50

20

20

10

10

0

0 C01

C02

C03

C04

C05

C06

C07

C08

C09

C10

C11

C12

C13

C14

C16

C19C20C21C22C23C24C25C26C27C28C29C30C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C59

satellite

satellite

a)BDS-2

b)BDS-3

Fig. 4. BDS-2/BDS-3 SNR(CNYR)

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4.2 Pseudo Range Multipath Multipath is an important issue of data quality in GNSS observing stations. It is mainly due to the interference delay effect caused by the multipath signal propagation, which causes an additional delay amount in the time from the satellite signal to the receiver antenna. Multipath combination (MP) can usually be used to comprehensively evaluate pseudo range multipath and noise. It can be seen from Fig. 5 that the multipath results of each station are less than the empirical value (0.5 m). Taking cnyr station as an example, the multipath error of each satellite of BDS-2 and BDS-3 is shown in the figure below. From Fig. 5, it can be seen that the multipath error of BDS-3 B1I/B3I is significantly smaller than that of BDS-2, while the multipath error of BDS-3 B1C/B2a is larger than B1I/B3I, and slightly better than BDS-2 B1I/B3I. The overall multipath error of BDS-3 is better than BDS-2, which reflects the BDS-3 complete system has a better performance. 2.0

BDS2-B1I BDS2-B3I BDS3-B1I BDS3-B3I BDS3-B1C BDS3-B2a

1.8 1.6 1.4

0.30

B1I B3I

0.25

0.20

1.0

unit:m

unit:m

unit:m

1.2

0.15

0.8

0.10

0.6 0.4

0.05

0.2 0.0

bjf1

lha1

icuk

taht

gwbd

Station

a)Each station

zhon

cnyr

0.00 C06

C07

C08

C09

C10

C11

C12

C13

C14

0.30 0.28 0.26 0.24 0.22 0.20 0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00

C16

satellite

b)BDS-2 satellites(cnyr)

B1I B3I B1C B2a

C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C32 C33 C34 C35 C36 C37 C38 C39 C40 C41 C42 C44 C45 C46

satellite

c)BDS-3 satellites(cnyr)

Fig. 5. Analysis result of multipath

5 User Equivalent Ranging Error Analysis User equivalent range error (UERE) mainly describes the error correction accuracy of user observation data, which includes the satellite orbit, satellite clock, ionospheric measurement, noise, etc. errors in the navigation system broadcast information. It can be simply understood as the quality of each satellite signal. This section selects observation data from August 1, 2020 to August 31, 2020. Under the premise that the coordinates of each station are accurately known, the single-frequency pseudorange calculation work is carried out to calculate the difference of each site on a global scale. The residual RMS value of satellite observations is used to analyze the UERE accuracy in different regions. Table 6 shows that the BDS-3 UERE of each frequency point is in the range of 0.5– 1.0 m. Whether in key service areas, global regions, or even polar region, B1C UERE has the best accuracy, while B3I has poor accuracy. In key areas, BDS-2 UERE is better than BDS-3; Figs. 6 plot the UERE accuracy statistics of different frequency of BDS-2 and BDS-3 satellites in key areas and on a global scale. It can be seen that BDS-3 satellites B1I and B1C are better than B3I and B2a respectively, whether in global aeras or in key areas. The main reason may be that the frequency of the B1I and B1C signals is higher, and the ionospheric delay correction residual is relatively small. The average value of B1C UERE is better than B1I. This is mainly related to the ionospheric models of the

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S. Fan et al. Table 6. Statistics of the BDS UERE in different regions System Signal Region Polar

Key Global

BDS-2 B1I

0.72

0.61 0.73

B3I

0.80

0.69 0.84

BDS-3 B1I

0.67

0.61 0.64

2

0

0

C08

C09

C10 C11

C12

0.71 0.70

C13

C14

C16

5

B1I-Key B3I-Key B1C-Key B2a-Key

BDS-3 UERE Accuracy in Global Aera

B1I-Global B3I-Global B1C-Global B2a-Global

4

3

2

1

C07

0.62

3

1

C05 C06

B2a

UERE(m)

3

C04

0.54 0.56

4

UERE(m)

UERE(m)

4

C03

0.82 0.88

0.47

5

B1I-Key B3I-Key B1I-Global B3I-Global

C02

0.96

B1C

BDS-3 UERE Accuracy in Key Aera

BDS-2 UERE Accuracy in Key and Global Area 5

C01

B3I

2

1

0 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C32 C33 C34 C35 C36 C37 C38 C39 C40 C41 C42 C43 C44 C45 C46 C59 C60

C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C32 C33 C34 C35 C36 C37 C38 C39 C40 C41 C42 C43 C44 C45 C46 C59 C60

PRN

PRN

a)BDS-2(Key)

b)BDS-3 (Key)

PRN

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Fig. 6. BDS-2/BDS-3/UERE accuracy in different area

two. B1I and B3I mainly use the Klobuchar ionospheric model, while B1C and B2a use the BDGIM model. The accuracy of the BDGIM model is better than that of Klobuchar. In order to further analyze the UERE accuracy of different stations, this article selects some stations from the world, involving key areas, global areas and polar region. Figure 7 respectively shows the UERE results of different sites and different satellites. The sites in different regions are divided by blue dashed lines. From left to right, they are the key area, the global area, and the polar area. It can be seen from Fig. 7 that the UERE values of other stations have little change on BDS-2 satellites, except for taht and zhon stations. This may be related to the BDS-2 satellite distribution and ionospheric model; As far as the BDS-3 satellite is concerned,

Fig. 7. BDS-2/BDS-3/UERE accuracy in different site

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in the global scope, regardless of the new and old frequency points, UERE value of each satellite does not change much, and B1C is better than B1I as a whole.

6 Positioning Performance Analysis The positioning accuracy describes the error between the actual value and the true value, it can be used to evaluate the service performance of GNSS. Based on the measured data of iGMAS, The article carried out the pseudorange positioning performance of each frequency signal, Specifically including B1I, B3I, B1C and B2a of BDS, L1C and L2C of GPS. BDS Horizontal Position Accuracy in 2020.08

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Fig. 8. BDS-2/BDS-3/positioning accuracy in different site

Figure 8 respectively shows the analysis results of each site at BDS different frequency signals. The stations in different regions are divided by blue dashed lines. From left to right, they are the key area, the global area and the polar area; the red solid line is positioning accuracy index limit corresponds to 5 m and 10 m respectively. From this figure, it can be concluded that the positioning performance of BDS-3 B1C is the best, and the positioning accuracy of BDS-2 + BDS-3 B1I is the second. The positioning accuracy of each station at different frequency meets the service performance specifications. Firstly, the statistical positioning results of all stations are analyzed, then gets the result of the different areas positioning accuracy. The specific statistical results are shown in Table 7:

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System

Signal

Region Polar

BDS-2 BDS-3

Polar

Polar

Horizontal

Vertical

Horizontal

Vertical

Horizontal

Vertical

B1I

6.34

6.77

1.42

3.12

3.54

5.07

B3I

6.17

7.84

1.56

4.42

3.47

5.64

B1I

1.59

4.21

1.47

2.88

1.65

3.60

B3I

1.60

5.90

1.64

3.84

1.91

4.37

B1C

1.34

2.46

1.43

2.37

1.49

2.49

B2a

3.07

5.26

3.16

5.46

2.91

4.85

BDS-2 + BDS-3

B1I

1.34

3.89

1.17

2.18

1.56

3.01

B3I

1.80

5.52

1.52

3.74

2.00

4.50

GPS

L1C

2.67

4.48

2.60

3.54

2.49

3.73

L2C

3.71

6.25

3.32

4.87

3.32

5.25

GNSS Horizontal Position Accuracy in 2020.08

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Fig. 9. Position accuracy of GNSS different signals in different stations

The specific analysis of BDS and GPS is shown in Fig. 9 and Fig. 10. The blue dashed line of Fig. 10 is frequency band boundary. The following conclusions can be drawn from the figure:1). In the comparison of positioning accuracy between BDS-3 and GPS, the B1C frequency is the best, and B1I is the second; 2) The positioning accuracy of BDS-3 is better than GPS under the same frequency or similar frequency.

Analysis of the BDS-3 Complete System on Positioning Performance GNSS Horizontal Position Accuracy in 2020.08

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Fig. 10. Position accuracy of GNSS different signals in different regions

7 Summary Compared with BDS-2, BDS-3 exhibits significant improvement in coverage, availability and reliability. This paper uses the measured data of the iGMAS to analyze the coverage performance, data quality, UERE and positioning performance, and try to provide reference information for BDS users in polar region. It can be known through experiment, calculation and analysis: (1) The BDS-3 complete system has better coverage performance in the polar region. The number of visible satellites is more than 10, the PDOP value is less than 1.6, and the PDOP availability is equal to 100%, which can indicate that the addition of BDS-3 satellites makes the space geometric configuration better, it is easy to meet the user’s navigation and positioning needs. If the user’s ranging error is certain, the BDS-3 positioning accuracy will be greatly improved. (2) The average SNR values for B1I/B3I of BDS-3 satellites are 3–5 dB/Hz higher than those of BDS-2 satellites, and BDS-3 pseudorange multipath error is smaller than BDS-2. Through BDS-3 B1I, B3I, B1C and B2a signals, B1C and B2a SNR is slightly lower than that of B1I and B3I; the multipath of B1C and B2a is greater than B1I and B3I; (3) If the satellite distribution is certain, the smaller the UERE value, the higher the positioning accuracy. B1C UERE is better than B1I, which means that the B1C positioning accuracy will be better than B1I; Whether in polar region or not, the value of B1I UERE is almost the same, Which may be caused by the improvement of the accuracy of the BDSK8 model in high latitudes; (4) Whether in the BDS-2 service area, or in the global or even polar region, the positioning accuracy of each BDS-3 signal meet the service performance specifications, and the positioning accuracy of the B1C frequency is the best; under the same frequency, BDS Positioning accuracy is better than GPS positioning accuracy; (5) The new BDS-3 satellites makes the BDS space geometric configuration conditions better; UERE value of each BDS-3 satellite has little change within the globe, and the accuracy of BDS-3 is better than BDS-2. The improvement of satellite distribution

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and UERE has improved the BDS-3 positioning accuracy, allowing users to enjoy undifferentiated positioning services in the polar region and even the world.

Acknowledgements. We are immensely grateful to the iGMAS Team for years of hard work and all major breakthroughs they have achieved in a series of core technologies. We would also like to thank our colleagues from the Monitoring and Assessment Center (MAC) of iGMAS who provided insight and expertise that greatly assisted the research. This work was funded by the National Natural Science Foundation of China (Grant No. 41874041) and supported by ZFS (ZFS19001D-ZTYJ08, Y9E0151M26).

References 1. Arctic Issues Research and Writing Group. Arctic Issues Research, pp. 1–10. Navy Press, Beijing (2011) 2. Xu, W., Jia, X., Qiao, F., et al.: Preliminary assessment of positioning performance of BDS navigation system in north and south polar region. J. Geodesy Geodyn. 38(12), 1268–1273, 1284 (2018) 3. Zhang, H., Su, W., Yu, C., et al.: Positioning performance analysis of Beidou area and GLONASS system in the Arctic. Ship Electron. Eng. 38(8), 50–54 (2018) 4. Zhou, R., Chen, M.: Analysis on the navigation and positioning covering performance of BDS in Polar region. In: China Satellite Navigation Conference (CSNC) (2017) 5. Du, Y., Wang, Z., An, J., et al.: Positioning analysis of Beidou navigation satellite system over ocean and Antarctic regions. Chin. J. Polar Res. 27(1), 91–97 (2015) 6. Wang, Z., Du, Y., Xiong, Y., et al.: Preliminary assessment of positioning performance of Beidou navigation system at Zhongshan station Antartica. Geomatics Inf. Sci. Wuhan Univ. 42(8), 1027–1034 (2017) 7. Hui, Z., Qi, Z.: Analysis of New BDS-3 satellite on positioning performance in Polar region. Geomatics World 27(03), 126–130 (2020) 8. Yang, Y., et al.: Preliminary assessment of the navigation and positioning performance of BeiDou regional navigation satellite system. Sci. China Earth Sci. 57(1), 144–152 (2013). https://doi.org/10.1007/s11430-013-4769-0 9. Jiao, B., Hao, J., Chen, M., et al.: Performance analysis of BDS in Antarctica. J. Navig. Positioning 5(04), 64–69 (2017) 10. Guo, S., Cai, H., Meng, Y., et al.: BDS-3 RNSS technical characteristics and service performance. Acta Geodaetica et Cartographica Sinica 48(7), 810–821 (2019) 11. Yue, M., Xiaolin, J., Xiaoyong, S., et al.: Analysis of space signal performance of basic BDS-3 navigation satellite system . J. Geomatics Sci. Technol. 36(02), 111–115 (2019) 12. Yang, Y., Mao, Y., Sun, B.: Basic performance and future developments of BeiDou global navigation satellite system. Satell. Navig. 1(1), 1–8 (2020). https://doi.org/10.1186/s43020019-0006-0 13. Jin, S., Su, K.: PPP models and performances from single- to quad-frequency BDS observations. Satell. Navig. 1(1), 1–13 (2020). https://doi.org/10.1186/s43020-020-00014-y

Development of High-Precision Ionospheric Monitoring System in China: Taking ROTI Map as an Example Chengli She1,2(B) , Haitao Liu3,4 , Jun Yu2 , Peiyuan Zhou2 , and Hongzheng Cui2 1 Qianxun Spatial Intelligence (Zhejiang) Inc., Deqing 313200, Zhejiang, China

[email protected]

2 Qianxun Spatial Intelligence Inc., Shanghai 200438, China 3 State Key Laboratory of Lunar and Planetary Sciences, Macau University

of Science and Technology, Macau 999078, China 4 CNSA Macau Center for Space Exploration and Science, Macau 999078, China

Abstract. The ionosphere has always been one of the important error sources in GNSS navigation and positioning applications. The refined real-time monitoring of the ionosphere can provide more accurate information for calibration of ionospheric errors in high-precision positioning. Based on over 2,000 GNSS monitoring stations of the Beidou Ground-Based Augmentation System, this paper proposed a framework for the development of a high-precision ionospheric monitoring system in China, planning to provide a group of ionospheric products. Taking ROTI map as an example, the post-processing version has a spatial resolution of 0.2° in both longitude and latitude, with a temporal resolution of 30 s. The ROTI map with high-precision can not only indicate the area where the GNSS signal is severely affected by the ionosphere, but also provide an optimal strategy for satellite data selection in high-precision positioning applications. Keywords: Ionosphere · Total electron content (TEC) · Rate of TEC index (ROTI) · Beidou Ground-Based Augmentation System (GBAS)

1 Introduction In recent years, GNSS has been developing rapidly. The comprehensive completion of the Beidou Satellite Navigation and Positioning System (BDS) led by China has attracted widespread attention, and related applications are also accelerating by BDS. Nowadays, people have more and more precise requirements for positioning, timing, and navigation (PNT), where signals from navigation satellites are playing an increasingly important role in human production and life. The ionosphere acts as the only way for GNSS signals to propagate from upper satellites to the ground, whose impact on GNSS navigation and positioning is crucial. For a long time, the ionosphere has always been a key factor affecting the accuracy of GNSS signal processing. Specifically, the ionospheric total electron content (TEC), as the line integral of the ionospheric electron density along the propagation path of © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 187–196, 2021. https://doi.org/10.1007/978-981-16-3142-9_17

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the GNSS signal, is generally used to measure the influence of the ionosphere upon the GNSS signal. Constrained by the limitations of observation conditions, the ionospheric TEC is generally obtained by GNSS observations from fixed ground-based stations. Directly, the corresponding products are generated by ionospheric TEC observations, such as time series from single or multiple stations, and maps from local or global region. In addition, TEC derived parameters are also adopted as indicators for monitoring the ionosphere, for example, the rate of TEC index (ROTI). As early as 1997, Pi et al. [1] analyzed the global distribution of ionospheric irregularities based on the scattering ROTI map calculated by global GPS observations. In particular, the ionosphere in Europe is plagued by auroral phenomena at night. Then, based on more than 700 GNSS stations located in the middle and high latitudes of the northern hemisphere, Cherniak et al. [2] develop regional ROTI map (geomagnetic latitude above 50°) under geomagnetic coordination, with bins of 2° along geomagnetic latitude and 8 min along geomagnetic local time, to specifically locate the active position of ionosphere in European area in research and applications. However, the situation for China is quite different from Europe, since both the northern and southern regions of China have always been affected by the ionosphere, only the area in mid-latitudes is relatively less affected. On the one hand, for the southern region, such as Guangdong, Guangxi, Hainan provinces, generally located in geomagnetic low latitudes, the ionospheric equatorial abnormalities during the daytime and irregularities at nighttime occurs. On the other hand, for the northern region, such as Heilongjiang, Jilin, and Xinjiang provinces, the ionosphere is easily disturbed by the expansion of the aurora egg which expanded from polar region to lower latitudes at night. These phenomena have caused various impacts on the GNSS positioning in China. Therefore, the development of a map product which can reveal the ionospheric state grid by grid, has very important value in applications especially in real-time scenarios. In order to meet the demand for real-time products of ionospheric maps, we plan to develop a high-precision ionospheric monitoring system, based on more than two thousand Beidou Ground-Based Augmentation System (GBAS) monitoring stations which are constructed and operated independently by ourselves. The planning products can provide rich information of ionosphere for real-time high-precision positioning. This paper will explain the architecture of this system, and take the development of ionospheric ROTI map during a major magnetic storm as an example.

2 High-Precision Ionospheric Real-Time Monitoring System in China 2.1 System Architecture Based on the BDS GBAS stations, the architecture of the ionospheric monitoring system is shown in Fig. 1. The network, cloud, services and terminals constitute a complete closed-loop ecosystem. In this system, the network is the basis for the operation of the entire system which is composed of a number of densely distributed GBAS stations. The cloud, which relies on Alibaba cloud computing capabilities, is the core of the system

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implementation, and is responsible for the real-time Collection, processing and output of data. Meanwhile, the service of ionospheric monitoring, acting as relatively independent service, reuses the data resources on the cloud to obtain a group of products in the form of maps. Finally, the ionospheric products can be delivered to users by network protocols such as NTRIP in real-time, sharing the real-time perception of the ionospheric status at both the server and terminals, in order to alleviate the impact of the ionosphere on positioning as much as possible.

Fig. 1. Architecture of ionospheric real-time monitoring system

2.2 Network-Cloud-Map-End Integrated Solutions The network-cloud-end integrated solution is an emerging collaborative solution in the Internet era. The cloud platform organically combines massive data resources and outof-conventional computing power. It provides a modular scheduling method suitable for loading various calculations and easy delivering to different users. Before, GNSSbased ionospheric monitoring solutions were mainly implemented by GPS monitoring stations. The average distance between these monitoring stations can reach more than 100 km or even longer. The equipment in those stations is slowing updated, and generally not support the G/R/C/E multi-GNSS signals. Therefore, the ability to finely detect the ionosphere is limited. At the same time, those solutions are usually only available for professional users, such as the military and scientific research institutes, instead of ordinary users. According to the solution proposed in this paper, ordinary users can also obtain real-time information of ionosphere like professional users, by this way various terminals can be adapted more flexibly. Meanwhile, the applications from different terminals can help improve and broaden the ionospheric monitoring services, to build a more diverse ecosystem. 2.3 High-Precision Ionospheric Map Service The goal of the high-precision ionospheric map service is to provide grided real-time ionospheric map datasets in China, as shown in Fig. 2. The TEC map is obtained from the original phase and pseudo-range observations, and the TEC disturbance map comes from the TEC map subtracting the background map, and the ROTI map is grided from the ROTI observations. TEC map is the most commonly used one among them, and TEC disturbance map is the trend of future development. Belehaki et al. [3] proposed a set of methods for real-time detection and tracking of TID from GNSS observations in Europe, providing more diversified services for European ionospheric monitoring.

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Fig. 2. Outputs of ionospheric real-time monitoring system

3 Taking ROTI Map as an Example 3.1 Algorithm for ROTI Map Processing As one of the products in the ionospheric monitoring system, ROTI map is taken as an example in this section. The data flow from GNSS observation to ROTI map is shown in Fig. 3.

Fig. 3. Data flow of ionospheric ROTI map

The technology of extracting ionospheric TEC from GNSS observation data is very mature. In this paper, the assumption of local spherical symmetry and thin-layer model are adopted, and the vertical TEC estimation is performed station by station, as shown in literature [4]. At first, the ionospheric slant TEC (STEC) should be converted to the vertical TEC (VTEC) at the ionospheric pierce point (IPP):  p  p p (1) VTECrmn ,ti = STECrmn ,ti × MF θrmn,ti Where r m , pn and t i represents the m-th GNSS station, the n-th GNSS satellite and the i-th epoch. θ is the elevation angle at the IPP (generally 350–450 km) towards the satellite. MF stands for mapping function with the expression as follows:  p  p (2) MF θrmn,ti = sin θrmn,ti During a continuous period of time, for a pair of one satellite and one monitoring station, the rate of change of VTEC during this period is recorded as ROT (Rate of TEC) in the following formula: p

p ROTrmn,ti

=

p

VTECrmn ,ti − VTECrmn ,ti−1 ti − ti−1

(3)

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Correspondingly, the ROTI (Rate of TEC index) can be obtained by statistic of ROT:   J  J 2   pn p p ROTIrm ,ti =  ROTrmn,ti−j  −  ROTrmn,ti−j 2 (4) j=1

j=1

Where t i-j represents the time j epochs before the current time t i , t i-1 represents the time only one epoch before the current time t i . J is an integer, and < > represents the average. p Now, ROTI rmn ,ti is a variable closely related to both stations and satellites, referring to the ROTI over a group of discrete IPPs. Since the locations of these IPPs are scattering and may overlap, it is inconvenient to distinguish the ionospheric changes among them. Therefore, a mapping processing is adopted here: igrid

GridROTIti

=

N M  

p

ROTIrmn,ti /MN

(5)

m=1 n=1 igrid

refers to the ROTI value in the igrid-th grid at the time t i , Where GridROTI ti obtained by averaging the scattering ROTI of all IPPs within the grid at that time. The map is divided by unique step of geographic longitude and latitude, composed of twodimensional grids. M and N denote the number of GNSS stations and visible satellites, respectively. By Eq. (5), a gridded ROTI map at time t i can be obtained. Then, from comparison among the ROTI maps at adjacent moments, the overall trend of ROTI changes is revealed. Furthermore, according to the correlation between ROTI and ionospheric scintillation, the location and amplitude of the ionospheric scintillation can be determined in time. Considering the ROTI and ionospheric scintillation levelling over the IPPs, the gridded ROTI and ionospheric scintillation is classified into four levels, as shown in the table below. Similar to the algorithm of ROTI map construction, TEC maps are also generated from the IPP VTEC of each pair of station and satellite, without any interpolation method, as grided map with discrete points to describe the ionospheric TEC (Table 1). Table 1. Relationship of GridROTI and ionospheric scintillations classification Range of GridROTI (unit: TECU/min) Level of scintillation [0, 0.1)

None

[0.1, 0.3)

Weak

[0.3, 0.5)

Moderate

≥0.5

Strong

3.2 ROTI Map During a Strong Magnetic Storm On September 7–8, 2017, the sun erupted with strong coronal mass ejection (CME) events, and the M7.3 and X1.3 class solar flares on 7 September and the M8.1 class

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solar flare on 8 September, along with a lot of energy released into interplanetary space. Consequently, the earth’s magnetic field undergone two violent disturbance processes and two magnetic storms occurred. The first magnetic storm began approximately at 22:00 UT on September 7, and the second one began near 11:30 UT on September 8. Taking the second magnetic storm as an example, at 13:00 UT on September 8, Dst index reached -120 nT. An hour later, Dst index reached a minimum of -122 nT, and the geomagnetic field recovered to the quiet status until September 11. The geomagnetic Dst indices during this period are shown in Fig. 4. The colors indicate the level of magnetic storm events, green, cyan, orange, and pink color referring to small, moderate, strong, and gigantic geomagnetic storm events, respectively. Seen from Fig. 4, a strong magnetic storm occurred during this period, which means that the energy injected into the earth’s magnetic field was very strong, and there are many case studies carried out, such as various changes in the stratosphere and ionosphere.

Fig. 4. Dst indices in September 1–15, 2017

For example, Dimmock et al. [5] utilized European stations around the polar region to measure the geomagnetically induced current during the magnetic storm, and the results showed that the induced current increased abnormally. Velinov et al. [6] analyzed the number of cosmic ray neutrons during the magnetic storm, and they found that the number of neutrons during the storm decreased sharp ly and the ionization in the stratosphere was significantly weakened. In addition to the phenomena in the magnetosphere and atmosphere, the response of the ionosphere is also worthy of attention. Yasyukevich et al. [7] analyzed the GNSS TEC from approximately 4,200 global stations during the case of X9.3 class flares on September 6, and found that the global TEC variation differs from the quiet time, 15-16 TECU increase in the low latitude and only 8-10 TECU at the middle latitude. Mendoza et al. [8] used five IGS stations in the Philippines-Taiwan area to analyze the TEC changes in the ionosphere near the equator and confirmed that the TEC increased by about 15 TECU during the storm time. In particular, for the impact of the magnetic storm on September 8 in and around China, Aa et al. [9] adopted GNSS data from 38 IGS stations in China and 260 station in Crustal Movement Observation Network of China (CMONOC) to extract the TEC map and ROTI map, and found that there is an obvious electron density depletion structure in the ionosphere along the southeast-northwest direction of China, which moved rapidly to high latitudes along the magnetic line. This caused a drastic change in the ionospheric

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Fig. 5. Maps of TEC in and around China during 13:00–14:00 UT on 8 September 2017

TEC, which was reflected in the ROTI map as a strip of ROTI maximum along this direction, and TEC decrease over depletion by about 5–15 TECU. For comparison, based on the data from 1,292 GNSS stations operated by Qianxun Spatial Intelligence (Zhejiang) Inc., the TEC map and ROTI map during the main phase of the second storm (13:00–14:00 UT, September 8, 2017) are shown in Figs. 5 and 6, respectively, in order to understand the ionospheric response characteristics from a more detailed perspective. In the literature [9], the resolution of the ROTI map is 1° in both the latitude and longitude directions, and the grid ROTI is obtained from the median ROTI value of the IPPs in a grid every 5 min. In this paper, ROTI maps and TEC maps

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are obtained under more fine-grained resolution. In detail, the latitude and longitude resolution of the ROTI map is 0.2°, and the time resolution is 30 s. The latitude and longitude resolution of the TEC map is 0.1°, and the time resolution is 15 s.

Fig. 6. Maps of ROTI in and around China during 13:00–14:00 UT on 8 September 2017

As shown in Fig. 6, the details of the ROTI map are very clear. During the main phase of the magnetic storm, the ROTI in Northeast China and North China was very small, and the time change rate of the ionospheric TEC was very small. Compared with the TEC map in Fig. 5, the ionospheric TEC is mainly controlled by the background and has no obvious fluctuations, which means the GNSS-based positioning in this area is scarcely affected by the magnetic storm. On the contrary, for the link between Gansu and Guangdong, the ionospheric electron density depletion structure generated in low latitudes and quickly propagated along the magnetic line to high latitudes. In Xinjiang, Tibet and other places, due to the lack of observations, only rough changes can be captured. Taking the TEC map around Xinjiang at 13:00 UT as an example, despite the wide blanks, the ionospheric enhancement could be recognized. Seen from the ionospheric TEC maps in Fig. 5, the ionospheric changes in lowlatitude regions such as Guangdong and Guangxi are rather complicated, both the depletion and enhancement in electron density, whose temporal variation indicates that the source of the ionospheric changes comes from the lower latitude regions. As a typical example, Fig. 7 lists the number of GNSS satellites available in Guangdong and Guangxi on September 8, 2017. The standard for “available” satellites is that the time change rate of GNSS TEC is relatively small, with the ROTI from a satellite-station pair is less than a threshold. From 00:00–12:30 UT, the number of available satellites in each constellation system is relatively stable, with the sum above 15. At about 12:30 UT, the number of available satellites turns to drop sharply, even less than 5 satellites available in total, and this worse situation continues until 16:00 UT. It gradually recovers afterwards, returning to a total of more than 15 satellites around 18:00 UT. Particularly, between 12:30–16:00 UT, due to the significant impact upon the ionosphere, the estimation of GNSS TEC will also be affected accordingly. As a result, the ionospheric error in GNSS positioning is difficult to be accurately corrected, which will eventually lead to the increase of positioning error by GNSS. In practice, GNSS positioning requires at least 4 satellites. Notice that, there is a period when the number of available satellites is less than 4, which

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means that the positioning cannot be completed only by GNSS observations, and special consideration is needed in applications.

Fig. 7. Number of available satellites in Guangdong and Guangxi provinces on 8 Sep., 2017

4 Conclusion and Outlook This paper explains how to utilize the Beidou GBAS in China to develop the framework of the ionospheric real-time monitoring system. As an example, the implementation process of ROTI map is introduced in details. Moreover, both ROTI and TEC maps of China during the main phase of a strong magnetic storm are shown as an example, in order to analyze the different impacts of different regions in China. Guangdong, Guangxi, and Hainan have been significantly affected, where both the electron density depletion and enhancement phenomena coexists. In Gansu and Shanxi provinces, the electron density is mainly depletive, while in Xinjiang and Qinghai, the electron density is mainly enhanced. The entire Northeast and North China are barely affected. In practice, this real-time ionospheric monitoring system can be landed by getting through the link of the entire architecture, and is still under continuous development so far. In the near future, we look forward to launch it in various applications, as the live weather reports in public lives done. Acknowledgements. This research was supported by the National Natural Science Foundation of China (41704158). The geomagnetic Dst indices comes from the World Data Center for Geomagnetism, Kyoto, Japan.

References 1. Pi, X., Mannucci, A.J., Lindqwister, U.J., Ho, C.M.: Monitoring of global ionospheric irregularities using the worldwide GPS network. Geophys. Res. Lett. 24(18), 2283–2286 (1997) 2. Cherniak, I., Krankowski, A., Zakharenkova, I.: Observation of the ionospheric irregularities over the Northern Hemisphere: Methodology and service. Radio Science. 49(8), 653–662 (2014) 3. Belehaki, A., Tsagouri, I., Altadill, D., Blanch, E., Borries, C., Buresova, D., Chum, J., Galkin, I., Juan, J.M., Segarra, A., Timoté, C.C.: An overview of methodologies for real-time detection, characterisation and tracking of traveling ionospheric disturbances developed in the TechTIDE project. J. Space Weather Space Climate 10, 42 (2020)

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4. She, C., Yue, X., Hu, L., Zhang, F.: Estimation of ionospheric total electron content from a multi-GNSS station in China. IEEE Trans. Geosci. Remote Sens. 58(2), 852–860 (2019) 5. Dimmock, A.P., Rosenqvist, L., Hall, J.O., Viljanen, A., Yordanova, E., Honkonen, I., André, M., Sjöberg, E.C.: The GIC and geomagnetic response over Fennoscandia to the 7–8 September 2017 geomagnetic storm. Space Weather. 17(7), 989–1010 (2019) 6. Velinov, P.I., Tassev, Y.: Long term decrease of stratospheric ionization near the 24-th solar cycle minimum after G4–Severe geomagnetic storm and GLE72 on September 8–10, 2017. Comptes rendus de l’Académie bulgare des Sciences 71(8), 1 Jan 2018 7. Yasyukevich, Y., Astafyeva, E., Padokhin, A., Ivanova, V., Syrovatskii, S., Podlesnyi, A.: The 6 September 2017 X-class solar flares and their impacts on the ionosphere, GNSS, and HF radio wave propagation. Space Weather 16(8), 1013–1027 (2018) 8. Mendoza, M.M., Macalalad, E.P., Juadines, K.E.: Analysis of the Ionospheric Total Electron Content during the Series of September 2017 Solar Flares over the Philippine-Taiwan Region. In: 2019 6th International Conference on Space Science and Communication (IconSpace) 2019 Jul 28, pp. 182–185. IEEE, 28 July 2019 9. Aa, E., Huang, W., Liu, S., Ridley, A., Zou, S., Shi, L., Chen, Y., Shen, H., Yuan, T., Li, J., Wang, T.: Midlatitude plasma bubbles over China and adjacent areas during a magnetic storm on 8 September 2017. Space Weather 16(3), 321–331 (2018)

LEO Constellation Design Based on Dual Objective Optimization and Study on PPP Performance Xin Nie1(B) , Min Li2 , Fujian Ma3 , Lei Wang1,2,3 , and Xu Zhang1,2,3 1 China Academy of Space Technology (CAST), Beijing 100094, China 2 Shandong University, Weihai, China 3 Wuhan University, Wuhan, China

Abstract. Low-orbit satellites have the advantages of rapid observation geometric changes and strong reception signals. The LEOs play a significant role in accelerating the convergence speed of precise point positioning, and help to provide high-precision positioning services indoors or in areas with severe signal obstruction. However, due to the constraint of the orbit height of low orbit satellites, a larger number of satellites are needed to achieve global coverage compared with medium and high orbit satellites. This paper proposes a LEO constellation design method based on dual-objective optimization, which uses fewer satellites to achieve global coverage. The PPP performance under different boundary conditions is analyzed through simulation. The method proposed in this paper can be widely used in the design of LEO satellite navigation augmentation system, and the research results provide reference and support for the corresponding system demonstration and analysis. Keywords: LEO · Dual objective optimization · Precise point positioning

1 Introduction GNSS precision point positioning technology can achieve static centimeter to millimeter level, dynamic decimeter to centimeter level high-precision absolute positioning, but this technology still has two problems [1]. First, that convergence time is too long. To achieve centimeter level or even millimeter level, for single-system positioning, it usually takes 20 min or more to converge. The reconvergence time is almost as long as the first convergence time, which greatly reduces its availability and reliability. Second, The GNSS constellation usually adopts mid-to-high orbit. The satellite signal is attenuated seriously during the propagation process, resulting in weak signal strength on the ground, which is not conducive to positioning services indoors or in cities, canyons, forests and other areas with severe signal obscuration. Anti-jam performance is difficult to guarantee. Low-orbit satellites have the advantages of rapid observation geometric changes and strong ground reception signals. They play a significant role in accelerating the convergence speed of precise point positioning, and help to provide high-precision positioning services indoors or in areas with severe signal obscuration [2, 3]. Compared © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 197–207, 2021. https://doi.org/10.1007/978-981-16-3142-9_18

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with medium and high orbit satellites, due to the constraint of the orbit height of low orbit satellites, a larger number of satellites are needed to achieve global coverage. This paper proposes a LEO constellation design method based on dual-objective optimization which uses coverage performance and the number of satellites as optimization goals, to achieve global coverage performance and uses with fewer satellites. Based on the design of the constellation scheme and the measured data, the PPP performance based on the LEO constellation under different boundary conditions is analyzed through simulation. The method proposed in this paper can be widely used in the design of LEO satellite navigation enhancement system, and the research results provide reference and support for the corresponding system demonstration and analysis. 1.1 LEO Satellite Features LEO satellites generally have an orbit height of 400 km to 1500 km. Compared with the medium and high orbits used by GPS and Beidou GNSS systems, they have the following characteristics: (1) The track is low, the signal attenuation is small, and the received signal strength is high, which is conducive to positioning in a sheltered environment and indoors. Since LEO satellites have a lower orbit than MEO satellites, the signal fading is small. According to the calculation of the LEO satellite orbit height of 1100 km and the MEO satellite orbit height of 21528 km, considering the use of a single beam antenna, the antenna beam angle of the LEO is is twice the angle of the MEO. k=

arcsin(35786/36886) arcsin(R/R + HLEO ) = ≈ 2, arcsin(R/R + HMEO ) arcsin 35786/57786

where R is the radius of the earth, HLEO and are the height of LEO and LEO, respectively. According to the formula of the relationship between antenna aperture and half-beam angle D = 70 λ/θ1/ 2 , if the aperture of a single-beam antenna is 1/2, the antenna gain will decrease by 6 dB. In summary, when the single-beam antenna is used, the satellite transmitting power is the same, and the power reaches the ground is enhanced by 20 dB (Fig. 1).

Fig. 1. Schematic diagram of satellite distance and coverage of different orbital altitudes

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(2) The orbit is low and the coverage area of a single satellite is small. According to calculations, 7 LEO satellites are required to cover the visible range of 1 MEO satellite [4], and a larger number of satellites are required to achieve the same coverage effect. (3) The observation geometry changes quickly, which is conducive to rapid convergence. As shown in Fig. 2, LEO running for 31 s is equivalent to the geometrical change degree of GPS running for 20 min. In the same time period, the LEO trajectory is longer, the geometry changes quickly, and the convergence time during PPP positioning will be greatly shortened. (4) The perturbation force is complicated, and the precise orbit determination and prediction are difficult. During the operation of LEO satellites, the dynamic orbit determination model is more complicated under the influence of various forces such as the earth’s gravity field, ocean tide, solid tide, sunlight pressure, and atmospheric resistance.

Fig. 2. Comparison of LEO and MEO satellite observation geometry

1.2 Analysis of the Influence of Atmospheric Drag on the Number of Low-Orbit Satellites Taking into account the 31 × 31-order earth gravity field model, ocean tide, solid tide, sunlight pressure, Jacchia 1970 atmospheric drag model and three-body gravity [5], the satellite surface-to-mass ratio is 0.01 m2 /kg, and the orbit height of satellite is between 500 km and 1100 km, the impact was carried out. The analysis results are shown in Table 1. It can be seen that the atmospheric resistance mainly has a significant influence on the orbital semi-major axis between 500 km and 800 km, so the proposed low-orbit satellite constellation orbit height is between 900 km and 1500 km.

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Orbit height (km)

Semi-major axis (m)

Eccentricity

Inclination

RAAN

Perigee angular distance

500

8131.5

600

951.5

700 800

Mean anomaly

6.09e−04

0.0162

0.0639

9.1467

359.9227

8.18e−05

0.0018

0.0071

3.0328

359.7060

497.98

4.56e−05

9.05e−04

0.0037

1.5349

359.6837

157.03

1.37e−05

2.74e−04

0.0011

2.2769

10.8145

900

31.91

2.52e−06

5.51e−05

2.18e−04

−0.1777

3.9658

1000

32.66

1.73e−06

5.43e−05

2.18e−04

−0.2131

2.4606

1100

15.64

1.49e−06

−3.78e−05

1.14e−04

0.0470

−0.0169

1.3 Optimal Design of Low-Orbit Navigation Constellation Based on Dual Objective Optimization The adopted constellation configuration is Walker constellation, expressed as N/P/F, where N is the total number of satellites, P is the number of orbital planes, and F is the phase factor. The low-orbit satellites that make up the global navigation constellation should meet two primary conditions: GDOP should be as small as possible to meet user navigation accuracy requirements, and the number of satellites should be as small as possible to reduce system construction costs. Therefore, two objective functions are set: ⎧   ⎨ Fitness1 = max max max GDOP rp , t, c t∈(0,TP ) F∈(0,P−1) rP∈Earth (1.1) ⎩ Fitness2 = s × p Dividing the world into a grid of 6° × 6°, the largest GDOP value among all grid points in the P satellite configurations during the satellite orbit period T is Fitness1, Fitness2 is the number of satellites. Use parallel NSGA-III algorithm [6, 7] for optimization search. 1.3.1 Single Walker Constellation Design The global average number of visible satellites is 4, 5, and 6, and the number of visible satellites varies with latitude when the orbit height is 900 km. It can be seen that the number of visible satellites in the world under a single Walker constellation is unevenly distributed. 1.3.2 Compound Walker Constellation Design Due to the uneven global distribution of a single Walker constellation, a hybrid Walker constellation composed of orbital heights of 900 km and 1200 km is designed, and the parallel NSGA-III algorithm is used to search. When the average number of visible satellites is 4, 5, and 6, the results are shown in Table 2.

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Fig. 3. The number of satellites varies with latitude

Table 2. Composite constellations corresponding to different visible satellite numbers Average visible satellites 4 5 6

Orbital height (km)

Constellation configuration

Orbital inclination (deg)

900

W56/8/4

42.85

1200

W32/8/2

87.59

900

W81/9/1

36.42

1200

W40/10/1

85.0

900

W64/8/4

37.85

1200

W60/10/4

87.85

The number of visible satellites in each hybrid constellation varies with latitude as shown in Fig. 4. It can be seen that the compound Walker constellation composed of two orbital heights can achieve a more uniform global distribution (Fig. 5 and 6).

Fig. 4. The number of visible satellites in 4 mixed constellations of average visible stars varies with latitude

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Fig. 5. The number of visible satellites in 5 mixed constellations of average visible stars varies with latitude

Fig. 6. The number of visible satellites in 6 mixed constellations of average visible stars varies with latitude

1.4 Research on the Performance of Low-Orbit/GNSS Multi-system PPP 1.4.1 LEO/GNSS Multi-system Fusion Positioning Model The theoretical method and mathematical model of LEO/GNSS fusion positioning: The real-time orbit and clock error information of LEO satellites can be obtained through the precise orbit determination of LEO satellites. Assuming that the station receiver tracks the satellite, the original basic observation equations of LEO/GNSS pseudorange and carrier phase can be expressed as: s s s s = μsr xr + tr − t s + dr,j − djs + βr,j Iz,r + msr Zr + εr,j pr,j   s s s s lr,j = μsr xr + tr − t s − βr,j Iz,r + msr Zr + λsj Nr,j + bsr,j − bsj + ξr,j ,

(1.2)

s and l s is the observed value minus calculated value (OMC) of the pseudorange where pr,j r,j and carrier phase observations, in meters; j is the frequency number; μsr is the linearized receiver-to-satellite unit line vector, xr is the receiver column vector of coordinate increments relative to the prior position, tr and t s are the clock difference between the s are the frequency-dependent UCD on receiver and the satellite respectively, djs and dr,j the receiver and the satellite respectively, and Iz,r is the total zenith ionospheric delay. s = γ s · 40.3 f 2 is the frequency-dependent factor, where γ s Is the ionospheric βr,j r r j projection function, fj is the corresponding frequency, Zr is the tropospheric zenith s is the integer ambiguity, λs is the delay, msr is the corresponding projection function, Nr,j j

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corresponding wavelength, bsr,j and bsj is the frequency-dependent UPD on the receiver s are ξ s the measurement noise of the pseudorange and and satellite respectively, and εr,j r,j carrier phase observations. In addition, due to different signal frequencies and signal structures, multi-system GNSS combined PPP should consider IFB. Taking the GPS system as the reference system, the ionospheric combined observation equation of the four-system combined PPP can be expressed as s,G s,G = μrs,G xr + t r + mrs,G Zr + εr,IF pr,IF

(1.3)

s,G

s,G s,G lr,IF = μrs,G xr + t r + N r,IF + mrs,G Zr + ξr,IF s,i s,i pr,IF = μrs,i xr + t r + IFBrs,i−G + mrs,i Zr + εr,IF

(1.4)

s,i

s,i s,i lr,IF = μrs,i xr + t r + IFBrs,i−G + N r,IF + mrs,i Zr + ξr,IF

In the formula, G represents GPS, i ∈ {R, C, E, L} respectively represents GLONASS, BDS, Galileo system and low-orbit satellite; the receiver clock error parameter can be expressed as G t r = trG + dr,IF

(1.5)

At the same time, the IFB parameters and ISB parameters are respectively s,i G IFBrs,i−G = dr,IF − dr,IF

(1.6) s,G

In the formula, the ionospheric-free combined floating-point ambiguity N r,IF , and s,i

N r,IF includes the ionospheric-free combined UPD at the receiver end and the satellite s,i G are the ionospheric-free combined UCD at the satellite end. The end; dr,IF and dr,IF ambiguity can then be expressed s,G

s,G s,G G N r,IF = Nr,IF −dr,IF −dIF s,i

s,i s,i N r,IF = Nr,IF −IFBrs,i−G −dIF

(1.7)

Suppose that the receiver observes satellites, where nG , nR , nE , nC , nL are the numbers of GPS, GLONASS, BDS, Galileo and LEO satellites, respectively. Let the weight matrix of the observation value be P, the observation equation of the low-orbit satellite/GNSS combined PPP can be expressed as L = AX + e

(1.8)

where is L the OMC vector, A is the design matrix, X is the parameter vector, and e is the measurement noise vector. Assuming that N and W are the normal equation information after the adjustment of the previous epoch, the PPP parameter estimation result of the combination of low-orbit satellite and GNSS can be expressed as

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−1    AT PL + W = N −1 W Xˆ = AT PA + N V = AXˆ − L

V T PV σˆ 0 = n−t

(1.9)

In the formula, N and W is the normal equation after contributing the observation information of this epoch, V is the residual vector of dimension, Xˆ is the parameter vector of dimension, and σˆ 0 is the unit weight STD. 1.4.2 GNSS/LEOConstellation Simulation GNSS includes GPS, GLONASS, Galileo and BDS-3 systems. There are 30 satellites in the BDS-3 full constellation, including 3 geostationary orbit satellites (GEO), 3 inclined geostationary orbit satellites (IGSO) and 24 medium orbit (MEO) satellites [8]. GPS, GLONASS, and Galileo satellites are consistent with the officially announced constellation configuration. The constellation of the LEO satellite is configured as a polar-earth orbit satellite. Two configurations are set up here, namely the Walker (96/8/1) constellation and the Walker (64/8/4) + Walker (60/10/4) composite constellation. 1.4.3 Simulation of Observation Data In order to evaluate the LEO constellation to augument the BD-3 PPP positioning performance, the MGEX station IFNC, which can observe BD-3 satellites in China, is used with a sampling interval of 1s and a sampling duration of 5h. The observation information is as follows: GPS satellites are L1 (1575.42 MHz) and L5 (1176.45 MHz) dual-frequency observation data; the observation frequencies of BDS-3 are B1C (1575.42 MHz) and B2a (1176.45 MHz), LEO uses dual-frequency observation data of B1C and B2a. The observation data simulation fully considers various error sources. First, the observable angular distances of different types of satellites are carefully calculated and distinguished, and the carrier phase and code pseudorange observation noise are optimized. The dry component of the tropospheric delay is calculated by the Saastamoinen model, the wet component is estimated by the actual PPP, and the mapping function is GMF. The receiver clock error and the inter-system error parameter ISB adopts the estimated value of the measured data as the analog value input. Both the satellite clock error and the receiver clock error use MGEX clock error products. Each ambiguity of each satellite consists of a constant integer deviation and a decimal floating-point value. The code pseudorange and carrier phase noise are set to 0.1 m and 5 mm, respectively. In addition, phase entanglement, relativistic effects and solid tide corrections are accurately calculated by known models. 1.4.4 Simulation Analysis In order to analyze the LEO-enhanced GNSS positioning effect in the “urban canyon” environment, the PPP performance of GPS/GLONASS/Galileo/BD-3/LEO (GRECL)

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under signal occlusion was simulated and analyzed. In terms of signal occlusion simulation, considering the urban high-rise environment, the signal may be intermittent when the carrier is in motion. Therefore, cut-off height angles of 10, 20, 30, and 40° are set. The process of re-convergence of the precision point positioning service after signal interruption was considered in the simulation process. The occlusion is 1 min each time, with an interval of 15 min. The combined positioning result of 96 LEO low-orbit satellite and GREC system is shown in Fig. 7. When the RMS of the three-dimensional PPP result is better than 0.1 m, the positioning result is considered convergent.

Fig. 7. Different GPS/BDS/LEO positioning results with cut-off angles of 10 to 40°

(1) The convergence time of single GPS (G), GPS/BDS (GC) combination, GPS/LEO (GL) combination, GPS/BDS/LEO (GCL) combination system is 20.6, 16.2, 4.2, and 4.0 min, respectively. An observation station JFNG (Jiufen, Shanxi, China) in a mid-latitude area can observe an average of 3–4 LEO satellites, which can shorten the convergence time to less than 5 min, which is 75.3% shorter than the GC convergence time. (2) The positioning accuracy of single GPS is basically 5–10 cm within the first 1 h, which is significantly lower than the GC, GL and GCL solutions. When the height cut-off angle is 10, 20, and 30°, the results of each type of solution are basically not affected. Especially for the GL solution, about 11 satellites can be observed without lowering the altitude angle. When the cut-off angle reaches 30°, although the number of satellites observed is the same as GPS (only 5), due to the adopted sequence inertia adjustment, the accuracy is Can still maintain the previous level. When the cut-off angle is 40°, the number of GPS and GL observable satellites drops to 3, and PPP can no longer be achieved. The GC and GCL results are basically not affected, mainly because the number of observable satellites can still be maintained at about 10.

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Figure 8 shows the positioning results of Walker (64/8/4) + Walker (60/10/4) loworbit satellites and GREC at different observation elevation angles. The positioning convergence time of GREC is about 9 min. Due to the increase in the number of LEO satellites, the positioning time of GRECL is shortened to 1–2 min.

Fig. 8. Different GPS/BDS/LEO positioning results with cut-off angles of 10 to 40°

1.5 Conclusion Compared with medium and high orbit satellites, due to the constraint of the orbit height of low orbit satellites, a larger number of satellites are needed to achieve global coverage. This paper proposes a LEO constellation design method based on dual-objective optimization which uses coverage performance and the number of satellites as optimization goals to achieve global coverage performance with fewer satellites. Based on the design of the constellation scheme and measured data, the PPP performance based on the LEO constellation under different boundary conditions is analyzed through simulation, including the PPP performance under different constellation configurations, multisystem combinations, and typical use scenarios is given. Single GPS (G), GPS/BDS (GC) combination, the convergence time is 20.6, 16.2 min, respectively, GREC positioning convergence time is about 9 min. With LEO participates in positioning, the convergence time is greatly shortened. 96 LEO satellites can shorten the convergence time to less than 5 min, which is 75.3% shorter than the GC convergence time. When the number of satellites increases to about 120, the GRECL positioning time is shortened to 1 min. At the same time, for high observing cut-off angles, multiple systems will help improve the continuity and availability of positioning services. The method proposed in this paper can be widely used in the design of LEO satellite navigation enhancement system, and the research results provide reference and support for the corresponding system demonstration and analysis.

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References 1. Li, X., Li, X., Liu, G., et al.: Triple-frequency PPP ambiguity resolution with multi-constellation GNSS: BDS and Galileo. J. Geod. 93, 1105–1122 (2019).https://doi.org/10.1007/s00190-01901229-x 2. Lawrence, D., Cobb, S., Gutt, G.: Navigation from LEO: Current capability and future promise, GPS world [OL]. http://gpsworld.com/ navigation-from-leo-current-capability-andfuture-promise/,2019 3. Fischer, J.: STL - Satellite Time and Location [OL]. https://www.orolia.com/sites/default/files/ document-files/STL-MaritimeApplicationsV4.pdf (2017) 4. Reid, T.: Orbital Diversity For Global Navigation Satellite Systems. Stanford University (2017) 5. Montenbruck, O., Gill, E., Kroes, R., et al.: Rapid orbit determination of LEO satellites using IGS clock and ephemeris products. GPS Solution 9, 226–235 (2005) 6. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: nsga-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002) 7. Deb, K., Jain, H.: An evolutionary many-objective optimization algorithm using referencepoint-based nondominated sorting approach, part I. IEEE Trans. Evol. Comput. 18(4), 577–601 (2014) 8. China Satellite Navigation Office, Development of the BeiDou Navigation Satellite System(Version 4.0) [OL] (2019). http://www.beidou.gov.cn/xt /gfxz/ 201912/P020191227430565455478.pdf

Research on Civil GNSS Signal Authentication Service Design Xiaomin Jia(B) , Ranran Su, Wentao Liang, Fei Shen, Chong Zheng, Zheng Wang, Xuan Wang, and Linfeng Xu Beijing Satellite Navigation Center, Beijng, China

Abstract. GNSS authentication enhances the signal with signatures to help users to validate that the received signal is from a reliable source. Over the past years GPS and Galileo has been advancing system level implementation and test towards an operational GNSS authentication enhancement, so as to tackle the rise of spoofing risks that poses increasingly severe threats to civilian user community. Started with a briefing on GNSS authentication technology categories and the authentication services adopted by GPS and Galileo, main design requirements and a performance metric framework of GNSS authentication are presented for practical market application. The paper then puts forward one solution for BDS civil signal authentication based on BDS characteristics, which introduces the TESLA protocol originally used for navigation message authentication (NMA) into the field of spread code authentication (SCA) to reduce communication overhead and allows for fast and independent authentication. The preliminary design and performance analysis of the mechanism on BDS new-generation signals is presented. Keyword: GNSS authentication · Spoofing · Authentication performance metrics · BDS · Navigation message authentication (NMA) · Spread code authentication (SCA)

1 Introduction In a GNSS simulator exhibition at the ION GNSS+ 2017 conference held in US, the location and time of cell phones of many attendees were spoofed to somewhere in Europe in Jan. 2014, due to improper termination of the output port [1]. The incident highlights the pressing problems faced by GNSS. First, With the advancement of simulator and SDR, it is becoming trivially easy to spoof a GNSS Receiver. Second, spoofing causes increasingly severe damage due to the rapid popularization of smart devices which use GNSS-based PNT services. Moreover, benefit drivers behind spoofing are strengthening. Secure PNT is critical to safety-of-Life applications, critical infrastructure, financial applications, etc. [2]. GNSS authentication for open signal has been proposed and studied in literature [2–9] as a system-level anti-spoofing enhancement, which improves the security of GNSS services by adding extra cryptographic signatures or marks to signals. In recent

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 208–218, 2021. https://doi.org/10.1007/978-981-16-3142-9_19

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years, GPS, Galileo, and ICAO have accelerated development and test of civil GNSS authentication to provide secure civil PNT services. This paper presents an analysis and characterization of design considerations and performance metrics of GNSS authentication. The paper then proposes a BDS civil GNSS authentication scheme based on BDS signal features, and details the design concepts, authentication protocol and message structure, then gives a preliminary performance analysis.

2 Technical and Service Perspective GNSS authentication mainly applies at data and spreading code level, and can be distinguished into three categories, Navigation Message Authentication (NMA), Spreading Code Authentication (SCA) and the combination of SCA and NMA [2]. GNSS authentication [2, 8] is introduced to achieve signal origin authentication, signal integrity authentication, as well as a certain level of resistance to replay attacks. Replay attacks lead to errors of measurements and thus wrong PNT resolution. GNSS authentication can increase the unpredictability of signal [8, 9], thus preventing some types of replay attacks. NMA facilitates authentication of both the origin and integrity of data by adding signatures or MACs to the navigation data [2]. It can achieve a certain level of symbol unpredictability [3, 10, 11], but is still vulnerable to some replay attacks [9]. SCA replaces part of spreading code stream with cryptographically generated chips (hereafter “auth chips”) for origin authentication. It better tackles replay attacks [3], because spreading code operates at a higher chip rate and is hidden under thermal noise. It is difficult to estimate the auth chips and replay. SCA also provides more fine-grained signal unpredictability. GPS plans to carry out SIS test of L1C authentication mechanism Chimera in NTS-3 program [12, 13]. L1C Chimera uses a combination of NMA and SCA. L1CD introduces digital signatures to the data, and L1CP inserts auth chips into the spreading code. Chimera has two variations, “slow channel” and “fast channel”. In “slow channel”, keys used to generate auth chips are derived from L1CD digital signatures, with an authentication period of 3 min. While in “fast channel”, keys are generated by a dedicated key infrastructure and delivered to users through an external channel [5, 13], with an authentication period of 3 or 6 s. Galileo provides OSNMA and CAS for Open Service and Commercial Service, respectively. OSNMA is expected to be operational in 2021 [14]. CAS is expected to provide initial service in 2021–2022 [15]. OSNMA applies NMA to E1B message, and use an authentication protocol based on Timed Efficient Stream Loss-tolerant Authentication (TESLA) protocol, adapted to Galileo [4]. About 40 bits per odd page are used to broadcast OSNMA message, with an effective data rate of 20 bps. CAS is based on Spreading code Encryption (SCE) [15], using a mechanism similar to SAS [9], which encrypts the pilot signal E6C and broadcasts the E6C spreading code verification sequence in a dedicated field of E6B data.

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3 Design Considerations Main design considerations for civil GNSS authentication include [2, 5, 6, 8, 15]: 1. Openness. Cryptography used should maintain the openness of the PNT service, as well as a public key distribution. Users need not to store private keys. 2. Backward compatibility. Users uninterested should not be affected. 3. Navigation performance. Authentication used should have no or minimum impact on the performance of navigation services in any environment. 4. Adaption to navigation signals. GNSS SIS is high-noise, low-bandwidth, one-way channel with high data error rate (BER) [2]. Feasible authentication calls for low communication overhead and adaption to those channel conditions. 5. Security. Cryptography used should be sufficient to prevent prediction or forging of messages or signals, providing information or signal unpredictability to deal with replay attacks, ensuring security for one to several decades. 6. Scalability. The authentication mechanism should support multiple configurations, with scalability to system upgrades and increasing security threats. 7. Receiver overhead. Allow receivers to quickly complete authentication and issue alarms, with low storage and computation overhead and minimized security requirements, avoiding storage of private keys. 8. Independence. Authentication should be able to work independently based on space signals, supporting standalone or low-end users. 9. System implementation. Careful balancing of the constraints and capability of SIS, satellite and ground facilities is needed to make changes to data or code.

4 Performance Metrics Framework A GNSS authentication service should provide users with secure PNT while maintaining navigation performance. Therefore, performance metrics need to measures both the navigation performance and security of real-time authentication. Table 1 shows the performance metric framework and their impacting factors [5, 6, 8]. Figure 1 depicts the relationship between performance metrics. This section expands the analysis of NMA metrics on the basis of literature [8], adding SCA-related performance metrics and analysis. 4.1 Navigation Performance Metrics The main navigation performance metrics examined are Accuracy, Availability and Time to First Authenticated Fix (TTFAF) when authentication is used by users [6]. SCA causes a certain level of spreading code correlation power loss to the users and the degree of loss can be examined with the Correlation Loss metric [5].

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Table 1. Performance metrics and authentication schemes Type

Metric

NMA

SCA

Navigation Performance metrics

AccuracyAuth

UERE Auth : Authenticated navigation data less than total navigation data or an older version of navigation data is used for authentication DOP Auth : User has more troubles receiving authentication data than standard data, satellites authenticated in view less than satellites in view

UERE Auth : SCA brings correlation loss, impacting measurements under high-noise environments DOP Auth : Correlation loss impacts signal reception under certain environments or satellites authenticated in view less than satellites in view

AvailabilityAuth

User has more troubles receiving authentication data than standard data, satellites authenticated in view less than satellites in view

Correlation loss impacts signal reception under certain environments or satellites authenticated in view less than satellites in view

TTFAF

Time to receive authenticated data longer than that of standard data

Time to receive all auth chips for one authentication

Lcorr

–

DF

AER

Number of bits of Number of chips and data authenticated data and bits generated or used in authentication data, system authentication calculation BER

TBA

Depends on authentication mechanism, impacted by data rate and message structure

DF

–

NNA

= Number of bits of – authenticated and authentication data, impacted by authentication mechanisms, should be configurable

Authentication metrics

Critical design parameters

Depends on authentication mechanism, should be configurable

(continued)

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Type

Metric

NMA

SCA

Security metrics

SKS

Determined by authentication mechanism and cryptography used

Determined by authentication mechanism and cryptography used

MPT

Determined by authentication mechanism, impacted by data rate and message structure

Determined by authentication mechanism, impacted by insertion rule

USR DF

– –

Depends on authentication mechanism, should be configurable

Fig. 1. Performance metrics and their relevance

1) AccuracyAuth : the user position accuracy when only the authenticated signals are used. Can be approximated by the following formula. AccuracyAuth [m] = UERE Auth [m] ∗ DOP Auth

(1)

2) AvailabilityAuth : the percentage of time that the user can correctly receive at least 4 authenticated satellite signals in a specific environment. When the number of authenticated satellite signals that a receiver can receive under any conditions or the authenticated part (data or spreading code) of the signal is inconsistent with the standard service, the accuracy or availability of the service will be affected. For NMA, a successful authentication requires the receiver to correctly receive both the authenticated data and the authentication data (after data decoding and error correction). While for SCA, it requires the received authentication spreading code chips errorless or correlation passed (depending on the verification rule), these requirements also affect the accuracy and availability. 2) TTFAF: the time taken by a receiver to complete the first position fix using the authentication signals of at least 4 satellites. System TTFAF can be approximated

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statistically. Whereas user TTFAF depends on which time slot the SIS is at out of the authentication period when the receiver is started and the length of the authentication period. 3) Correlation loss: the correlation power loss caused by insertion of auth chips to the spreading code, and depends on the auth chips insertion rule and proportion (denoted by Duty Factor, DF). Literature [16] gives the formula of the average correlation loss Lcorr when puncture is used for insertion. DF is described below. Lcorr (dB) = 20 ∗ log 10 [1 − DF]

(2)

4.2 Authentication Metrics To examine the impact of authentication solutions on navigation service performance and security, literature [8] proposed two authentication performance metrics, Authentication Error Rate (AER) and Time Between Authentications (TBA). 1. AER: refers to the error probability of the authentication signal under no attack. For NMA, AER [5] mainly depends on the number of bits of data participating in authentication (including the authenticated and authentication data) in a single authentication period and the system BER. Literature [8] gives AER calculation formula for NMA. NNA is the total number of bits participating in authentication. For SCA, AER mainly considers the impact of spreading code verification, and is determined by the chip error rate and the verification rule used. If a chip-by-chip comparison verification is used, AER calculation is similar to NMA. If the correlation adjudication is used for verification, AER will be relatively small. AER = 1 − (1 − BER)NNA

(3)

For a combined use of NMA and SCA, AER calculation requires a more rigorous modelling that takes the relationship between the two-level working flow into account, which is left to later work. 2. TBA: refers to the time interval for a single signal to complete two consecutive authentications. TBA depends on authentication solution. 4.3 Security Metrics Security metrics consider cryptographic security and resistance against replay attacks. Signal unpredictability helps to improve detection of replay attacks. MPT [8], USR [8] and DF can be used to examine signal unpredictability of a solution. 1. Symmetric key strength (SKS): represents the equivalent symmetric key length that the authentication cryptography can provide, expressed in bits [5, 8]. 2. Maximum Predictable Time (MPT): refers to the maximum predictable time that the signal is transmitted.

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3. Unpredictable Symbol Rate (USR): represents the proportion of unpredictable symbols, for NMA solutions. 4. DF: DF is proposed in [5] to measure correlation loss. We propose the use of DF to measure the proportion of unpredictable chips for SCA solutions as well. (MPT, USR) or (MPT, DF) can simultaneously examine the proportion and distribution of unpredictability of a signal for NMA or SCA solutions.

5 Preliminary Design of an Authentication Proposal for BDS This section proposes a preliminary design of an authentication mechanism for BDS civil signal BDSSA (BDS Signal Authentication). Among BDS new generation civil signals [17–23], The B1C, B2a, and B2b-I (MEO/IGSO satellites) signals provide global open service, and the BDSBAS-B1C and BDSBAS-B2a signals provide regional SBAS service, while the PPP-B2b-I and PPP-b2b-Q signals are used for regional PPP service. For open service, B1C is the primary signal, authenticating B1C may serve more users. However, B2a has a higher data rate, allowing for a smaller TBA. Moreover, users who need authentication generally are high-end users, who either already support B2a or are not sensitive to the cost of adding it. We characterize both signals for a thorough analysis and comparison. For SBAS service, ICAO is formulating a data authentication mechanism [24], which BDSBAS-B1C authentication will follow with. For PPP service, this paper characterizes PPP-B2b-I. 5.1 BDSSA Design Features Based on the above analysis, BDSSA mainly adopts the following principles. 1. Bit Commitment. To sustain the openness of civil service to allow for broader usage of authentication and backward compatibility, and to make sure receivers need not to store private keys or implement private algorithms, the cryptography adopted should be public, supporting public key distribution [3–6]. Bit commitment (or delayed key transmitting) algorithms transmit the cipher text first, and then send the key after a certain delay, which guarantees the security of key before the cipher text is received. Security is realized by keeping a certain time interval between cipher text and key transmission to prevent forging of the signal [5, 13]. In this way, bit commitment algorithms achieve publicity and public distribution of keys. GPS Chimera [5] and Galileo OSNMA [4] both leverage bit commitment principle. In addition, the bandwidth requirement of bit commitment algorithms is much less than that of digital signature algorithms, thereby reducing NNA and TBA. OSNMA reduces the communication bandwidth requirements significantly by using and adaption of a bit commitment algorithm TESLA [4].

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2. One-way key chain BDSSA adopts a one-way function to generate the key chain for authentication generation, thus keys distributed can be verified by the one-way function, further reducing the meta-information required for key transmission while improving security. One-way function has the feature that the next variable can be calculated quickly through the current variable, but the computational complexity of inverse calculation of the current variable through the next variable is extremely high [8]. 3. Time liaison The BDS system time is introduced into the BDSSA authentication calculation to further improve cryptography security and prevent pre-computing attacks. 5.2 BDSSA Protocol BDSSA authenticates the spreading code. BDSSA employs the design concept of TESLA protocol [4], which is only used for data authentication, into the spreading code authentication domain, using bit commitment to facilitate security while reducing communication overhead of transmitting keys, especially through SIS. An independent SCA mechanism relying only on BDS SIS is achieved and TBA is reduced as much as possible at the same time. In order to increase successful verification rate under high-noise conditions, BDSSA adopts a one-keychain-for-all-satellite design feature similar to OSNMA [4], in which all satellites use keys from one single key chain. In a given authentication period, different satellites use consecutive keys in the order of PRN numbers. Receivers only need to receive one key broadcast on one satellite to complete verification of the auth chips of all satellites in view. The single key chain significantly reduces the key verification overhead, while reducing AER [4]. For the independent use of the authentication service by standalone receivers, the BDSSA key is broadcast through navigation data. For receivers that support external channels such as 5G, an A-BDSSA variation of BDSSA can be enforced, in which BDSSA key is distributed through a high-speed external channel, significantly reducing TBA and improving the ability to prevent replay attacks. 5.3 BDSSA Message Structure The B1C signal B-CNAV1 subframe 3 allows for definition of new page types, each page containing 234 bits. The B2a and PPP-B2b-I supports definition of new message types, each containing 234 bits and 456 bits, respectively. The BDSSA message type is structured as shown in Fig. 2. Each BDSSA page contains two fields, KROOT and ASK. KROOT is used to broadcast the root key of the key chain and configuration parameters. KROOT data is broadcast in multiple pages. PNUM represents the total number of pages (denoted as packages) used for KROOT data, PIDX represents the package index, and OPType indicates the type of data distributed in the KDATA domain. KDATA domain distributes the root key and its digital signatures,

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or the configuration parameters, etc. Configuration parameters include key length, DF, code insertion rules, etc. ASK is used to broadcast keys, and 1–4 keys can be broadcast according to the configuration of cryptographic parameters. B1C and B2a supports a key length of 98–196 bits, and PPP-B2b-I supports a key length of 98–394 bits.

Fig. 2. BDSSA message structure

5.4 Preliminary Performance Analysis This section gives a preliminary analysis of main performance metrics of BDSSA on B1C, B2a, and PPP-B2b-I. Two key length configurations are used, 98 and 196 bits, respectively. The preliminary results of some metrics are shown in Table 2. Table 2. Preliminary performance analysis Metric SKS = 98

SKS = 196

B1C

B2a

PPP-B2b-I B1C

B2a

PPP-B2b-I

TBA

≥90 s

≥15 s

≥8 s

≥15 s

≥8 s

AER

See analysis

DF

Configurable, depending on the distribution and DF of auth chips

MPT

Configurable, depending on the distribution and DF of auth chips

USR

≤5.2%

≤15.6% ≤11.4%

≥90 s

≤5.2%

≤15.6% ≤11.4%

Constrained by signal message structure, BDSSA message works as independent pages or messages, and cannot be evenly distributed across pages/messages. Therefore, TBA depends on the fastest repetition period of the page/message type. Within one single page/message, reducing key length (SKS) is beneficial to reducing the system and receiver implementation overhead, but does not improve TBA. AER depends on the number of auth chips inserted in a single authentication period and the number of authentication data bits. The number of authentication data bits in one BDSSA authentication period is a constant value (234 or 456). The number of auth chips depends on the DF. A smaller DF Helps to reduce AER. The accurate AER calculation needs careful treatment of both the influence of the message and the spreading code at the same time.

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6 Conclusion It is of great significance for BDS to provide security enhancement for civilian services. This paper carefully analyzes the design considerations of civil GNSS authentication for both NMA and SCA, and a performance metric framework including navigation performance metrics, security metrics and authentication performance metrics is constructed. This paper then presents a preliminary BDSSA authentication mechanism for the new generation BDS civil signals, and a preliminary performance analysis is shown. Analysis shows that through the use of bit commitment, one-way function, and time liaison, BDSSA can significantly reduce communication overhead while enforcing authentication. Independent use of B1C, B2a and PPP-B2b-I can achieve a TBA of 90s\15s\8s, respectively, which is sufficient to provide a certain level of anti-replay capability for critical infrastructure or financial applications. Further research is needed for careful tuning of BDSSA design, system & receiver implementation and verification based on simulation.

References 1. O’Driscoll, C.: What is navigation message authentication? InsideGNSS, Jan/Feb, pp. 26–31 (2018) 2. Wullems, C., Pozzobon, O., Kubik, K.: Signal authentication and integrity schemes for next generation global navigation satellite systems. European Navigation Conference GNSS, Munich, Germany (2005) 3. Scott, L.: Anti-Spoofing & Authenticated Signal Architectures for Civil Navigation Systems. ION GNSS, Portland, OR, pp. 1543–1552 (2003) 4. Fernández-Hernández, I., Rijmen, V., Seco-Granados, G., Simón, J., Rodríguez, I., Calle, J.D.: A navigation message authentication proposal for the galileo open service NAVIGATION. J. Inst. Navigation 63(1), 85–102 (2016) 5. Anderson, J.M., Carroll, K.L., DeVilbiss, N.P., Gillis, J.T., Hinks, J.C., O’Hanlon, B.W., Rushanan, J.J., Scott, L., Yazdi, R.A.: Chips-message robust authentication (Chimera) for GPS civilian signals. In: 30th ION GNSS+, Portland, Oregon, pp. 2388–2416 (2017) 6. Fernandez-Hernandez, I., Rijmen, V., Seco-Granados, G., Simón, J., Rodríguez, I.: Design Drivers, Solutions and Robustness Assessment of Navigation Message Authentication for the Galileo Open Service. ION GNSS+ 2014, Tampa, FL, pp. 2810–2827 (2014) 7. Wang, S., Liu, H., Tang, Z., Ye, B.: Binary phase hopping based spreading code authentication technique. Satellite Navigation 2(1), 1–9 (2021). https://doi.org/10.1186/s43020-02100037-z 8. Fernández-Hernández, I.: GNSS Authentication: Design Parameters and Service Concepts. European Navigation Conference, Rotterdam, Netherlands (2014) 9. Pozzobon, O.: Keeping the spoofs out – Signal Authentication Services for future GNSS. InsideGNSS May/June(2011), 48–55 (2011) 10. Cancela, S., Navarro, J., Calle, D., Reithmaier, T., Dalla Chiara, A., Da Broi, G., FernándezHernández, I., Seco-Granados, G., Simón, J.: Field testing of GNSS user protection techniques. In: 32nd ION GNSS+ 2019, Miami, Florida, pp. 1824–1840 (2019) 11. O’Driscoll, C., Fernández-Hernández, I.: Mapping bit to symbol unpredictability in convolutionally encoded messages with checksums, with application to galileo OSNMA. In: 33rd ION GNSS+:3738–3750 (2020)

218

X. Jia et al.

12. Way, Way Out in Front- Navigation Technology Satellite-3: The Vanguard for SpaceBased PNT. https://insidegnss.com/way-way-out-in-front-navigation-technology-satellite-3the-vanguard-for-space-based-pnt/. 28 June 2020 13. Cameron, A.: AFRL tests Chimera to battle spoofers and hackers. https://www.gpsworld. com/afrl-tests-chimera-to-battle-spoofers-and-hackers/. 24 July 2019 14. Galileo Open Service Navigation Message Authentication Is Available for Testing. https:// insidegnss.com/galileo-open-service-navigation-message-authentication-is-available-for-tes ting/. 1 Dec 2020 15. Fernandez-Hernandez, I., Vecchione, G., Díaz-Pulido, F.: Galileo authentication: a programme and policy perspective. In: 69th International Astronautical Congress, Bremen, Germany:IAC-18.B2.4.1 (2018) 16. Scott, L.: Proving Location Using GPS Location Signatures: Why it is Needed and A Way to Do It. (ION GNSS+ 2013), Nashville, TN (2013) 17. BeiDou Navigation Satellite System Signal In Space Interface Control Document Open Service Signal B1C (1.0). http://www.beidou.gov.cn/xt/gfxz/201712/P02017122674134201 3031.pdf. 22 December 2020 18. BeiDou Navigation Satellite System Signal In Space Interface Control Document Open Service Signal B2a (1.0). http://www.beidou.gov.cn/xt/gfxz/201712/P02017122674235736 4174.pdf. 22 December 2020 19. BeiDou Navigation Satellite System Signal In Space Interface Control Document Open Service Signal B2b(1.0) .http://www.beidou.gov.cn/xt/gfxz/202008/P02020080336205911 6442.pdf. 22 December 2020 20. BeiDou Navigation Satellite System Signal In Space Interface Control Document Precise Point Positioning Service Signal PPP-B2b(1.0). http://www.beidou.gov.cn/xt/gfxz/202008/ P020200803362062482940.pdf. 22 Dec 2020 21. BDSBAS-B1C. BeiDou Navigation Satellite System Signal In Space Interface Control Document Satellite Based Augmentation System Service Signal BDSBAS-B1C (1.0). http://www. beidou.gov.cn/xt/gfxz/202008/P020200803362065480963.pdf. 22 December 2020 22. Du, Y., Wang, J., Rizos, C., El-Mowafy, A.: Vulnerabilities and integrity of precise point positioning for intelligent transport systems: overview and analysis. Satellite Navigation 2(1), 1–22 (2021). https://doi.org/10.1186/s43020-020-00034-8 23. Lu, J., Guo, X., Su, C.: Global capabilities of BeiDou Navigation Satellite System. Satellite Navigation 1(1), 1–5 (2020). https://doi.org/10.1186/s43020-020-00025-9 24. Neish, A., Walter, T.: Securing GNSS – A Trip Down Cryptography Lane (2020). https://ins idegnss.com/securing-gnss-a-trip-down-cryptography-lane/. 20 May 2020

Key Technical Characteristics and Performance of BeiDou Navigation Augmentation System Based on LEO Constellation Xing Li1(B) , Lang Bian2 , Xia Guo1 , and Yansong Meng2 1 Beijing Institute of Tracking and Telecommunication Technology, Beijing 100094, China 2 Academy of Space Information Systems, Xi’an 710100, China

Abstract. This paper studied a BeiDou navigation augmentation system architecture based on the LEO constellation and analyzed the key factors that affected the performance of the system. The paper also carried out four aspects of the system design and the performance quantification analysis, such as establishing and maintaining Spatio-temporal reference, constellation design, signal design, and user positioning calculation. The paper’s research results can also be used to reference the design and construction of the new generation of the PNT system. Keywords: BeiDou Navigation System (BDS) · Positioning, Navigation, and Timing (PNT) Architecture · Low Earth Orbit (LEO) Constellation · Navigation Augmentation

1 Introduction The BDS-3 system was completed constructed and put into service on July 31, 2020. The space segment of the system consists of 30 satellites (24 MEO, 3 GEO and 3 IGSO). The global positioning accuracy less than 10 m, the velocity measurement accuracy less than 0.2 m per second, the timing accuracy is better than 20 ns, the service availability is better than 99%, and the performance in the Asia-Pacific region is much better [1]. However, the navigation system that only relies on the MEO/GEO/IGSO satellites has been faced with significant bottlenecks in improving accuracy, security and coverage. Therefore, it is necessary to look for some new technical approaches. Since 2008, the concept of comprehensive PNT system [2, 3] has become a new research hot spot, which refers to the systematic development of the corresponding augmentation, supplement and backup mean based on the idea of the system and the method of SoS (System of System), with the MEO/GEO/IGSO satellite constellation as the core, to realize complementary advantages. According to the latest PNT architecture, there are some limitations to the current augmentation methods. For example, the Ground Augmentation System (GAS) has limited coverage and is difficult to be constructed and maintained in remote areas and offshore. The landing level of the space-based augmented signal based on medium and high-orbit satellites is similar to that of current satellite navigation signals. The © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 219–230, 2021. https://doi.org/10.1007/978-981-16-3142-9_20

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continuous improvement of signal power is limited by satellite energy consumption and weight resources constraints. The LEO satellites, with the characteristics of higher landing level, information rate and ground speed (GS), are more than 20 times lower from the ground than MEO/GEO/IGSO satellites. Therefore, LEO satellites are very suitable to complement with the MEO/GEO/IGSO satellites, and have been paid much more attention [4]. Based on summarizing the System architecture of the BS Joint LEO Constellation, and aiming further to improve the high accuracy and fast convergence service capability, this paper will study the key technical systems and solutions of the LEO augmentation system, and give the results of performance analysis and evaluation, to provide a reference for the development of the next generation of BDS.

2 System Architecture The BeiDou Satellite Navigation Augmentation System based on the LEO constellation establishes Spatio-temporal reference of the BDS and augments and its performance by constructing reasonable LEO constellation and broadcasting augmented navigation signals and message information. The system architecture is shown in Fig. 1. 2.1 Space Segment The space segment consists of the LEO constellation and the BDS constellation, which relies on the completed global BDS-3 System. The LEO constellation can depend on several domestic, commercial constellations, some of which can be equipped with navigation augmentation functions and load some high-accuracy GNSS receivers to get BDS downstream navigation signals. Meanwhile, they can also generate the Spatio-temporal reference handed to the GNSS system, determine the orbit of LEO satellites, and calculate the time synchronization data under the ground system’s corresponding supports, as well as generate and broadcast the augmented navigation information, to realize the BDS navigation augmentation service. 2.2 Ground Segment The ground segment consists of the BDS ground segment and the LEO ground segment. The former is based on the existing the BDS ground monitoring station, the measurement and control station, as well as the operation and control station, which can continuously monitor BeiDou navigation signals and provide real-time observation data. The latter consists of the LEO constellation master control centre, the uplink station, as well as the measuarement and control station. As an operational control centre of the whole system, the LEO constellation management centre can collect all the raw observations of the LEO navigation signals and BDS navigation signals to carry out system time synchronization processing and satellite clock bias prediction, satellite orbit processing, and broadcast ephemeris forecasting. Meanwhile, the centre is also responsible for task planning and scheduling, operation management and control of the whole system. The monitoring station is equipped with a monitoring receiver for LEO augmentation service

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to continuously monitor the augmented signals of LEO navigation and provide real-time observation data. According to the plan, the uplink station receives the command from the centre and uploads various parameters to the visible LEO satellite. Measurement and control station is used for telemetry and remote control mission management of LEO constellation. 2.3 User Segment The user segment is mainly configured with various user terminals, which can obtain the position and time service information by calculating and processing the signals received by the BeiDou and LEO satellites.

Fig. 1. The architecture of the BeiDou navigation augmentation system based on the LEO constellation

3 Key Technical System and Performance Analysis To realize the navigation augmentation with LEO constellations, the critical technical problems restricting its service performance, are necessary to be solved through the practical technical system design, to obtain user satisfaction. The key elements involve many aspects, and the first is to solve the establishment and maintenance of the Spatiotemporal reference of the LEO satellite, which is the fundamental basis of realizing the service capability of the LEO satellite. The second is to construct a reasonable constellation architecture to easily obtain excellent coverage ability and achieve high accuracy geometric characteristics. The third is to design easy-to-use LEO satellite navigation signals provides users with the physical links of accurate ranging and data transmission. The fourth is to create a simple and efficient positioning solution algorithm, which is convenient for the user to obtain the required accurate and reliable position and time information through the comprehensive processing of observation data.

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3.1 Construction and Maintenance of LEO Spatio-Temporal Reference The constraints of satellites themselves limit the construction and maintenance of LEO Spatio-temporal reference, so we cannot copy the scheme of MEO/GEO/IGSO satellites. In terms of the temporal reference, due to the limitation of the weight, volume, energy consumption, cost and other factors, it is challenging to configure high-performance atomic clocks to maintain the time system of LEO satellites. In terms of spatio reference, the multi-orbit perturbation force received by LEO satellites are higher than that received by MEO/GEO/IGSO satellites, so it is necessary to use a better way and more precise model parameters to determine the high-accuracy orbit. To solve the above problems, the paper uses the BeiDou satellite system as the Spatio-temporal reference of the LEO satellite. The high-precision space-borne BeiDou receiver can be mounted on the LEO satellite to receive data, to construct the Spatio-temporal reference of the LEO satellite matching the BeiDou Navigation Satellite System. The constraints of satellites themselves limit the construction and maintenance of LEO Spatio-temporal reference, so we cannot copy the scheme of MEO/GEO/IGSO satellites. In terms of the temporal reference, due to the limitation of the weight, volume, energy consumption, cost and other factors, it is challenging to configure highperformance atomic clocks to maintain the time system of LEO satellites. In terms of spatio reference, the multi-orbit perturbation force received by LEO satellites is higher than that received by MEO/GEO/IGSO satellites, so it is necessary to use a better way more precise model parameters to determine the high-accuracy orbit. The paper uses the BeiDou satellite system as the LEO satellite’s Spatio-temporal reference to solve the above problems. The high-precision space-borne BeiDou receiver can be mounted on the LEO satellite to receive data, to construct the Spatio-temporal reference of the LEO satellite matching the BeiDou Navigation Satellite System. 3.1.1 Orbit Determination and Forecast by Autonomous Calculation on the Single LEO Satellite It is tough to determine and forecast the precise orbit of LEO satellites, because the atmospheric resistance, the Earth non-spherical gravity and the general relativity effect of LEO satellites are stronger than those of MEO and IGSO satellites. Therefore, the perturbed motion of LEO satellites is more complex, and its parameter requirements of the orbit determination model are higher as well. Usually, there are two kinds of methodologies to determine the orbit of LEO satellites. The first type of the approaches is on the bias of the ground processing. We can uniformly observe MEO/GEO/IGSO satellites based on the ground segment, and make precise orbit determination and prediction of LEO satellites by GNSS measurement data transmitted from LEO satellites. This method requires multiple transmissions of data between the satellite and the ground. However, when the constellation scale is larger, the control is more complicated, and the requirement for link stability is higher. The second type of approaches is based on autonomous satellite processing. The MEO/GEO/IGSO satellites are observed directly from the LEO satellites to receive GNSS precise orbit and clock error. Then the orbit is determined and forecast by way of autonomous calculation on the satellite. This method relatively increases the requirements of the on-board processing capacity of the satellite,

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but it is less dependent on the ground segment and more robust overall. Considering the constraints of space-borne hardware resources and processing capacity, we can use simplified dynamics to process the data from the space-borne receiver and carry out real-time computation on the satellite. The in-orbit observation data of the first test satellite of Hongyan are used to simulate in-orbit processing and verification on the ground, and the inner coincidence is compared shown in Fig. 2. It is shown that the along, corss and radial RMS values of the precision orbit determination are 1.7 cm, 1.1 cm and 2.2 cm, respectively, and the orbital URE is 2.3 cm, which met the requirements of precision orbit determination.

Fig. 2. The precision orbit determination results of the first test satellite of Hongyan

3.1.2 Establishing the High-Precision Temporal Reference Based on the SpaceBorne Crystal Oscillator Time and frequency is the core of the satellite navigation system. To maintain high accuracy and high stability of the time and frequency on the satellite, the space-borne atomic clocks such as hydrogen clock, rubidium clock and cesium clock are widely used on MEO/GEO/IGSO satellites of BDS, GPS and other satellite systems. Meanwhile, considering the requirements of life and reliability, 3 to 4 clocks are generally configured. Besides, the higher requirements of the weight, power consumption, cost of the satellite are put forward. Compared to MEO/GEO/IGSO satellites, the LEO satellite has far less carrying capacity but far more quantity. If the LEO satellite also adopts the configuration scheme of space-borne atomic clocks, the cost will be unacceptable. Therefore, the available alternative scheme must be adopted. The options include CSAC (Chip Scale Atomic Clock), small rubidium clock, and high-stability crystal oscillators. Their primary performance is shown in the following table. The low stability performance of the CSAC cannot meet the requirement of millimetre carrier phase measurement. The volume, weight, and power consumption of the small rubidium clock are several times higher than those of other schemes, which indicates that the satellite platform requires more resources and the short-stability performance is difficult to meet the requirements. Although the high stability crystal oscillator can achieve excellent short-term stability index, its disadvantage is that maintaining stability in the long term is weak.

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Therefore, the method of handing high-stability crystal oscillators by GNSS signals can achieve better short-stability and long-stability indexes, which can effectively reproduce the performance of space-borne atomic clock on MEO/GEO/IGSO satellites on LEO satellites at low cost, and meet the requirements of LEO satellites for time-frequency signal generation and maintenance. Table 1. Alternative Scheme for Space-borne Clocks No.

Indicators

CSAC (MEMS)

CSAC (traditional)

Small rubidium clock

High-stability Crystal Oscillators

1

Output frequency

10 MHz

10 MHz

10 MHz

10 MHz

1s

≤1 × 10–10

≤8 × 10–11

≤3 × 10–12

≤3 × 10–13

10s

≤3 × 10–11

≤3 × 10–11

≤1 × 10–12

≤5 × 10–13

100s

≤1 × 10–11

≤8 × 10–12

≤2 × 10–13

≤2 × 10–12

1000s

≤5 × 10–12

≤4 × 10–12

≤1 × 10–13

≤3 × 10–12

10000s

≤3 × 10–12

≤4 × 10–12

≤1 × 10–13

≤1 × 10–11

2

Stability

3

Drifting Rate Per Day

≤5 × 10–12

≤2 × 10–11

≤1 × 10–12

≤1 × 10–10

4

Power Consumption

≤220 mW

≤2W

≤30 W

≤5 W

5

Weight

≤60 g

≤250 g

≤1800 g

≤650 g

Volume

≤ 21 cm3

≤160 cm3

≤ 2100 cm3

≤320 cm3

6

3.2 LEO Satellite Navigation Augmentation Constellation LEO satellite constellation is a crucial element to improve navigation performance. Its goal is to obtain excellent coverage performance and observation geometry and consider the many indicators such as system cost, fault tolerance, and stability. In essence, it is a multi-objective and multi-constraint optimization problem, which means to find the constellation configuration parameters satisfying the target performance under various constraints. As for the parameters design of LEO constellations, one type is the orbit with a small and medium inclination of 40–60°. Such orbital satellites have better performance in multi-repetition coverage of densely populated areas in middle and low latitudes, so they are suitable for the core constellation of navigation augmentation. The other type is the near-polar orbit with an inclination near to 90°, which is mainly used in the LEO

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communication system to meet the requirements of the single coverage required by communication and is suitable for the mixed and supplement constellation of navigation augmentation to improve the coverage performance in high latitudes. The other is the near-polar orbit with an inclination of more than 80°, and satellites in this kind of orbit are often used in LEO communication systems. It is mainly used to meet single coverage requirements for communication and is suitable for improving the coverage performance in high latitudes as a complement constellation for navigation augmentation. The above two types of orbital features and coverage effects are different so that their function is also different. Therefore, the combination of the above two options is a more balanced solution for navigation augmentation. Based on this consideration, to facilitate the analysis and calculation in the following paper and without generality loss, the orbital altitude is set as 1000 km. The available constellation configuration scheme is shown in the table below. Based on this consideration, to facilitate the analysis and calculation in the following paper with the generality, the orbital altitude is set as 1000 km. The available constellation configuration scheme is shown in Table 2. Table 2. Main parameters of LEO constellation No.

Constellation

Orbital altitude

Orbital inclination

Quantity of the satellites

Orbital configuration

1

Core (L150)

1000 km

30°

30

Walker 30/3/1

1000 km

55°

90

Walker 90/9/1

1000 km

86°

30

3 orbital planes; 10 evenly distributed satellites per orbital plane

2

Communication + Navigation (L72)

1000 km

88°

72

6 orbital planes; 12 evenly distributed satellites per orbital plane

3

Communication + Navigation (L144)

1000 km

88°

144

12 orbital planes; 12 evenly distributed satellites per orbital plane

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3.3 Augmented Navigation Signal System The navigation signals of major navigation satellite systems in the world are the same as those of BeiDou Navigation Satellite System, whose frequencies are all selected in the L-band (as shown in Fig. 16). The adoption of some similar frequency domain parameters,such as frequency point, modulation mode, and the bandwidth, on the one hand, can solve the problem of the lack of frequency resources, on the other hand, it can reduce the burden of providing reference frequency for different centre frequency in the receiver, simplify the design and manufacture of receiver for the multi-system satellite navigation system, and reduce the power consumption, cost and weight. In the aspect of signal interoperation, the same or similar carrier frequency has a significant impact on the development cost and technical complexity of navigation receiver. The selection of other characteristics of navigation signals, such as modulation mode, signal structure, spread spectrum code, only needs to adjust the receiver baseband processing software, which has a relatively small impact. Based on the above considerations, the L frequency band is selected as the working frequency band of LEO navigation augmented signal. The signal adopts the modulation mode similar to BeiDou, and the same family of spread spectrum code parameters. Simultaneously, considering the general needs of dual-frequency applications, dual-frequency signals are used to augment navigation on LEO satellites.

Fig. 3. Signal spectrum diagram of Four GNSS

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3.4 The Precise Positioning Method Based on the Mixed Constellation Augmentation 3.4.1 Analysis of LEO Satellites Acceleration Precise Positioning Convergence The fast motion of LEO satellites can effectively improve the geometric characteristics of the positioning equation of GNSS medium and high-orbit satellites. Assuming that the user’s clock is completely synchronized with the system and all kinds of errors are corrected, as well as, and the ambiguity of the initial carrier phase observation value has been accurately determined using the pseudo-distance reference, the position of the receiver can be determined with only three satellites. The simplified positioning equation is as follows: ⎡ ∂f ∂f ∂f ⎤⎡ ⎤ ⎤ ⎡ X L1 ∂X ∂Y ∂Z ⎢ ∂f 1 ∂f1 ∂f1 ⎥⎣ (1) ⎣ ∂X2 ∂Y2 ∂Z2 ⎦ Y ⎦=⎣ L2 ⎦ ∂f ∂f ∂f L3 Z ∂X3 ∂Y3 ∂Z3

In the above equation, each row of the coefficient matrix represents the unit vector of the satellite direction of the receiver, the unknown variable is the change of the position of the receiver, and the right side of the equation is the change of the observed value on the unit vector of the satellite of the receiver. The above equation is expressed in matrix form as follows: Gx = b

(2)

According to matrix theory, the condition number of matrix of an invertible square matrix G can be defined as cond (G) = ||G||||G−1 ||, where • represents the matrix norm. When the solutions x, δx of the equation satisfy Gx = b, G(x + δx) = b + δb, the following equation is available: δx δb δb 1 ≤ ≤ cond (G) x b cond (G) b

(3)

Fig. 4. Illustrating the effect of the addition of LEO satellites on the solution based on the twodimensional diagram

 When the relative error δb b of b is fixed, the smaller the condition number cond (G), the larger the lower boundary and the smaller the upper boundary of the

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relative error of the solution. It shows that the smaller the condition number is, the more controllable the error of the solution is, the higher the accuracy of the solution is, and the faster the convergence speed is. As shown in the figure above, in the simplified two-dimensional space, the rapidly changing geometric characteristics of LEO satellites can effectively reduce the conditions number, improve the accuracy of the solution, and significantly improve the convergence rate. 3.4.2 Precision Positioning Simulation Analysis on MEO/GEO/IGSO Constellations Based on BDS-3, the mixed constellation scenarios are respectively constructed, as shown in Fig. 5, BDS + 150LEO, BDS + 150LEO + 72LEO and BDS + 150LEO + 72LEO + 144LEO. Moreover, the observation data of different latitude stations are simulated, and the precision positioning simulation based on hybrid constellation augmentation is verified.

Fig. 5. Schematic diagram of the mixed constellation architecture

Select three stations at high, middle and low latitudes respectively, select Beidou B1C and B2A dual frequency signals, set the convergence threshold as 0.1M, cut-off altitude angle as 15° and count the convergence time under the above three scenarios. It can be seen that when the elevation mask is 15°, the addition of LEO constellation will significantly improve the convergence speed regardless of the latitude of the station distribution. Moreover, for the same station, the convergence is faster when more LEO satellites are introduced. As shown in Fig. 6, for the three stations at low latitude, middle latitude and high latitude, the convergence time can be shortened from 17 min 30 s, 19 min 35 s and 24 min 55 s to 0 min 40 s, 34 s and 45 s with only BDS, respectively, and the degree of shortening is 96.19%, 97.16% and 96.99%, respectively. As shown in Fig. 6, when 150 LEO satellites are added, compared with the situation when only BeiDou satellites are included, for the three stations at low, medium and high latitudes, the convergence time is shortened from 17 min 30 s, 19 min 35 s, 24 min 55 s to 0 min 40 s, 34 s and 45 s respectively, and the degree of shortening is 96.19%, 97.16% and 96.99%, respectively. With the addition of the mixed constellation, the convergence rate is higher and higher, and the convergence time is reduced to 25s, 22s and 21s respectively when 150 + 72 + 144 LEO satellites are added.

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Fig. 6. Comparison of convergence time at high, medium and low-latitude stations Table 3. Convergence time at high, medium, low latitude stations (elevation mask = 15°) LEO High-latitude station Medium-latitude stations Low-latitude stations constellation Convergence Degree Convergence Degree Convergence Degree time of time of time of reduction reduction reduction 0

24 55”

0%

19 35”

0%

17 30”

0%

L150

00 45”

96.99%

00 34’

97.10%

00 40”

96.19%

L150 + L72

00 34”

24.44%

00 28’

17.65%

00 33’

17.50%

L150 + L72 00 21” + L144

38.24%

00 22”

21.43%

00 25”

24.24%

4 Conclusion According to the establishment and maintenance of Spatio-temporal reference, constellation design, signal design and user positioning calculation, the paper carries out the system design and quantitative analysis of precision positioning performance based on the hybrid constellation. The simulation results show that the convergence time can be shortened by more than 96% by adding LEO augmentation core constellation (L150) to the BeiDou system. On this basis, the convergence time can be further shortened by 17% and 21% by adding LEO augmentation mixed constellations (L72 and L144). The research results of the paper can provide a reference for the design and construction of a new generation of PNT system.

References 1. BeiDou Satellite Navigation System Open Service Performance Standards (2.0), China Satellite Navigation Office, December 2018 2. Yang, Y.: Concepts of comprehensive PNT and related key technologies . Acta Geodaetica et Cartographica Sinica 45(5), 505–510 (2016) 3. U.S. Department of Defence, Department of Transportation, National Positioning, Navigation, and Timing Architecture Implementation Plan, April 2010 4. Cohen, C.E., Rabinowitz, M., Parkinson, B.W.: The application of leos to cycle anbiguity resolution on navstar transmissions for kinematic carrier-phase positioning. Institute of Navigation, ION97, 1(1), September 1997

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5. Rabinowitz, M., et al.: A system using leo telecommunication satellites for rapid acquisition of integer cycle ambiguities. IEEE PLANS 98, April 1998 6. Parkinson, B.W., Rabinowitz, M., Gromov, K., Cohen, C.E.: Architectures for joint gps/leo satellite carrier phase receivers designed for rapid robust resolution of carrier cycle ambiguities on mobile platforms. In: Proceedings of the Institute of Navigation ION GPS-2000, September 2000 7. Rabinowitz, M.: PhD Thesis: Precision Navigation Using Low Earth Orbit Telecommunication Satellites. PhD thesis, Department of Electrical Engineering, Stanford University (2000) 8. Li, X., et al.: Improved PPP ambiguity resolution with the assistance of multiple LEO constellations and signals. 2, 11(2), 408–424 (2019) 9. Reid, T.G., Neish, A.M., Walter, T.F., Enge, P.K.: Leveraging commercial broadband LEO constellations for navigation. In: Proceedings of the ION GNSS+ 2016, Portland, OR, USA, 12–16 September 2016, pp. 2300–2314 10. Li, X., et al.: Performance analysis of a navigation system combining BeiDou with LEO communication constellation. China Satellite Navigation Conference (CSNC) 2020 Proceedings 11. Meng, Y., et al.: Global navigation augmentation system based on Hongyan satellite constellation . Space Int. 10, 20–27 (2018) 12. Shen, D., et al.: A global navigation augmentation system based on LEO Communication constellation. J. Terahertz Sci. Electron. Inf. Technol. 17(2), 209–215 (2019)

Satellite Navigation System Time Delay Automatic Calibration Technology and Ground Verification Wei Wang(B) , Yilong Liu, Jun Lu, Ying Chen, Haitao Wei, Guoyi Zhang, and Chengpan Tang Beijing Institute of Track and Communication Technology, Beijing 100094, China

Abstract. The satellite navigation system uses TOA (Time of Arrival) technology to complete positioning, navigation, and timing. Therefore, the performance of the navigation system is directly related to the delay of the equipment. During the construction of the global satellite navigation system, the delay of receiving equipment and sending equipment need to be accurately calibrated. In the current delay calibration process, manual operation takes up a few time and introduces certain errors, which would affect the accuracy of delay calibration. This paper has carried out the research on the automatic calibration technology of satellite navigation system delay, and some ground verification. The verification results show that the technology can effectively improve the efficiency and accuracy of delay calibration. Keywords: Delay · Automatic calibration · Ground verification

1 Introduction The satellite navigation system is based on the time of arrival (Time of Arrival, TOA) principle for ranging positioning, which measures the time elapsed by the signal from a known source to the user receiver using pseudo-range measurement technology. The method can obtain the combined delay from a source to the receiver. Since the navigation system needs to accurately process the transmission and reception link delay, the transmission and reception link delay is one of the most important error items in satellite positioning and navigation. The transmission and reception link delay will not only affect the positioning, timing accuracy and navigation performance of the satellite navigation system, but also affect the normal operation of the satellite navigation system. Satellite navigation system time delay calibration is generally divided into two categories, which is transmission link delay calibration and reception link delay calibration. In the current calibration technology, the transmission link delay is calibrated manually using a high-speed oscilloscope [1, 3, 7, 8], and the reception link delay is calibrated with combined delay calibration method, which obtaining reception link delay by subtracting transmission link delay from combined link delay [2, 4–6].

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 231–240, 2021. https://doi.org/10.1007/978-981-16-3142-9_21

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It takes up a lot of time in the process of manual delay calibration of numerous satellite navigation system equipment. At the same time, manual operation will introduce some errors into the satellite navigation system. Therefore, it is necessary to carry out research work on the time delay automatic calibration technology.

2 Satellite Navigation System Delay Classification Satellite navigation system delay is divided into three categories, which is satelliteto-ground link delay, inter-station link delay and inter-satellite link delay. Satellite-toground link delay include up-link transmission delay of ground equipment, up-link reception delay of satellite, down-link transmission delay of satellite and down-link reception delay of receiver. Inter-station link delay include inter-station link transmission delay and inter-station link reception delay. Inter-satellite link delay include inter-satellite link transmission delay and inter-satellite link reception delay. The delay distribution of satellite navigation system is shown in Fig. 1.

Fig. 1. Delay distribution of satellite navigation system

2.1 Satellite and Ground Equipment Delay The up-link transmission delay is the inherent time delay of the ground station equipment, which is the delay between the time when the up-link signal is generated and the time it leaves the ground station. The up-link reception delay is the inherent time delay of the satellite equipment, which is the delay between the time when the up-link signal arrives at the satellite and the time when the signal reception is completed. The down-link transmission delay is the inherent time delay of the satellite equipment, which is the delay between the time when the down-link signal is generated and the time it leaves the satellite.

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The down-link reception delay is the inherent time delay of the receiver, which is the delay between the time when the down-link signal arrives at the receiver and the time when the signal reception is completed. Delay distribution of satellite-to-ground link is shown in Fig. 2.

Fig. 2. Delay distribution of satellite-to-ground link

The up-link transmission delay and up-link reception delay will affect the satelliteto-ground time synchronization accuracy, and down-link transmission delay will affect the ranging of receiver. Therefore, it is necessary to carry out accurate delay calibration of the satellite-to-ground link. 2.2 Inter-station Link Delay The inter-station link transmission delay is the inherent time delay of the inter-station link signal, which is the delay between the time when the inter-station link signal is generated and the time it leaves the ground station; Satellite retransmission delay is the inherent time delay of the satellite, which is the delay between the time when the inter-station link signal arrives at the satellite and the time when it leaves the satellite; The inter-station link reception delay is the inherent time delay of the ground station, which is the delay between the time when the inter-station link signal arrives at the ground station and the time when the signal reception is completed; Delay distribution of inter-station link is shown in Fig. 3. The transmission delay of the inter-station link and the reception delay of the interstation link will directly affect the time synchronization between the stations. If the time between the stations cannot be accurately synchronized, it will cause the deviation of the broadcast time of some satellites, which will affect the system performance.

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Fig. 3. Delay distribution of inter-station link

2.3 Inter-satellite Link Delay Inter-satellite link transmission delay is the inherent delay of the satellite, which is the delay between the time when the inter-satellite link signal is generated and the time when it leaves the satellite. Inter-satellite link reception delay is the inherent delay of the satellite, which is the delay between the time when the inter-satellite link signal arrives at the satellite and the time when the signal reception is completed. Delay distribution of inter-satellite link is shown in Fig. 4.

Fig. 4. Delay distribution of inter-satellite link

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Inter-satellite link transmission delay and inter-satellite link reception delay will directly affect the inter-satellite ranging. Therefore, it is necessary to carry out accurate delay calibration.

3 Automatic Time Delay Calibration Method Because manual operation affects the efficiency and precision of delay calibration, we proposes an automatic time delay calibration method. The calibration method divides satellite-to-ground link delay, inter-station link delay and inter-satellite link delay into transmission delay and reception delay, and then uses combined delay calibration method combined with switch network to complete automatic delay calibration, as described below. 3.1 Automatic Calibration Method of Transmission Delay Let the number of transmission equipment be M, and the number of calibration equipment be N. An M✕N switch network equipment is used to connect the transmission equipment and the calibration equipment, instead of manual connection with cable. At the same time, the 1PPS signal generated by transmission equipment is connected to time interval counter. The time delay calibration process works under synchronized 1PPS and 10 MHz signals, as shown in Fig. 5.

Fig. 5. Schematic diagram of automatic calibration method of transmission delay

The steps for automatic calibration of the transmission delay are shown below: (1). Complete the delay calibration of the transmission delay calibration equipment, let the reception delay after calibration be TRi , i = 1, 2, . . . , N . (2). Record the time interval between the reference 1PPS and the 1PPS generated by the transmission equipment, which is Tij , i = 1, 2, . . . , N ; j = 1, 2, . . . , M .

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(3). Record the pseudorange measured by the transmission delay calibration equipment, which is ρij , i = 1, 2, . . . , N ; j = 1, 2, . . . , M . (4). Get the transmission delay TSj = ρij − Tij − TRi , i = 1, 2, . . . , N ; j = 1, 2, . . . , M . (5). Repeat steps (2) to (4), until the time delay calibration of all transmission equipment is completed. 3.2 Automatic Calibration Method of Receiving Equipment Delay Let the number of the reception equipment be M, and the number of reception calibration equipment be N. An M × N switch network equipment is used to connect the reception equipment and the reception delay calibration equipment, instead of manual connection with cable. At the same time, the 1PPS signal generated by reception equipment is connected to time interval counter. The time delay calibration process also works under synchronized 1PPS and 10 MHz signals, as shown in Fig. 6.

Fig. 6. Schematic diagram of automatic calibration method of reception delay

The steps for automatic calibration of the reception delay are shown below: (1) Complete the delay calibration of the reception delay calibration equipment, let the transmission delay after calibration be TSi , i = 1, 2, . . . , N . (2) Record the time interval between the reference 1PPS and the 1PPS generated by the reception equipment, which is Tij , i = 1, 2, . . . , N ; j = 1, 2, . . . , M . (3) Record the pseudorange measured by the reception equipment, which is ρij , i = 1, 2, . . . , N ; j = 1, 2, . . . , M . (4) Get the reception delay TRj = ρij − Tij − TSi , i = 1, 2, . . . , N ; j = 1, 2, . . . , M . (5) Repeat steps (2) to (4), until the time delay calibration of all reception equipment is completed.

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4 Ground Test Verification Results 4.1 Equipment Self-calibration Result In order to verify the above automatic calibration method, a set of calibration equipment, L-band switch network equipment, Ka-band switch network equipment and time interval counter are equipped in the ground system. The above equipment is used to calibrate the reception delay, down-link transmission delay and inter-satellite link delay of satellite navigation simulator. First, perform the self-calibration of the calibration equipment, and the results are shown in Fig. 7 and Table 1.

Fig. 7. Automatic time delay self-calibration results

Table 1. Self-calibration results of automatic calibration equipment Test results

Up-link/ns

Down-link B1/ns

Down-link B3/ns

Inter-satellite link/ns

Maximum

3707.70

10416.62

3915.34

3445.44

Minimum

3707.52

10416.49

3915.30

3445.36

0.09

0.06

0.01

0.03

Stability

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4.2 Automatic Time Delay Calibration Result After the calibration equipment is calibrated, automatic delay calibration is performed with four satellite simulators. The automatic calibration results are shown in Table 2. Table 2. Automatic calibration results of satellite simulator Testing object

Up-link reception delay (stability)/ns

Inter-satellite transmission delay (stability)/ns

Inter-satellite reception delay (stability)/ns

Satellite simulator 1

520.12(0.21)

554.73(0.26)

999.20(0.29)

Satellite simulator 2

528.33(0.35)

549.66(0.27)

988.31(0.28)

Satellite simulator 3

524.51(0.33)

649.76(0.32)

890.51(0.39)

Satellite simulator 4

627.43(0.27)

453.46(0.28)

1105.91(0.32)

During the calibration process, the calibration time of each satellite is 10 min, and the total calibration time is 10 × 4 = 40 min, since the up-link reception delay, inter-satellite transmission delay and inter-satellite reception delay are calibrated in parallel. Assuming that each time delay calibration takes 2 min to prepare in the manual calibration case, and it is expected to take up to (2 + 2 + 2 + 10) × 4 = 64 min when a single person completes the preparations in serial and completes the calibration of three links in parallel. We can see that the efficiency has increased by 60%. In addition, in the ground test and verification system, the time delay calibration results were used to complete the orbit determination of satellite simulators, and the orbit determination accuracy of the system was increased from the original 5 m to smaller than 2 m, as shown in Table 3 and Fig. 8. Table 3. Orbit determination result data sheet Testing object

3 Dimention accuracy (m) before calibration

3 Dimention accuracy(m) after calibration

Satellite simulator 1

4.638

0.757

Satellite simulator 2

4.621

0.595

Satellite simulator 3

4.405

1.329

Satellite simulator 4

4.723

1.384

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Fig. 8. Orbit determination results

The above test results show that time delay automatic calibration of satellite-to-earth link and inter-satellite link can effectively improve the system operation accuracy. In the engineering system, the time delay automatic calibration technology can be used to accurately and efficiently calibrate the ground equipment, which would contribute to the improvement of BeiDou satellite navigation system service performance.

5 Summary This paper proposes an time delay automatic calibration technology, and has carried out the technical verification in the ground test and verification system. The verification results show that the time delay calibration stability is better than 0.2 ns, which effectively reduces the error introduced by manual operation, and it will increases the calibration efficiency by 60% at the same time. Time delay automatic calibration will improve the time synchronization accuracy and inter-satellite ranging accuracy of the satellite navigation system, which would make the BeiDou satellite navigation system operation more precise and stable. Acknowledgments. Thanks to the ground test and verification system team for their cooperation and data support.

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References 1. Guo, S., Wang, W., Gao, W., Lu, J.: Design and implementation of the ground test and verification bed for BeiDou navigation satellite system. Acta Geodaetica Cartogr. Sin. 49(9), 1074–1083 (2020) 2. Li, G., Wei, H., Sun, S.: Navigation equipment delay measurement technology. J. Radio Eng. 41(12), 32–35 (2011) 3. Wei, H., BaoGuo, Yu., Li, G., Yuan, L.: The accurate method for the equipment time-delay and research on testing technology in satellite navigation system. J. SCIENTIA SINICA Phys. Mech. Astronomica 40(5), 623–627 (2010) 4. Zhang, J., Yi, Q., Wang, W., Wei, H.: The Methods of Measuring the delay of the Transfer Link and Receiver Link for navigation (2011) 5. Zhu, J., Li, Z.: Research on time delay measurement technology for satellite navigation receivers. J. ACTA METROLOGICA SINICA 40(5), 910–913 (2019) 6. Yuan, L., Chu, H., Wang, H., Gu, Q., Zhao, W.: The measure technique research of the satellite navigation equipment time delay. J. SCIENTIA SINICA Phys. Mech. Astronomica 41(5), 629–634 (2011) 7. Plumb, J., Larson, K.M., White, J., Powers, E.: Absolute calibration of a geodetic time transfer system. J. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Trans. 11(52), 1904–1911 (2005) 8. Zhong, X., Chen, H., Li, J., Liu, Y., Du, W.: A high accuracy absolute calibration method of transmit time delay of BPSK modulator. J. Space Electron. Technol. 4, 13–17 (2011)

Preliminary Assessment of BDS-3 PPP Service Performance Chenghe Fang1,2(B) , Yinhu Ma1,2 , Changjiang Geng1,2 , Hongliang Cai3 , Yifang Zhao1,2 , Tianyang Sun1,2 , Qi Li1,2 , and Cheng Liu3 1 Test and Assessment Research Center, China Satellite Navigation Office,

1 Fengyingdong Road, Beijing 100094, China 2 GNSS System Engineering Center, China Academy of Aerospace Electronics Technology,

1 Fengyingdong Road, Beijing 100094, China 3 Beijing Institute of Tracking and Telecommunications Technology,

26 Beiqing Road, Beijing 100094, China

Abstract. The BDS-3 has been officially commissioned since July 31, 2020. As one of the seven services of BDS-3, precision point positioning is free to users in China and its surrounding areas. In order to assess the performance of BDS3 PPP service, the observation data from eight domestic stations were analyzed in terms of the accuracy of corrections, the coverage of service, the positioning accuracy, and the convergence time. The coverage of service was assessed based on the combination of the number of effectively corrected satellites and the DOP values, and the convergence time was calculated using a slide-and-restart method. The results prove that: 1) The averages of signal in space ranging error (SISRE) (RMS) are 0.10 m and 0.14 m for BDS-3 and GPS respectively. 2) The availabilities of PPP service of BDS-3 only and BDS-3&GPS dual system are both higher than 90% in China and its surrounding areas. 3) The average convergence time of the kinematic PPP of BDS-3 is 17 min (0.3 m horizontally and 0.6 m vertically). After convergence, the average accuracy (95% confidence level) reaches 0.17 m horizontally and 0.26 m vertically. The average convergence time of the kinematic PPP of BDS-3&GPS dual system is 10 min (0.2 m horizontally and 0.4 m vertically). After convergence, the average accuracy (95% confidence level) reaches 0.11 m horizontally and 0.22 m vertically. Keywords: BDS-3 · Precise point positioning (PPP) · Signal in space ranging error (SISRE) · Service performance · Assessment · iGMAS

1 Introduction BDS-3 is a new generation of BeiDou navigation satellite system independently built by China which integrates RNSS, PPP, satellite-based augmentation, short message communication, and medium-orbit search and rescue services [1], and has been officially commissioned since July 31, 2020. BDS-3 PPP service is the first built-in and operational PPP service among all GNSSs (Galileo plans to provide PPP service by E6 signal which, however, is not yet operational. In addition, Japan’s regional GNSS, © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 241–255, 2021. https://doi.org/10.1007/978-981-16-3142-9_22

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QZSS, launched CLAS high-precision service in 2018 [2–4]) which covers both China and its surrounding areas. Lots of work have been done with respect to the construction, methodology and assessment of PPP service. Wuhan University has established a widearea differential augmentation system for GPS, namely MASS, of which the dynamic positioning accuracy is better than 10 cm horizontally and 20 cm vertically [5]. There are also scholars using MGEX and iGMAS data to calculate the BDS-3 real-time orbit and clock offset. The results proved that the accuracy of real-time PPP solutions could reach decimeter-level [6]. In 2016, Lou et al. carried out the assessment of the enhanced service performance of QZSS in China, and the results proved that the positioning accuracy of LEX service could reach sub-meter level of 0.2 m horizontally and 0.5 m vertically [7]. In 2019, Zhang et al. analyzed the positioning performance of the BDS comprehensive zone corrections. The results showed that the dynamic positioning error in 3D of the dual-frequency user with comprehensive zone corrections converged to 0.5m in about 25 min, and the positioning accuracy (RMS) after convergence was 0.15 m horizontally and 0.2 m vertically [8]. In 2020, Hu et al. assessed the accuracy of CNES CLK93 BDS realtime orbit and clock product, as well as kinematic and static PPP solutions. The results showed that the accuracy of BDS-3&GPS combined PPP could reach decimeter-level and centimeter-level in kinematic and static modes respectively [9]. Yang et al. assessed comprehensively the service performance of Beidou-3 in detail, and concluded that the designed index requirements were met [10]. In the same year, Jin et al. analyzed the positioning results of BDS single-frequency, dual-frequency, three-frequency and fourfrequency PPP models in detail. The results showed that BDS multi-frequency signals could improve the PPP positioning performance, and the accuracy after convergence could reach centimeter-level [11]. In 2020, Lu et al. used the receiver software (SDR) to collect the PPP-B2b signal, and studied the time-varying characteristics, integrity and stability of the corrections [12]. Presently, the BDS-3 PPP service is at an early stage of which the related studies are quite few. This article will carry out preliminary analysis and assessment on the performance of BDS-3 PPP service in terms of the accuracy of corrections, the coverage of service, the positioning accuracy, and the convergence time, aiming to provide users with beneficial references.

2 Technical Features The BDS-3 PPP information is modulated on the B2b signal [13], and broadcast by three geostationary (GEO) satellites (PRN59/60/61). The carrier frequency of the B2b signal is 1207.14 MHz and the bandwidth is 20.46 MHz. The B2b signal can provide PPP service to the four systems of BDS, GPS, Galileo and GLONASS. Table 1 lists the defined message types, and Table 2 the nominal validity period of the message. Based on the received PPP messages, the status and features of the current PPP-B2b service are summarized as follows (as of December 20, 2020): 1) The actual message types received by the user are within 1–4; 2) Only corrections of BDS-3 and GPS satellites which are visible in the Asia-Pacific region are broadcast;

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Table 1. Message types Message type

Message content

1

Satellite mask

2

Satellite orbit correction and user range accuracy index

3

Differential code bias

4

Satellite clock correction

5

User range accuracy index

6

Clock correction and orbit correction - combination 1

7

Clock correction and orbit correction - combination 2

8–62

Reserved

63

Null message

Table 2. Nominal validity period of the message Message content

Message type

Nominal validity period (s)

Satellite mask

1

–

Satellite orbit correction

2, 6, 7

96

Differential code bias

3

86400

Satellite clock correction

4, 6, 7

12

User range accuracy index

2, 5, 6, 7

96

Note: The “nominal validity period” gives the recommended period for various types of messages. Data quality is guaranteed for messages beyond this period.

3) The broadcast interval of orbit corrections, differential code bias, and user range accuracy index is 48 s, and that of clock corrections is 6 s or 12 s; 4) PPP corrections broadcast by 3 GEO satellites are the same; 5) The message of type 3 only contains the differential code bias for BDS-3 satellites, with no information of other GNSSs. In addition, the corresponding relationships between the messages of orbit and clock corrections of each GNSS and the IODN are as follows: 1) BDS: corresponding to the IODC in CNAV1 message; 2) GPS: corresponding to the IODC in LNAV message;

3 Assessment Method of the Service Performance 3.1 SISRE SISRE mainly consists of the satellite orbit error and the clock error. The specific assessment strategy is:

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1) Based on the PPP corrections and the navigation messages, calculate the corrected earth-centered earth-fixed (ECEF) satellite orbit coordinates and satellite clock offset (refer to PPP-B2b ICD for the specific algorithm). 2) Calculate the difference between the corrected orbit and the final precise orbit on a daily basis and with a sampling rate of 30 s (if the sampling time is not aligned, Lagrangian interpolation is used to interpolate the precise orbit). Then convert the difference to radial, along, and cross directions for each satellite. 3) In the same way, calculate the difference between the corrected clock offset and the final precise clock offset, and obtain the mutual difference (clk1 ) sequence of the clock offset of each satellite. 4) Select a reference satellite (e.g. the average of clock offsets difference of all satellites in one epoch), and calculate the difference between clk1 of other satellites and the corresponding value of the reference satellite to eliminate the influence caused by the different reference clocks. The result is a double difference (dif_clk) sequence of clock offset. 5) In order to calculate the accuracy of the phase clock, the following formula is used to eliminate the clock offset reference of each satellite. n dif_clki (1) δt = dif_clk − i=1 n Where n is the number of samples. 6) Calculate the PPP-B2b SISRE as follows:    2 SISRE = (wR · R − cδt)2 + wA,C · A2 + C 2

(2)

Where, wR and wA,C are weights related to the height of the satellite, as shown in Table 3. R, A, and C are the orbit errors in the radial, along, and cross directions respectively. δt represents satellite clock error. c represents the speed of light. Table 3. Values of the weights 2 wA,C

System

wR

GPS

0.98 1/49

BDS(MEO)

0.98 1/54

BDS(IGSO,GEO) 0.99 1/127

3.2 Service Coverage To assess the coverage of BDS-3 PPP service, the broadcast navigation messages and PPP correction messages of a regression period of 7 days are used. The global area is divided into regular grids of 1° × 1°. With a sampling rate of 300 s and a cut-off elevation

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angle of 7°, considering the broadcast field of three GEO satellites, the availability of PPP service at each grid point is analyzed based on various conditions such as the number of effectively corrected satellites, PDOP, HDOP, and VDOP. The specific calculation strategy and the corresponding steps are as follows: 1) First calculate the coordinates of a grid point, and identify the effectively corrected satellites based on a) the matching principle of PPP correction message and the broadcast message, b) the availability status of the PPP service of the satellite in the reserved flag, c) the nominal validity period of the PPP correction message, d) user ranging accuracy (URA), and e) the health status of RNSS message, etc. Satellites of which PPP service are not available, no PPP correction message, PPP correction message is invalid, PPP correction message expires, URA exceeds the threshold, or the health status is unhealthy, should be filtered out in order to obtain all effectively corrected satellites. 2) Calculate the ECEF coordinates of all matching satellites in 1) and the elevation angle relative to the grid point; 3) Based on the cut-off elevation angle threshold, satellites not meeting the requirements are further eliminated; 4) Calculate PDOP, HDOP, and VDOP at the grid point based on the obtained effectively corrected satellites and record the number of them. 5) Finally, for all grids in a regression period, analyze availability based on the number of effectively corrected satellites and DOPs with certain conditions to obtain the coverage of the PPP service. The threshold of the number of effectively corrected satellites is chosen as follows: Since the kinematic PPP of BDS-3 single system needs to estimate 5 time-varying parameter (3 positional components, 1 receiver clock offset, and 1 tropospheric residual error) in addition to static parameters such as ambiguity, the number of effectively corrected satellites for a single epoch should be at least 5. Likewise, since the kinematic PPP of BDS-3&GPS dual system needs to estimate not only the 5 time-varying parameters, but also 1 inter-system time deviation time-varying parameter, the number of effectively corrected satellites is at least 6 for one single epoch. 3.3 PPP Accuracy and Convergence Time 3.3.1 Model and Strategy The observation model of the ionosphere-free combination of dual-frequency carrier phase and pseudo-range observations is: PIF = ρrs + cδtr − cδt s − δrel + δtrop + δtide + εPIF

(3)

LIF = ρrs + cδtr − cδt s − δrel + λIF NIF + δwrap + δtrop + δtide + εLIF

(4)

Where, PIF and L IF are the ionosphere-free observations of pseudo-range and carrier phase respectively, which can eliminate more than 99% osf the ionospheric delay; ρrs

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is the geometric distance between the receiver and the satellite. The receiver position is the unknown parameter to be estimated, and the satellite position is corrected by the orbit corrections; δtr is the receiver clock offset, which is also an unknown parameter; δts is the satellite clock offset corrected by the clock corrections; λIF is the wavelength of the ionosphere-free combination; N IF is the ambiguity unknown parameter of the ionosphere-free combination; δtrop is the tropospheric delay, of which the dry delay part can be corrected by an appropriate tropospheric model, and the wet delay part is treated as an unknown parameter; δwrap is the phase wind-up error; δtide is the tidal effect error; δrel is the relativistic effect; εIF is the multipath error, antenna PCO and observation Table 4. Configuration and estimation of PPP parameters Observations

Corrections for the observation model

Observations

BDS-3: B1C&B2a, GPS: L1&L2

Sampling interval

30 s

Cut-off elevation angle

7°

Observation weight

Based on the elevation angle

Observation noise

Pseudo-range 0.6 m, phase 0.01 cycle

Satellite orbit

Corrected by orbit corrections

Satellite clock offset

Corrected by clock corrections

Phase wind-up

Corrected by model

Earth deformation

IERS Conventions 2010

Antenna PCO

GPS: Corrected by IGS14 model BDS-3: Officially published values

Ionospheric delay

Ionosphere-free combination

Tropospheric delay

Initial value: SAAS + GMF, wet delay residual part is set as an unknown parameter

DCB

Corrected by DCB corrections

Estimation of parameters station coordinates

Filter

Dynamic: Single epoch + white noise estimation Static: Constant estimation;

Receiver clock offset

Single epoch + white noise estimation

Residual of tropospheric zenith wet delay

Random walk parameter estimation

Ambiguity

Piecewise constant estimation, floating point solution

Inter-system bias

Random walk parameter

Square root information filter

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noise of the ionosphere-free combination. The specific configuration and estimation of PPP parameters are shown in Table 4. It should be noted that during the assessment, quality control is not carried out, i.e. satellites with residuals of bad quality are not excluded. In addition, for dual system PPP, equal weights are adopted during processing for BDS-3 and GPS. 3.3.2 Assessment Method The positioning accuracy is assessed according to the method of real-time kinematic PPP solution based on the post-event data. Calculate the difference sequence between the 24-h single-day positioning result and the real position of the receiver, and obtain the accuracy of positioning as the 95% percentile of the sequence after the first convergence. The convergence condition is defined as follows (hereinafter referred to as CC 1): BDS3 single system PPP converges to 0.3 m horizontally and 0.6 m vertically for the first time, and lasts for more than 5 min; BDS-3&GPS dual system PPP converges to 0.2 m horizontally and 0.4 m vertically for the first time, and lasts for more than 5 min. Since users may use PPP service at any time of the day, and the actual number of effectively corrected satellites, the accuracy of corrections, and ionospheric activity at different times may affect the actual convergence time, this article proposed a slide-andrestart method (SRM) to calculate PPP convergence time. SRM solutions are obtained by applying a 60-s sliding window and 2-h calculation period to the observation data, and the corresponding convergence times are recorded in the meantime. Based on the aforementioned definition of CC 1, another condition (hereinafter referred to as CC 2) is added as follows: single and dual system PPP converges to 0.1 m horizontally and 0.2 m vertically for the first time, and lasts for more than 5 min.

4 Analysis of BDS-3 PPP Service Performance 4.1 Data Source Data from iGMAS are used to assess the BDS-3 PPP service performance. iGMAS stations support 4 open signals of BDS-3, i.e. B1I, B3I, B1C and B2a. There are 8

Fig. 1. Distribution of tracking stations

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C. Fang et al. Table 5. Receivers and antenna types of stations Station

Location

Receiver type

Antenna type

BJF1

Beijing

CETC-54-GMR

LEIAR25.R4 LEIT

CHU1

Changchun

BD070

LEIAR25.R4 LEIT

GUA1

Urumqi

BD070

LEIAR25.R4 LEIT

KUN1

Kunming

Unicore UR4b0

NOV750.R4 NOVS

LHA1

Lhasa

CETC-54-GMR

NOV750.R4 NOVS

SHA1

Shanghai

Unicore UR4b0

NOV750.R4 NOVS

WUH1

Wuhan

CETC-54-GMR

LEIAR25.R4 LEIT

XIA1

Xi’an

BD070

LEIAR25.R4 LEIT

iGMAS stations in China, each of which is equipped with high-precision receiver for measuring (see Table 5). In addition, the BDS-3 PPP messages are received by a FRII-Plus receive located in Beijing. 4.2 Analysis of SISRE Based on the final precise orbit and clock products from iGMAS, the SISRE of BDS-3 and GPS satellites that have PPP corrections were assessed within the period of July 31, 2020 to October 15, 2020. The results are shown in Fig. 2. 0.30 SISRE (RMS) (m)

0.25 0.20

GPS

BDS-3

0.15 0.10 0.05 0.00

1921232527293234363840424446 2 4 6 8 10121517192225272931 PRN

Fig. 2. SISRE(RMS)

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From Fig. 2, the SISRE of corresponding BDS-3 and GPS satellites are smaller than 0.2 m. Statistically, the average of SISRE of BDS-3 satellites is 0.10 m, and that of GPS is 0.14 m. 4.3 Analysis of Service Coverage Figure 3 shows the distribution of the BDS-3 PPP service availability at global scale under different statistical conditions from August 24 to August 30, 2020. The number of effectively corrected satellites of each sub-figure is at least 5. Among them, Fig. 3(a) shows that the availability in the entire China can reach more than 90% under the condition of PDOP ≤ 6. Figure 3(b), under the condition of HDOP ≤ 2 and VDOP ≤ 4, shows that, except for the northwest China of which the availability is a bit low (70% –90%), the availability in the rest areas is higher than 90%. Figure 3(c), under a worse condition of HDOP ≤ 1.5 and VDOP ≤ 3, shows that the availability of the northern and western China is further decreasing and the area below 90% is further expanded. Only the central, southern and eastern part of China are higher than 90%. Figure 3(d), under the worst condition of HDOP ≤ 1 and VDOP ≤ 2, shows that the availability of almost entire China is below 50%.

(a) No.of Vis Sat≥5 & PDOP≤6

(b) No.of Vis Sat≥5, HDOP≤2 & VDOP≤4

(c) No.of Vis Sat≥5, HDOP≤1.5 & VDOP≤3

(d) No.of Vis Sat≥5, HDOP≤1 & VDOP≤2

Fig. 3. BDS-3 PPP service availability coverage under various conditions (elev ≥ 7°)

Figure 4 shows the distribution of the BDS-3&GPS PPP service availability at global scale (1° × 1°) under different statistical conditions from August 24 to August 30, 2020. The number of effectively corrected satellites of each sub-figure is at least 6. Among them, Fig. 4(a) shows the availability distribution with PDOP ≤ 6, Fig. 4(b) with HDOP ≤ 2 and VDOP ≤ 4, and Fig. 4(c) with HDOP ≤ 1.5 and VDOP ≤ 3. From these figures, it can be seen that the availability within the entire China is higher than 90%. Figure 4(d), under the condition of HDOP ≤ 1 and VDOP ≤ 2, shows that, except for the lower availability in the western region, the rest area is higher than 90%.

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(a) No.of Vis Sat≥6 & PDOP≤6

(c) No.of Vis Sat≥6, HDOP≤1.5 & VDOP≤3

(b) No.of Vis Sat≥6, HDOP≤2 & VDOP≤4

(d) No.of Vis Sat≥6, HDOP≤1 & VDOP≤2

Fig. 4. BDS-3&GPS PPP service availability coverage under various conditions (elev ≥ 7°)

4.4 Analysis of Positioning Accuracy and Convergence Time Figure 5 shows the horizontal and vertical positioning accuracy (95%) time series of the BDS-3 single system and BDS-3&GPS dual system kinematic PPP solutions after the first convergence based on iGMAS domestic tracking stations from July 31 to October 15, 2020.

Fig. 5. Positioning accuracy time series of BDS kinematic PPP resolution

From Fig. 5, it can be seen that, except for a few poor positioning results which might be caused by bad observation quality, low accuracy of corrections, insufficient effectively corrected satellites, or large PDOP, most of the horizontal and vertical positioning accuracy (95%) of the BDS-3 single system kinematic PPP solutions are within

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0.3 m and 0.6 m, and that of BDS-3&GPS dual system are mostly within 0.2 m and 0.4 m, respectively. Table 6 shows the average positioning accuracy and the time of first convergence at each station during the assessment. The results prove that, for each iGMAS station, the average horizontal and vertical accuracy (95%) of BDS-3 single system are 0.17 m and 0.26 m, and the average convergence time is about 11 min (≤0.3 m horizontally and ≤0.6 m vertically, and lasts for 5 min). With respect to BDS-3&GPS dual system, the average horizontal and vertical accuracy (95%) are 0.11 m and 0.22 m, and the average convergence time is about 9 min (≤0.2 m horizontally and ≤0.4 m vertically, and lasts for 5 min). Table 6. Positioning accuracy (95%) and convergence time (mean) with BDS-3 and BDS-3 & GPS kinematic PPP resolution (2020-7-31 to 2020-10-15) Station

Location

BDS-PPP

BDS&GPS-PPP

H/m

V/m

CT/min

H/m

V/m

CT/min

BJF1

Beijing

0.14

0.19

11.18

0.09

0.17

8.46

CHU1

Changchun

0.21

0.30

12.85

0.13

0.26

8.13

GUA1

Urumqi

0.23

0.30

13.21

0.14

0.25

8.90

KUN1

Kunming

0.12

0.25

9.80

0.10

0.25

7.65

LHA1

Lhasa

0.24

0.30

10.98

0.14

0.24

8.59

SHA1

Shanghai

0.15

0.27

9.47

0.10

0.23

9.72

WUH1

Wuhan

0.16

0.21

8.10

0.11

0.19

8.50

XIA1

Xi’an

0.13

0.22

8.80

0.09

0.20

8.16

0.17

0.26

10.55

0.11

0.22

8.51

Mean value CT: Convergence Time.

Figures 6(a) and 6(b) are the kinematic and static PPP results of BDS-3 single system and BDS-3&GPS dual system in the N, E, and U directions at BJF1 station from August 25 to August 27, 2020. From them it can be seen that, for both single and dual system after the first convergence, the kinematic positioning error could remain within 0.2 m horizontally and 0.3 m vertically, and static PPP could reach and stabilize at the centimeter-level both horizontally and vertically. The overall results of the BDS-3&GPS dual system are better than the BDS-3 single system. The aforementioned results of convergence time all start at 00:00:00 (BDT) every day. However, users might use the PPP service at any time of the day. Thus, a slide-andrestart method (SRM) is adopted to analyze the first convergence time. Figure 7 shows the convergence time at BJF1 station using SRM under CC 1, with a 2-h calculation period and a 60-s sliding window, from August 24 to August 30, 2020. The results prove that, during the period, the average convergence time of the BDS-3 single system kinematic PPP solutions at different start times is 15.10 min, of which 85.37% are less

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(a)2025-08-25

(b)2025-08-27 Fig. 6. Positioning error time series of static and kinematic PPP solutions of BDS-3 and BDS3&GPS at BJF1

than 30 min. Meanwhile, the average convergence time of the BDS-3&GPS dual system is 11.03 min, of which 87.64% are less than 20 min. Figure 8(a) is the convergence time of all stations using SRM for kinematic PPP solutions under CC 1, with a 2-h calculation period and a 60-s sliding window, with the 24-h data on August 4, 2020. The results prove that, the average convergence time at different start times of all stations with the BDS-3 single system is 17.56 min, among which 81.60% of them are shorter than 30 min, and the average convergence time of the BDS-3&GPS dual system is 10.38 min, among which 88.45% are better than 20 min. Figure 8(b) is the statistical results of the convergence time under CC 2. The results prove that the average convergence time of the BDS-3 single system is 42.07 min, of which 44.03% are less than 30 min, and the average convergence time of the BDS-3&GPS dual system is 25.21 min, of which 54.26% are less than 20 min. In addition, it can be seen

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Fig. 7. Convergence time using SRM at BJF1 from 2020-08-24 to 2020-08-30

Fig. 8. Convergence time of all stations on 2020-08-24

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that BDS-3&GPS dual system can significantly reduce the convergence time where the BDS-3 single system takes longer.

5 Conclusions This article introduces the basic information of BDS-3 PPP service, with brief description on its characteristics, structure, and corrections. The final precise orbit and clock products were used to assess the accuracy of PPP corrections. The results prove that the average SISRE (RMS) of BDS-3 is 0.10 m, and that of GPS is 0.14 m. The assessment of the availability of BDS-3 PPP service coverage was carried out based on the real collected messages under various combinatorial conditions involving the number of effectively corrected satellites, PDOP, HDOP, and VDOP. The results prove that, for both BDS-3 single system (number of effectively corrected satellites ≥ 5, HDOP ≤ 2 and VDOP ≤ 4) and BDS-3&GPS dual system (number of effectively corrected satellites ≥ 6, HDOP ≤ 1.5 and VDOP ≤ 3), the service availability could reach 90% in China and its surrounding areas. Moreover, the dual system presents a relatively larger coverage than the single. Based on data from iGMAS domestic stations, the kinematic PPP positioning accuracy assessment was performed on a daily basis, and the kinematic and static PPP results were compared. Afterwards, the convergence time at any time of a day was calculated using SRM. The results prove that, the kinematic PPP of BDS-3 single system takes about 17 min on average to converge to 0.3 m horizontally and 0.6 m vertically, and about 42 min to converge to 0.1 m horizontally and 0.2 m vertically. The average accuracy (95%) after convergence is 0.17 m horizontally and 0.26 m vertically. With respect to BDS3&GPS dual system, the kinematic PPP takes about 10 min on average to converge to 0.2 m horizontally and 0.4 m vertically, and about 25 min to converge to 0.1 m horizontally and 0.2 m vertically. The average accuracy (95%) after convergence is 0.11 m horizontally and 0.22 m vertical. Acknowledgements. In this paper, the observation data and computing resources of iGMAS were used. This paper is supported by the science and technology program projects No. 2021024 and No. 2021025 of Zhejiang Transportation Department.

References 1. Lu, J., Guo, X., Su, C.: Global capabilities of BeiDou Navigation Satellite System. Satellite Navigation 1(1), 1–5 (2020). https://doi.org/10.1186/s43020-020-00025-9 2. Göhler, E., Krol, I., Bodenbach, M., Winkel, J., Seco-Granados, G., Fenrandez-Herneandez, I.: A Galileo E6-B/C Receiver: Signals, Prototype, Tests and Performance, Ion Gnss, 16 September 2016 3. Borio, D., Senni, T., Fernandez-Hernandez, I.: Experimental Analysis of a Candidate Galileo E6-B Data Dissemination Scheme. In: 2020 International Technical Meeting of The Institute of Navigation, February 2020

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4. The Cabinet Office, Government of Japan, “Quasi-Zenith satellite system interface specification centimeter level augmentation service (IS-QZSS-L6–002) [DB/OL],” December 2019 5. Shi, C., Lou, Y.D., Song, W.W., et al.: Real-time wide-area precise positioning prototype system and preliminary results. Geomatics Inf. Sci. Wuhan Univ. 34(11), 1271–1274 (2009) 6. Cui, H.Z., Tang, G.S., Song, B.Y., et al.: Real-time BDS orbit and clock offset processing strategy. China Space Sci. Technol. 35(5), 1–7 (2015) 7. Lou, Y.D., Zheng, F., Gong, X., et al.: Regional QZSS augmentation service performance assessment in China. Geomatics Inf. Sci. Wuhan Univ. 41(3), 298–303 (2016) 8. Zhang, Y.Z., Chen, J.P., Yang, S.N., et al.: BDS wide-area differential analysis of PPP performance Based on BDS comprehensive zone corrections. Geomatics Inf. Sci. Wuhan Univ. 44(02), 4–10 (2019) 9. Hu, H.J., Zhao, X.W., Tao, Y., et al.: Performance assessment of BDS/GPS real-time precise point positioning. In: China Satellite Navigation Conference (CSNC) (2020) 10. Lu, X.C., Chen, L., Nan, S., et al.: Decoding PPP Corrections from BDS B2b Signals Using a Software-defined Receiver: an Initial Performance Evaluation. IEEE Sensors J. PP(99), 1 (2020) 11. Yang, Y., Mao, Y., Sun, B.: Basic performance and future developments of BeiDou global navigation satellite system. Satellite Navigation 1(1), 1–8 (2020). https://doi.org/10.1186/s43 020-019-0006-0 12. Jin, S., Su, K.: PPP models and performances from single- to quad-frequency BDS observations. Satellite Navigation 1(1), 1–13 (2020). https://doi.org/10.1186/s43020-020-000 14-y 13. China Satellite Navigation Office, “BeiDou Satellite Navigation System Signal In Space Interface Control Document Precise Point Positioning Service Signal PPP-B2b(Version 1.0)”, July 2020

Influence of Different ISB Processing Strategies on the Accuracy of Undifferenced FCBs and PPP-AR Positioning Wenlong Qi1 , Hongzhou Chai1(B) , Xu Kun2 , Wang Min1 , and Chong Yang1 1 Information Engineering University, Zhengzhou 450001, Henan, China 2 QianXun Spatial Intelligence Inc., Shanghai, China

Abstract. Aiming at the influence of inter-system bias (ISB) on the accuracy of undifferenced FCB. This paper estimates three different FCBs (WN-FCB, RWFCB, CV-FCB) based on white noise, random walk, constant strategies. And using the three FCBs to fixed ambiguity. The experimental results show that: in the wide-lane FCB, the accuracy of three wide-lane FCB products is equivalent; in the narrow-lane FCB, compared with narrow-lane CV-FCB, the precision of RW-FCB and WN-FCB is equivalent, better than CV-FCB. For the convergence time and positioning accuracy, PPP-AR based on RW-FCB and WN-FCB is significantly better than CV-FCB. Keyword: ISB FCB PPP-AR wide-lane FCB narrow-lane FCB

1 Introduction With the rapid development of BeiDou navigation satellite system (BDS), Galileo navigation satellite system and the construction of GPS Modernization [1–4], BDS/GPS precise point positioning (PPP) can provide more visible satellites and optimize the spatial structure, which can not only improve the positioning accuracy and reliability, but also accelerate the convergence of ambiguity, which is conducive to the rapid fixing of ambiguity [5–12]. Due to the different time reference and hardware delay of different navigation systems, inter-system bias (ISB) should be considered in multi-GNSS precise point positioning [11, 13, 14]. The correct handling of ISB is the key to multi-GNSS integrated positioning, so it has been studied by1many scholars at home and abroad. In paper [15], the source of intersystem bias is demonstrated by experiments, but the in-depth study on the time-varying characteristics of ISB is lacking. Paper [16] systematically analyzes the time-varying characteristics of ISB among GNSS navigation systems. The experimental results show that the ISB values among different navigation systems are stable in a single day, all better than 0.12 ns, but no further study has been conducted. Based on the analysis of the characteristics of ISB, paper [17] takes one day’s ISB as constant estimation to analyze the GNSS PPP positioning performance. Paper [6] and [18] respectively used ISB as

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 256–269, 2021. https://doi.org/10.1007/978-981-16-3142-9_23

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random walk process and white noise estimation to analyze GPS/GLONASS PPP positioning performance. Based on the precise ephemeris and clock offset products released by multiple analysis centers, paper [19] analyzes the impact of different ISB processing strategies on undifferenced and uncombined PPP. Most of the above researches focus on the time-varying characteristics of ISB and the influence of different ISB processing strategies on floating-point PPP location, but few studies on the influence of different ISB processing strategies on FCB estimation and PPP-AR. Based on BDS/GPS/Galileo undifferenced and uncombined PPP, ISB is estimated as constant, random walk and white noise respectively. 106 IGS/MGEX stations with global distribution are selected as service stations to generate three kinds of FCB (CV FCB, RW FCB and WN FCB respectively), and the accuracy of the three FCBs products is analyzed. 15 IGS/MGEX stations are selected as the users, and the influence of different FCBs products on PPP-AR is analyzed experimentally from three aspects of positioning accuracy, time to first fix and fixed rate.

2 BDS/GPS/Galileo Undifferenced and Uncombined PPP BDS/GPS/Galileo undifferenced and uncombined PPP takes the raw carrier and code observations as the observation equation to avoid noise amplification: ⎫ S,j j S,j S,j S S P = ρr + cdtS,r − cdt S,j + MrS T + γS,f I + dr,f − dj,f + ε(P )⎬ r,f

S,j Lr,f

=

j ρr

+ cdtS,r − cdt

S,j

+ MrS T

S,j − γS,f I1,r

1,r S,j S,j + λf (Nf + bSr,f

r,f S,j S − bj,f ) + ε(Lr,f )⎭

(1) Where: S denote BDS, GPS, Galileo navigation system, respectively; r is receiver; f is frequency, GPS for L1 and L2, BDS for B1 and B2, Galileo for E1 and E5; P and L denote code and carrier observations, respectively; ρ is the satellite -to- receiver geometric range; cdtS,r and cdt S,j are the receiver and satellite clock offsets, respectively; MrS and T are mapping function for troposphere delay and troposphere delay, respectively; S,j S and d S are satellite and receiver code I1,r is ionosphere delay of first frequency; dr,f j,f S,j

S,j

bias, respectively; λf and Nf are wavelength for Ambiguity and flout ambiguity; bSr,f and bSj,f are satellite and receiver phase bias, S,j

S,j

respectively; ε(Pr,f ) and ε(Lr,f ) denote measurement noise of code phase measurements. At present, the precise satellite clock producte released by the analysis center is calculated based on the P1 and P2 dual frequency ionosphere-free combination, including the hardware delay of pseudo range ionosphere cancellation at the satellite. cd ¯t S,j = cdt S,j + cdt S,IF

(2)

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With the precise satellite clock product correction, the expression of dual frequency BDS/GPS undifferenced and uncombined PPP is as follows: ⎫ G,j j G,j G,j Pr,1 = ρr + cd ¯tG,r + MrG T + I¯1,r − κDCBG + ε(Pr,1 )⎪ ⎪ ⎪ ⎪ ⎪ G,j j G,j G,j ⎪ G G Pr,2 = ρr + cd ¯tG,r + Mr T + γG,2 I¯1,r − γG,2 κDCB + ε(Pr,2 )⎪ ⎪ ⎪ ⎪ ⎪ ⎪ C,j j C,j C,j G C C Pr,1 = ρr + cd ¯tG,r + ISBC + Mr T + I¯1,r −κDCB + ε(Pr,1 )⎬ (3) C,j j C,j C,j ⎪ Pr,2 = ρr + cd ¯tG,r + ISBCG + MrC T + γC,2 I¯1,r − γC,2 κDCBC + ε(Pr,2 )⎪ ⎪ ⎪ ⎪ E,j j E,j E,j ⎪ ⎪ Pr,1 = ρr + cd ¯tE,r + ISBEG + MrE T + I¯1,r −κDCBE + ε(Pr,1 )⎪ ⎪ ⎪ ⎪ ⎪ E,j j E,j C,j G E C Pr,2 = ρr + cd ¯tG,r + ISBE + Mr T + γE,2 I¯1,r − γE,2 κDCB + ε(Pr,2 )⎭ ⎫ G,j j G,j G,j G,j G,j Lr,1 = ρr + cd ¯tG,r + MrG T − I¯1,r + λ1 N¯ 1 + κDCBG + ε(Lr,1 )⎪ ⎪ ⎪ ⎪ ⎪ G,j j G,j G,j G,j G,j ⎪ G G ⎪ Lr,2 = ρr + cd ¯tG,r + Mr T − γG,2 I¯1,r + λ2 N¯ 2 + γG,2 κDCB + ε(Lr,2 )⎪ ⎪ ⎪ ⎪ ⎪ C,j j C,j C,j C,j C,j G C C ¯ ¯ Lr,1 = ρr + cd ¯tG,r + ISBC + Mr T − I1,r + λ1 N1 + κDCB + ε(Lr,1 )⎬ C,j j C,j C,j C,j C,j ⎪ Lr,2 = ρr + cd ¯tG,r + ISBCG + MrC T − γC,2 I¯1,r + λ2 N¯ 2 + γC,2 κDCBC + ε(Lr,2 )⎪ ⎪ ⎪ ⎪ ⎪ E,j j E,j E,j E,j G,j G E G ⎪ Lr,1 = ρr + cd ¯tG,r + ISBE + Mr T − I¯1,r + λ1 N¯ 1 + κDCB + ε(Lr,1 )⎪ ⎪ ⎪ ⎪ ⎪ E,j j E,j E,j E,j E,j G E E ¯ ¯ Lr,2 = ρr + cd ¯tG,r + ISBE + Mr T − γE,2 I1,r + λ2 N2 + γE,2 κDCB + ε(Lr,2 )⎭ (4)

The expression of the above parameters is as follows: ⎫ cd ¯tG,r = cdtG,r + cdtG,IF ISBSG = d ¯trS − d ¯trG ⎪ ⎪ ⎪ ⎪ S S ⎪ ¯I S,j = I S,j + κDCBrS DCBrS = dr,1 − dr,2 ⎬ 1,r 1,r S,j S,j S,j S,j ⎪ λf N¯ f = λf (Nf + bSr,f − bSj,f )⎪ ⎪ ⎪ ⎪ 2 2 2 2 2 ⎭ γS,2 = f1 /f2 κ = f2 /(f1 − f2 )

(5)

Where: cd ¯tG,r is receiver clock offsets included ionosphere-free code bias; ISBSG S,j denote inter-system bias; I¯1,r is ionosphere delay included receiver DCB; Assuming that M satellites are observed, the number of parameters of BDS/GPS/Galileo dual frequency undifferenced and uncombined PPP is as follows: ⎫ S,j S,j S,j X = [X , Y , Z, T , cd ¯tG,r , ISBCG , ISBEG , (I¯ 1.r ), (N1 ), (N2 )]⎪ ⎪ ⎪ ⎪ S,j G,NG ¯ C,1 C,NC ¯ E,1 E,NE ⎪ G,1 ¯ ¯ ¯ ¯ ¯ (I ) = [ I ···I ,I ···I ,I ···I ]⎬ 1.r

S,j (N1 ) S,j (N2 )

1,r

1,r

1,r

1,r

1,r

1,r

⎪ = [N¯ 1G,1 · · · N¯ 1G,NG , N¯ 1C,1 · · · N¯ 1C,NC , N¯ 1E,1 · · · N¯ 1E,NE ]⎪ ⎪ ⎪ ⎪ ⎭ G,N C,N E,N G,1 C,1 E,1 E G C = [N¯ 2 · · · N¯ 2 , N¯ 2 · · · N¯ 2 , N¯ 1 · · · N¯ 1 ]

(6)

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3 Parameter Processing Strategy 3.1 ISB Processing Strategy The precision clock products released by IGS/MGEX Analysis Center unify the time of other navigation systems into the GPS time frame, However, when calculating the satellite clock difference, the reference clocks selected by different systems are different, and the hardware delay caused by the signal after entering the channel is different due to the different carrier characteristics of the navigation systems at the receiver, so GNSS PPP needs to handle ISB correctly. In this paper, ISB adopts three processing strategies: white noise, random walk and constant. 1) White noise processing strategy (PPP model based on this strategy is called PPP-WN model, the same below). The ISB is treated as white noise, and the epoch before and after ISB is considered to be independent of each other. When Kalman filtering is performed, the state transition coefficient is 0, and the process noise adopts a large variance, and the variance is set to 109 m2 : ISBrS ∼ N (0, σ 2 )

(7)

2) Random walk processing strategy PPP-AR). The ISB is treated as random walk, It is considered that there is correlation between the epoch before and after the ISB. The filtering solution of the previous epoch ISB ISBrS (K − 1) is transferred and consider time-varying part of ISB ωk , the state transition coefficient is 1 and the process noise is considered 0.001 m2 :  ISBrS (K) = ISBrS (K − 1) + ωk (8) ωk ∼N (0, 0.001) 3) Constant processing strategy (PPP-CV). When the ISB is treated as a constant, it is considered that the ISB is very stable between epochs and is not consider by the change of time, the state transition coefficient is 1 and the process noise is 0:  ISBrS (K) = ISBrS (K − 1) (9) σ2 = 0 3.2 FCB Processing Strategy High accuracy of FCBs is the premise of correctly fixing ambiguity and fast PPP convergence. Based on the time-varying characteristics of FCBS in wide/narrow-lanes, this paper uses Kalman filtering method to estimate FCBs. The specific processing strategies are as follows: 1) Wide-lane FCB estimation strategy at satellite end. The satellite side FCB is relatively stable in a single day. The reference [20] shows that the wide lane FCB can converge to within 0.1 cycle in the continuous arc without cycle slip and keep stable. Therefore, this paper takes the satellite wide-lane FCB as a constant estimation, and the specific processing strategies are as follows:

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FCBj,WL (K) = FCBj,WL (K − 1)



σ2 = 0

(10)

2) Wide-lane FCB estimation strategy at receiver end. The experiments in reference [20] show that the wide-lane FCB at the receiver end is not stable in a single day, and the maximum variation in one day can reach 0.4 cycle. Therefore, in this paper, the receiver wide lane FCB is taken as random walk estimation, and the specific processing strategies are as follows:  FCBr,WL (K) = FCBr,WL (K − 1) (11) σK2 = ω2 3) FCB estimation strategy for narrow-lane at satellite end. Compared with the widelane FCB at the satellite end, the FCB of the narrow-lane at the satellite end is stable for 10 min, and the interval between 10 min and 15 min has a certain change. Therefore, the 10 min FCB of the satellite end narrow-lane is taken as a constant estimation, and the interval of 10 min is taken as the random walk estimation. The specific processing strategies are as follows: ⎫ FCBS,NL (K) = FCBS,NL (K − 1)⎪ ⎬ σK2 = 0(t < 10 min) ⎪ ⎭ σK2 = ω2 (t >= 10 min)

(12)

4) Narrow-lane FCB estimation strategy at receiver end. Because the hardware delay part is easily affected in the observation environment, the FCB stability of narrow-lane at the receiver end is non-relatively. In this paper, white noise processing is carried out, and the specific processing strategies are as follows: FCBr,NL (K) ∼ N (0, ω2 )

(13)

4 Results and Discussion 106 IGS/MGEX stations are evenly selected in this paper. The distribution of the stations is shown in Fig. 1 (server stations in red and user stations in blue). The sampling interval of observation data is 30 s, and the observation time is 5–11 days in 2019. The precise ephemeris products with 5 min interval and precision clock products with 30 s interval are provided by GFZ. Three ISB processing strategies are used to generate FCB products, namely CV-FCB, RW-FCB and WN-FCB, respectively, and broadcast three kinds of undifferenced FCB products to fix the ambiguity.

Influence of Different ISB Processing Strategies

261

Fig. 1. Distribution of stations

4.1 Characteristic Analysis of FCBs The time-varying characteristics of FCBs and the accuracy of posteriori residuals are important indexes to evaluate the quality of FCBs. This paper will analyze the quality of three FCBs in these two aspects. 1) Analysis on undifferenced wide-lane FCB characteristics Three FCB products from 5 to 11, January, 2019 are selected to analyze the timevarying characteristics of long-time wide-lane FCB. Figures (a) and (b) are BDSMEO and BDS-IGSO satellite wide-lane FCB sequence diagrams, as shown in Fig. 2. It can be seen that the time stability of wide-lane CV-FCB, RW-FCB and WN-FCB is similar, but BDS-IGSO satellite wide-lane FCB is better than BDSMEO satellite. The main reason is that the number of MEO satellites is less, the continuous observation arc length is short, so the ambiguity convergence is low. In order to further analyze the time stability of three kinds of wide-lane FCB products, the STD of 7-day wide-lane FCB is counted, as shown in Fig. 3. It can be seen that the STD of three kinds of wide-lane FCB is basically the same, RW-FCB and WN-FCB are slightly better than CV-FCB. But the STD of IGSO FCB is less than 0.03 cycle, which is obviously better than that of MEO satellite. The distribution of FCB posterior residuals is an index that can directly reflect the accuracy of FCB products. The posterior residuals of wide-lane FCB with annual product date of the 6th day of 2019 are selected. As shown in Fig. 4, it can be seen that the posterior residuals distribution of satellite FCB of three BDS are basically the same. Table 1 is the residual distribution of three wide-lane FCB in 7 days. It can be seen from the table that the estimation accuracy of FCB of three wide lanes is basically the same, indicating that It shows that different ISB processing strategies have no effect on wide-lane FCB estimation accuracy.

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Fig. 2. Three wide-lane FCB series of BDS satellites from DOY 5 to DOY 11

Fig. 3. STD of undifferenced wide-lane FCB

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Fig. 4. Posterior residuals of three wide-lane FCBs

Table 1. Comparison of different wide-lane FCB residual distribution in seven days Date

Type CV-WL-FCB

5

6

7

8

9

10

11

RW-WL-FCB

WN-WL-FCB

Interval/cycle

Proportion

Interval/cycle

Proportion

Interval/cycle

Proportion

(−0.25, 0.25)

91.7%

(−0.25, 0.25)

91.8%

(−0.25, 0.25)

92.0%

(−0.15, 0.15)

82.8%

(−0.15, 0.15)

82.8%

(−0.15, 0.15)

83.0%

(−0.05, 0.05)

44.6%

(−0.05, 0.05)

44.8%

(−0.05, 0.05)

44.9%

(−0.25, 0.25)

93.4%

(−0.25, 0.25)

93.2%

(−0.25, 0.25)

93.1%

(−0.15, 0.15)

86.3%

(−0.15, 0.15)

86.1%

(−0.15, 0.15)

85.9%

(−0.05, 0.05)

49.4%

(−0.05, 0.05)

49.2%

(−0.05, 0.05)

49.0%

(−0.25, 0.25)

90.8%

(−0.25, 0.25)

90.6%

(−0.25, 0.25)

90.6%

(−0.15, 0.15)

83.3%

(−0.15, 0.15)

83.2%

(−0.15, 0.15)

83.2%

(−0.05, 0.05)

47.4%

(−0.05, 0.05)

47.5%

(−0.05, 0.05)

47.6%

(−0.25, 0.25)

91.1%

(−0.25, 0.25)

91.1%

(−0.25, 0.25)

91.1%

(−0.15, 0.15)

85.1%

(−0.15, 0.15)

85.2%

(−0.15, 0.15)

85.1%

(−0.05, 0.05)

49.2%

(−0.05, 0.05)

49.1%

(−0.05, 0.05)

49.2%

(−0.25, 0.25)

94.0%

(−0.25, 0.25)

93.6%

(−0.25, 0.25)

93.6%

(−0.15, 0.15)

86.2%

(−0.15, 0.15)

86.3%

(−0.15, 0.15)

86.4%

(−0.05, 0.05)

48.7%

(−0.05, 0.05)

49.6%

(−0.05, 0.05)

49.6%

(−0.25, 0.25)

92.9%

(−0.25, 0.25)

93.0%

(−0.25, 0.25)

92.9%

(−0.15, 0.15)

87.0%

(−0.15, 0.15)

87.2%

(−0.15, 0.15)

87.1%

(−0.05, 0.05)

50.3%

(−0.05, 0.05)

50.4%

(−0.05, 0.05)

50.3%

(−0.25, 0.25)

93.1%

(−0.25, 0.25)

93.0%

(−0.25, 0.25)

93.0%

(−0.15, 0.15)

86.5%

(−0.15, 0.15)

86.4%

(−0.15, 0.15)

86.4%

(−0.05, 0.05)

48.0%

(−0.05, 0.05)

47.8%

(−0.05, 0.05)

47.7%

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2) Analysis on undifferenced narrow-lane FCB characteristics The ionosphere-free ambiguity is affected by narrow-lane FCB, so high precision of narrow-lane FCB is the key to PPP-AR. Compared with wide-lane FCB, the stability of narrow-lane FCB is low. The FCB of narrow-lane with 10 min interval is estimated as random walk process, and once is estimated every 10 min. The single day time-varying characteristics of three kinds of narrow-lane FCB are shown in Fig. 5. (a) is IGSO satellite narrow-lane FCB, and (b) is MEO satellite narrow-lane FCB. And it can be seen that the FCB stability of IGSO satellite is better than that of MEO satellite.

Fig. 5. Three narrow-lane FCB series of BDS satellites

In order to further analyze the accuracy of different FCB products, Posterior residuals of the narrow-lane FCB product on the 6th day of 2019 is selected, and the distribution is shown in Fig. 6. It can be seen that the residual distribution of RW-FCB and WN-FCB in narrow-lane is similar, and it is obviously better than CV-FCB in narrow-lane, which increases about 10% in (−0.25, +0.25) cycle, 14% in (−0.15, +0.15) cycle, and 18% in (−0.05, 0.05) cycle. In Table 2, the residual distribution of three kinds of narrow-lane FCB in 7 days is counted. It can be seen from the table that compared with CV-FCB, RW-FCB and WN-FCB about improvement 7.5%, 10.6% and 12.2% in (−0.25, +0.25), (−0.15, +0.15) and (−0.05, +0.05), respectively, which indicates that different ISB

Fig. 6. Posterior residuals of three narrow-lane FCB

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265

processing strategies have great influence on FCB estimation accuracy of narrow-lane, and ISB should be regarded as random walk process or white noise estimation. The possible reason is that narrow-lane ambiguity is more sensitive to the error, and the inappropriate parameter processing strategy has a greater impact on the narrow-lane ambiguity, so the precision of narrow-lane FCB is relatively lower. Table 2. Comparison of different wide-lane FCB residual distribution in multi day Date

Type CV-NL-FCB

5

6

7

8

9

10

11

RW-NL-FCB

WN-NL-FCB

Interval/cycle

Proportion

Interval/cycle

Proportion

Interval/cycle

Proportion

(−0.25, 0.25)

82.8%

(−0.25, 0.25)

90.8%

(−0.25, 0.25)

90.8%

(−0.15, 0.15)

76.8%

(−0.15, 0.15)

88.6%

(−0.15, 0.15)

88.4%

(−0.05, 0.05)

54.9%

(−0.05, 0.05)

68.7%

(−0.05, 0.05)

68.7%

(−0.25, 0.25)

81.1%

(−0.25, 0.25)

91.7%

(−0.25, 0.25)

91.4%

(−0.15, 0.15)

73.5%

(−0.15, 0.15)

87.4%

(−0.15, 0.15)

96.9%

(−0.05, 0.05)

50.4%

(−0.05, 0.05)

68.1%

(−0.05, 0.05)

67.7%

(−0.25, 0.25)

80.8%

(−0.25, 0.25)

87.7%

(−0.25, 0.25)

87.6%

(−0.15, 0.15)

72.9%

(−0.15, 0.15)

82.1%

(−0.15, 0.15)

82.0%

(−0.05, 0.05)

53.5%

(−0.05, 0.05)

62.5%

(−0.05, 0.05)

62.3%

(−0.25, 0.25)

80.0%

(−0.25, 0.25)

89.3%

(−0.25, 0.25)

89.1%

(−0.15, 0.15)

73.6%

(−0.15, 0.15)

83.6%

(−0.15, 0.15)

83.5%

(−0.05, 0.05)

53.5%

(−0.05, 0.05)

65.5%

(−0.05, 0.05)

63.9%

(−0.25, 0.25)

84.1%

(−0.25, 0.25)

90.0%

(−0.25, 0.25)

98.4%

(−0.15, 0.15)

76.4%

(−0.15, 0.15)

84.8%

(−0.15, 0.15)

94.4%

(−0.05, 0.05)

53.3%

(−0.05, 0.05)

64.5%

(−0.05, 0.05)

64.5%

(−0.25, 0.25)

81.3%

(−0.25, 0.25)

85.9%

(−0.25, 0.25)

86.2%

(−0.15, 0.15)

74.2%

(−0.15, 0.15)

80.1%

(−0.15, 0.15)

80.0%

(−0.05, 0.05)

51.2%

(−0.05, 0.05)

61.4%

(−0.05, 0.05)

61.6%

(−0.25, 0.25)

86.2%

(−0.25, 0.25)

88.5%

(−0.25, 0.25)

89.6%

(−0.15, 0.15)

78.3%

(−0.15, 0.15)

83.3%

(−0.15, 0.15)

84.3%

(−0.05, 0.05)

54.8%

(−0.05, 0.05)

67.0%

(−0.05, 0.05)

66.9%

4.2 Positioning Result Analysis Table 3 Statistics the time to first fix and fixed rate of ambiguity of 13 stations using three FCB products. It can be seen from the table that PPPAR-RW and PPPAR-WN are better than PPPAR-CV model in average time to first fix and fixed success rate of

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ambiguity, with an increase of about 19.5% and 15.5%, respectively. Table 4 shows the positioning accuracy of 13 stations using three FCB products. The 3D positioning accuracy of PPPAR-CV model is 11.07 cm, 7.35 cm and 6.09 cm in 30 min, 60 min and 120 min, respectively. PPPAR-WN and PPPAR-RW are basically the same, but better than PPPAR-CV, which are improved by about 6.3 cm, 3.9 cm and 3.6 cm respectively. It can be seen that the inaccurate processing of ISB parameters has a great influence on the narrow-lane ambiguity which is more sensitive to the error, which influence the convergence accuracy of short-time ambiguity, reduces the estimation accuracy of FCB in narrow-lane, and further affects the time to first time, fixed rate and short-time fixed solution accuracy of ambiguity (Table 4). Table 3. Time to first fix and success rate Station

PPPAR-CV

PPPAR-RW

PPPAR-WN

First fixed time/min

Success rate/%

First fixed time/min

Success rate/%

First fixed time/min

Success rate/%

DARW

29.65

62.94

26.37

71.16

26.41

71.16

GMSD

25.83

66.35

24.33

79.68

23.33

81.35

HKSL

27.07

59.49

25.75

79.19

25.45

80.48

JFNG

32.25

59.03

27.08

78.36

26.95

82.45

KARR

29.05

84.42

18.5

92.91

17.54

89.50

METG

30.00

42.02

16.00

51.08

15.87

49.60

MRO1

25.27

91.85

21.33

92.12

21.92

91.92

NNOR

28.65

95.56

17.83

93.21

18.16

92.98

PERT

28.95

87.04

24.25

91.51

23.5

91.81

SEYG

36.25

37.40

29.25

65.70

29.6

56.99

STR1

25.59

86.54

23.45

91.20

23.66

89.42

SYDN

33.13

59.03

30.72

72.60

31.77

67.10

XMIS

26.36

74.76

19.25

88.44

19.13

86.28

平均

29.08

69.72

23.40

80.55

23.41

79.31

6.45

7.75

11.07

E

U

3D

6.37

5.06

2.66

6.33

5.03

2.63

1.21

PPPAR-WN

7.35

4.94

4.52

1.12

PPPAR-CV

1.21

PPPAR-RW

PPPAR-CV

1.96

60 min

30 min

N

Direction

3.92

2.94

1.68

0.79

PPPAR-RW

3.92

2.94

1.68

0.78

PPPAR-WN

Table 4. Positioning error of different PPP-AR cm

6.09

2.96

4.22

0.88

PPPAR-CV

120 min

3.65

2.64

1.65

0.81

PPPAR-WN

3.65

2.93

1.64

0.81

PPPAR-WN

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5 Conclusions In this paper, through different ISB processing strategies, using the 106 evenly distributed IGS/MGEX station network, are used to estimate three FCBs product, namely CV-FCB, RW-FCB and WN-FCB. The effects of different ISB processing strategies on FCBs estimation accuracy and PPP-AR positioning are analyzed: 1) When ISB is treated as constant, white noise and random walk process, the accuracy of FCB products in wide-lane FCB is equivalent. In narrow-lane FCB, the accuracy of WN-FCB and RW-FCB is the same, which is better than CV-FCB products. In the range of (−0.25, +0.25), (−0.15, +0.15), (−0.05, +0.05) cycle, the accuracy of WN-FCB and RW-FCB are increased by 7.5%, 10.6% and 12.2%, respectively. 2) In terms of the first convergence time and fixed success rate of ambiguity, PPPARWN and PPPAR-RW are basically the same, which are improved by about PPPARCV model, they are improved by about 19.5% and 15.5% respectively. 3) in terms of positioning accuracy, the 3D positioning accuracy of PPPAR-CV model is 11.07 cm, 7.35 cm and 6.09 cm at 30 min, 60 min and 120 min respectively, while PPPARRW and PPPAR-WN are basically equivalent, but better than PPPAR-CV, with an increase of about 6.3 cm, 3.9 cm, 3.6 cm at 30 min, 60 min, 120 min.

References 1. Yuanxi, Y.: Progress, contribution and challenges of compass/beidou satellite navigation system. Acta Geodaetica Cartogr. Sin. 39(1), 1–6 (2010) 2. Yangyin, X., Yuanxi, Y., Haibo, H., Jinlong, L., et al.: Quality analysis of the range measurement signals of test satellites in BeiDou global system. Geomat. Inf. Sci. Wuhan Univ. 43(8), 1214–1221 (2018) 3. Yang, Y.X., Li, J.L., Wang, A.B., et al.: Preliminary assessment of the navigation and positioning performance of BeiDou regional navigation satellite system. Sci. China Earth Sci. 57(1), 144–152 (2014) 4. Thoelery, S., Steigenberger, P., Montenbruck, O., et al.: Signal analysis of the first GPS III satellite. GPS Solutions 23, 92 (2019) 5. Jokinen, A., Feng, S., Milner, C., et al.: Improving fixed-ambiguity Precise Point Positioning (PPP) convergence time and accuracy by using GLONASS. In: International Technical Meeting of the Satellite Division of the Institute of Navigation. 2012, pp. 3708–3727 (2012) 6. Li, P., Zhang, X.: Integrating GPS and GLONASS to accelerate convergence and initialization times of precise point positioning. GPS Solutions 18(3), 461–471 (2014) 7. Jokinen, A., Feng, S., Schuster, W., et al.: GLONASS aided gps ambiguity fixed precise point positioning. J. Navigation 66(3), 399–416 (2013) 8. Tegedor, J., Øvstedal, O, Vigen, E.: Precise orbit determination and point positioning using GPS, Glonass, Galileo and BeiDou. J. Geodetic Sci. 4(1), 2081–9943 (2014) 9. Research on Methodology of Rapid Ambiguity Resolution for GNSS Precise Point Positioning. Wu Han: Wuhan University (2016) 10. Zhou, Z.: Theory and Methods of Precise Point Positioning and Its Quality Control with Multi-GNSS. Information Engineering University (2018) 11. Li, X., Ge, M., Dai, X., et al.: Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo. J. Geodesy 89(6), 607–635 (2015)

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12. Cai, C., Gao, Y., Pan, L., et al.: Precise point positioning with quad-constellations: GPS, BeiDou, GLONASS and Galileo. Adv. Space Res. 56(1), 133–143 (2015) 13. Lou, Y., Zheng, F., Gu, S., et al.: Multi-GNSS precise point positioning with raw singlefrequency and dual-frequency measurement models. GPS Solutions 20(4), 849–862 (2016) 14. Chen, J., Zhang, Y., Wang, J., et al.: A simplified and unified model of multi-GNSS precise point positioning. Adv. Space Res. 55(1), 125–134 (2015) 15. El-Mowafy, A., Deo, M., Rizos, C.: On biases in precise point positioning with multiconstellation and multi-frequency GNSS data. Measurement ence Technol. 27(3), (2016) 16. Jin, W., Yuanxi, Y., Qin, Z., et al.: Analysis of inter-system bias in multi-GNSS precise point positioning. Geomatics Inf. Sci. Wuhan Univ. 44(004), 475–481 (2019) 17. Liu, T., Yuan, Y., Zhang, B., et al.: Multi-GNSS precise point positioning (MGPPP) using raw observations. J. Geodesy 91(3), 253–268 (2017) 18. De Bakker, P.F., Tiberius, C.C.J.M.: Real-time multi-GNSS single-frequency precise point positioning. GPS Solutions 21(4), 1791–1803 (2017) 19. Feng, Z., Danan, D., Pan, L., et al.: Influence of stochastic modeling for inter-system biases on multi-GNSS undifferenced and uncombined precise point positioning. GPS Solutions 23(3), 59–71 (2019) 20. Xiaohong, Z., Pan, L., Xingxing, L., Feng, Z., Xiang, Z.: An analysis of time-varying property of widelane carrier phase ambiguity fractional bias. Acta Geodaetica Cartogr. Sin. 42(6), 798–803 (2013)

Co-channel Interference Cancellation Method Based on Deep Neural Network for LEO Satellite Systems Jie Sun, Zuping Tang(B) , Jiaolong Wei, and Yiwen Ren School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan 430074, China [email protected]

Abstract. Low earth orbit (LEO) satellite navigation augmentation system has higher ground received signal power and faster Doppler change than Global Navigation Satellite System (GNSS), improving the positioning accuracy with occlusion and shortening the time of integer ambiguity-fixing. Aggressive frequency reuse reduces the complexity of user receiver implementation, but causing harsh co-channel interference at the meantime. The co-channel interference cancellation can alleviate the interference and improve orbit determination precision with receivers on board LEO satellites. Hence, this paper proposes a method based on deep neural network, which can accurately reconstruct the transmitted signal component coupled into the receiver, and then eliminate its interference to the weak GNSS signal. Finally, a simulation analysis is carried out with the BDS B1 frequency signal, which illustrates that this method can be adapted to different types of non-ideal channels. This method has good co-channel interference cancellation effect, and provides a technical reference for signal broadcasting of LEO navigation augmentation. Keywords: Global navigation satellite systems · Low earth orbit navigation augmentation · Co-channel interference cancellation · Deep neural network

1 Introduction Global Navigation Satellite Systems (GNSS) can provide global continuous and realtime positioning services and is widely used in various fields. However, the existing GNSS have weak landing signal strength and low information transmission rate and other limitations. LEO satellites can complement medium-high earth orbit satellites. Compared with high-orbit satellites, LEO satellites have higher ground received signal power when the same satellite launches equivalent omnidirectional radiation power [1], and improve the positioning effect under obscured conditions. The fast motion of LEO satellites contributes to the obvious Doppler frequency shift, which is beneficial to improve the accuracy of speed measurement and detect cycle slip errors [2], thus it is conducive to rapid convergence of precise positioning. As an enhancement and supplement to the global satellite navigation systems, it improves the accuracy, availability and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 270–279, 2021. https://doi.org/10.1007/978-981-16-3142-9_24

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integrity of navigation and positioning. In the LEO satellite navigation augmentation system, the augmentation signal and the navigation signal are transmitted and received in the same frequency, which can reduce the complexity of the GNSS receiver, and is conducive to terminal implementation. However, when the center frequency of the augmentation signal is close to the navigation signal, and the power of enhancement signal is much higher than that of navigation signal at the GNSS receiver, the GNSS receiver’ normal operation will be seriously affected. Traditional interference cancellation techniques include air-domain interference cancellation, analog-domain interference cancellation, and digital-domain self-interference cancellation [3]. The interference suppression technology of the same frequency in the air-domain and analog-domain works in front of the analog-to-digital converter (ADC). The air interference suppression technology is complex to realize, which makes full uses of the natural isolation of the antenna, physical characteristics and beamforming technology to reduce the interference signal intensity in the same frequency. The analog-domain interference suppression technology suppresses the self-interference signal in the RF processing unit, and reconstructs the radio frequency domain self-interference signal by adjusting its time delay, amplitude and phase, and subtracts it from the received radio frequency signal. The digital domain interference suppression technique work after the ADC, for suppressing the interfering signal from the digital processing unit. The selfinterference signal in the digital domain is reconstructed and subtracted from the received digital signal. However, estimation and reconstruction errors of co-band interference channel parameters, amplifier nonlinearity and other factors restrict the effectiveness of these two interference suppression technologies, and the performance of anti-coband interference is limited, which cannot meet the requirements of the navigation enhancement platform for high-precision measurement processing. Digital-domain interference cancellation technology mainly focuses on accurately capturing channel state information and compensating for hardware errors [4]. As the nonlinear model at the receiver is being established [4], nonlinear interference signals are reconstructed to suppress interference, but the implementation of the interference cancellation model is more complicated. The extra receiving channel is used to extract the noise at the receiver [5], and suppresses the phase noise of the receiving end by sharing the crystal oscillator between the receiving channel and the extra receiving channel to suppressing the noise at the receiver, but this method sacrifices the system effective transmission rate. The present co-channel interference cancellation methods have the disadvantages of complex implementation and limited anti-co-band interference performance. To solve this problems, a digital domain interference cancellation method based on deep neural network is proposed in this paper, which accurately reconstructs the transmitted signal component coupled into the receiver in the digital domain. This method realizes low cost interference cancellation in the same frequency band transceiver, and avoids the weak GNSS signal being annihilated in the augmentation signal.

2 System Model The co-frequency transceiver model of the LEO navigation augmentation platform is shown in Fig. 1. It is assumed that the GNSS receiving antenna receives the GNSS

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signal for orbit determination and time synchronization, at the same time, the augmentation signal transmitting antenna transmits the augmentation signal with the same signal modulation and same frequency on LEO satellites. Inevitably, when the GNSS receiving antenna receives the GNSS signal, it will be mixed with the enhanced signal transmitted from the transmitting antenna. Here, SRGNSS is the GNSS signal, SRLEO is the augmentation signal coupled into GNSS receiver. STLEO is the augmentation signal emitted by LEO satellites. Under general circumstances, the power of SRLEO is much higher than that of SRGNSS , therefore GNSS signal will be annihilated in the augmentation signal, seriously affecting the normal work of GNSS receiver.

Fig. 1. The co-frequency transceiver model of the LEO navigation augmentation

2.1 RF Channel Model In order to accurately reconstruct the transmitted signal coupled into the receiver, first we establish a RF channel model to obtain the augmentation signal transmitted from the antenna, and then analyze the interference signal model of the augmentation signal propagating through the non-ideal channel to the GNSS receiving antenna. The LEO satellites receive GNSS signals for orbit determination and time synchronization, at the same time, they transmit augmentation signal at the same frequency and modulation. The non-ideal characteristics of the RF channel will cause distortion of the navigation signal. Taking the BeiDou Navigation Satellite System (BDS) B1 frequency as an example, in order to mitigate the distortion of combined signals when passing through the high power amplifier (HPA), the constant envelope multiplexing technology, namely POCET, is used to generate a standardized constant envelope multiplexing augmentation signal sTLEO ,ideal in the LEO satellites transmit antenna.

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The B1I signal SB1I (t) is SB1I (t) = AB1I CB1I (t)DB1I (t) cos(2π fB1I t + ϕB1I )

(1)

where AB1I is the B1I signal amplitude, fB1I is carrier frequency, ϕB1I is the carrier initial phase. The B1C signal SB1C (t) is SB1C (t) = AB1C (SB1C_data (t) + jSB1C_pilot (t)) cos(2π fB1C t + ϕB1C )

(2)

where AB1C is the B1C signal amplitude, fB1C is the carrier frequency, ϕB1C is the carrier initial phase. The composition structure of the B1A signal is similar to B1C signal, consisting of data signal and pilot signal. The B1A signal SB1A (t) is SB1A (t) = AB1A (SB1A_data (t) + jSB1A_pilot (t)) cos(2π fB1A t + ϕB1A )

(3)

where AB1A is the B1A signal amplitude, fB1A is the carrier frequency, ϕB1A is the carrier initial phase. The constant envelope combined signal at BDS B1 frequency is:    jθB1 I + PB1 A SB1 A (t)ejθB1 A + PB1 C SB1 C (t)ejθB1 C + IM (t) STLEO ,ideal (t) = PB1 I SB1 I (t)e (4) where Pi and θi is the power and initial phase of the ith transmitted signal, i = B1 I , B1 C, B1 A, IM (t) is an indispensable part for the composite signal to keep constant envelope. The linear distortion of the navigation signal generation unit and the frequency generation and up-conversion unit can be characterized by a pre-filter before HPA. The linear distortion of the output multiplexer and antenna can be characterized by a post-filter after HPA. The combined signal STLEO ,ideal first goes through the pre-filter and introduces linear distortion in the process of modulation and filtering. Then it goes through the memoryless nonlinear high power amplifier, and the memory characteristics of the HPA are incorporated into the post-filter. Next, the linear distortion of the multiplexer and antenna is introduced by the post-filter. Finally, the ideal augmentation signal STLEO ,ideal (t) is transmitted in RF (Fig. 2).

Fig. 2. Equivalent model of RF baseband channel

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The HPA is based on Saleh model. Assuming that r is the complex envelope amplitude of input signal, A(r) is the equivalent baseband signal amplitude and φ(r) is equivalent baseband signal phase offset. A(r) =

αφ r 2 αa r , ϕ(r) = 1 + βa r 2 1 + βφ r 2

(5)

where αa , βa , αφ , βφ determine the degree of amplitude and phase distortion. 2.2 Co-frequency Interference Signal Model of LEO Satellite Enhancement Signal The ideal augmentation signal propagates through the non-ideal channel and is received by the GNSS receiving antenna, including the influence of multipath effect: SRLEO =

L 

hl STLEO (t−τl )

(6)

l=1

where L is the number of multipath, hl is the amplitude attenuation of the l th path, τl is the transmission delay of the l th path. The combined signal received at the GNSS receiver is: Stotal = SRGNSS + SRLEO + n

(7)

where SRGNSS is the received GNSS signal, SRLEO is the augmentation signal coupled into the GNSS receiver, n is the noise of the channels (Fig. 3).

Fig. 3. The multiple signal spectrum obtained at the receiver

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3 Interference Cancellation Method 3.1 Interference Cancellation Model The interference cancellation signal process is shown in Fig. 4. In practice, the receiver doesn’t know the channel model and parameters. The “Estimation and simulation of transceiver coupling channel” module blindly estimates the channel characteristics, based on the prior information of the ideal transmitted signal and the received signal. Then the estimated value of the transmitted signal coupled into the receiver is obtained, which is used to eliminate the augmentation signal coupled into the received signal. To accommodate different types of channel, the method proposed in this article bases on neural network. Due to the existence of channel estimation error, there is an augmentation LEO . signal residual error in the eliminated signal SR,res

Fig. 4. Interference cancellation signals process

The reconstructed interference signal contains the influence of multipath effects, HPA nonlinearity, and residual frequency offset. The interference suppression process can be completed by subtracting the residual interference signal from the reconstructed signal, and the final residual interference signal is. LEO LEO = SRLEO − ST,ideal SR,res

(8)

The ideal cancellation is to minimize the mean square value of the system output error and realize complete cancellation, so as to achieve the purpose of interference cancellation, which is: LEO 2 LEO ) } = minE{(SRLEO − ST,ideal )2 } E{(SR,res

(9)

3.2 Network Model Due to the difficulty of extracting the parameters of the proposed RF channel model, this paper proposes to use the neural network method to realize the “Estimation and simulation of transceiver coupling channel” module. Neural networks have good nonlinear fitting and self-adaptive capabilities, and can complete complex tasks such as pattern classification, function approximation, and optimization calculations. It has been widely used in pattern recognition, system identification, signal processing, adaptive filtering,

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channel equalization and other fields [6, 7]. Our method is based on neural network to reconstruct the transmitted signal coupled into the receiver, then eliminate augmentation signals’ interference to weak GNSS received signals. The network is divided into an input layer, 3 hidden layers and an output layer. An adaptive gradient algorithm is used to train the network. The network uses the N = 256 sampling point before and the N = 256 sampling point after this moment of the augmentation signal, to obtain the value of the current sampling point of the received signal with distortion. Because the signal is composed of real and imaginary parts, the neural network can only handle real constant number. So the augmentation signal is divided into two parts, the real part and the imaginary part, as the neural network’s input data. Therefore, the input layer of the neural network has 2 nodes, while the number of nodes in the output layer is 2, and the number of neurons in the hidden layer is 1500, 800, and 250 respectively. The choice of activation function has a great influence on the output of the network. Since the ReLU activation function commonly used in neural networks has the effect of unilateral inhibition. All negative values are changed to 0 which will cause too much feature masking, and the model cannot learn to be effective feature, so the leaky_relu function is used as the activation function of the neural network (Table 1). Table 1. Network training parameters Batch_size

32

Optimization algorithm Adam Loss function

MSE

Epoch

15

4 Performance Analysis In order to verify the performance of the co-channel interference cancellation method based on deep neural networks, this paper carries out a simulation of the received signal coupled with the augmentation signal at the GNSS receiving antenna and the eliminated signal. The simulation parameters are as follows: Take the BDS B1 frequency signal as an example, the bandwidth is 36 MHz, the sampling rate is 100 Msps, and the data duration is 1 s. In the BeiDou Navigation Satellite System, two new service signals have been added to the B1 frequency: a civilian service B1C and a military service B1A. In order to facilitate interoperability with GPS and Galileo, the center frequency is adjusted to 1575.42 MHz. B1C adopts MBOC (6, 1, 1/11) modulation to achieve interoperability with GPS L1C and Galileo E1OS. The data component B1Cd uses BOC (1, 1) modulation, the pilot component B1Cp uses QMBOC (6, 1, 4/33) modulation, and the carrier phase of BOC (1, 1) and BOC (6, 1) is orthogonal. B1A uses BOC (14, 2) modulation, which is also composed of data components and pilot components. At the same time, in

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order to maintain backward compatibility, the Beidou second-generation navigation signal B1I needs to be simultaneously transmitted. The center frequency of B1I is located at 1561.098 MHz, and B1I uses BPSK (2) modulation. The parameters [8] are shown in Table 2: Table 2. Parameters of Beidou B1 frequency signal Signals Carrier frequency (MHz)

Modulation

B1Cd

BOC (1, 1)

1575.42

B1Cp

QMBOC (6, 1, 4/33)

B1Ad

BOC (14, 2)

B1Ap B1I

1561.098

BPSK (2)

In this article, the assumptions are as follows: (1) The signal-to-noise ratio of the GNSS signal received by the GNSS receiver is −20 dB; (2) The power ratio of the augmentation signal coupled into the GNSS receiver is 80 dB higher; (3) The ideal augmentation signal transmitted by the LEO satellite is known. In Fig. 5 and Fig. 6, “Ideal transmit signal after power adaptation” refers to the waveform of the ideal transmit signal after linear amplification. For convenience, the amplified signal power is matched with the received signal power in the receiver; “Interference distorted received signal” refers to the combined signal obtained at the GNSS receiver, and “Network-fitted received signal” refers to the estimated value of the transmitted signal coupled into the receiver. From the simulation result, it can be seen that

Fig. 5. Fragments and details of I-channel signal waveform

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Fig. 6. Fragments and details of Q-channel signal waveform

due to the existence of non-ideal factors such as nonlinear amplification, there is a significant difference between the ideal waveform and the received interference waveform, and the “received signal of network fitting” is almost the same as “received signal with interference distortion” received in the receiver. It shows that the neural network can fit the combined signal of the GNSS receiving antenna coupled with the augmentation signal better. To assess the effect of co-channel interference cancellation, the interference suppression ratio is used as the evaluation index, which is expressed as: γ=

SRLEO LEO SR,res

(9)

The residual error after interference cancellation is shown in Fig. 7. Statistical value of interference suppression ratio is γ =36 dB.

Fig. 7. The residual of interference signal estimation

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5 Conclusion This paper proposes a co-channel interference cancellation method based on deep neural network. Firstly, LEO augmentation system signal co-frequency interference signal is modeled and analyzed, then the weak GNSS signals is eliminated by accurately reconstructing the transmitted signal coupled into the receiver. The simulation and experimental results show that the method proposed in this paper can adapt to different types of non-ideal channels. If 2 the interference signal power is 60 dB higher than the noise, the interference signal could be mitigated to 36 dB. Therefore, the method has a limited suppression ability, since it is based on pure digital domain and has low cost, it can achieve the ideal effect by combining with other methods, which provides a technical reference for signal broadcasting of LEO augmentation system. Acknowledgments. This work is supported by the Guangdong Provincial Key Area R&D Programme. Project number 2019B010158001.

References 1. Yansong, M., et al.: Global navigation augmentation system based on hongyan satellite constellation. Space Int. 10, 20–27 (2018) 2. Xiaohong, Z., Fujian, M.: Review of the development of LEO navigation-augmented GNSS. Acta Geodaetica Cartogr. Sin. 48(09), 1073–1087 (2019) 3. Li, C., Zhao, H., Fei, W., et al.: Digital self-interference cancellation with variable fractional delay FIR filter for full-duplex radios. IEEE Commun. Lett. 22(5), 1082–1085 (2018). https:// doi.org/10.1109/LCOMM 4. Li, C., Guo, W., Liu, Y., et al.: Nonlinear distortion suppression in cooperative jamming cancellation system. J. Electron. Inf. Technol. 41(9), 2033–2038 (2019). https://doi.org/10.11999/ JEIT180919 5. Ahmed, E., Eltawil, A.M.: All-digital self-interference cancellation technique for full-duplex systems. IEEE Trans. Wireless Commun. 14(7), 3519–3532 (2015) 6. Liu, L., Zhang, J., Fan, Y., et al.: Survey of application of machine learning in wireless channel modelling. J. Commun. 42(02), 134–153 (2020). https://doi.org/10.11959/j.issn.1000-436x. 2021001 7. Gui, G., Wang, Y., Hao, H.: Deep learning based physical layer wireless communication techniques: opportunities and challenges. J. Commun. 40(02), 19–23 (2019). https://doi.org/10. 11959/j.issn.1000-436x.2019043 8. Zhang, M., Kou, Y.: Numerical algorithm for POCET optimal phase search. J. Beijing Univ. Aeronautics Astronautics 43(09), 1917–1923 (2016). https://doi.org/10.13700/j.bh.1001-5965. 2016.0701

A Pseudo-satellite Implementation Method Using High Precision Time Synchronization Ruifeng Zheng(B) Beidou Navigation Technology Co., Ltd., Beijing, China

Abstract. In this paper, a GNSS-based multi-frequency pseudo-satellite implementation method is proposed. The analysis results show that the GNSS multifrequency pseudo-satellite system (including Beidou and GPS) can be applied to the general receiver. The pseudo-satellite system can improve the positioning accuracy of the general receiver and improve the usability of the navigation system. Simulation analysis and test are carried out for the method. The experimental results show that the pseudo-satellite method is achievable and can significantly improve the availability and accuracy of the GNSS system. Keywords: Pseudo-satellite · Time-synchronous · Ephemeris · General receiver

1 Introduction With the application and popularization of GNSS satellite navigation system, pseudosatellite system has gradually become a research contents to enhance the positioning accuracy of GNSS system. In recent years, many people have carried out a lot of research on pseudo-satellites. Among them, reference [1] verified the indoor pseudosatellite system; reference [2, 3] established a four-dimensional model with altitude angle, azimuth angle and observation time as independent variables and double difference relative precision factor as dependent variables for mine application, and carried out optimization design verification; reference [4] proposed the concept of generalized pseudo-satellite and a new generation of GNSS enhancement system framework based on generalized pseudo-satellite.This is the most challenging task, as land, sea, space, air, underwater, indoor, and underground should all be connected to the “5G + BDS/GNSS” indoor/outdoor integrated network [5]. Based on the above analysis and application, further work is carried out in this paper. The purpose of this paper is to design a pseudo-satellite system and test the accuracy of the pseudo-satellite positioning system. The signal transmitted by the pseudo-satellite system designed in this paper can be received by the general receiver, which can supplement and improve the accuracy of the satellite system under special conditions. In this paper, the multi frequency pseudo-satellite enhancement system is implemented, and the design of the internal signal generation part of the pseudo-satellite signal generator is realized. In the development process of pseudo-satellite receiver, the problem that needs to be solved is to use general Beidou/GPS receiver to obtain the original navigation © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 280–288, 2021. https://doi.org/10.1007/978-981-16-3142-9_25

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observation, including pseudo-satellite information, doppler information, carrier phase and message information, etc. Through the design of a set of post-processing pseudosatellite positioning algorithm to post process the above information, the positioning solution of the pseudo-satellite enhancement system can be realized, and the output of the positioning results can be obtained, the positioning results are analysed.

2 Principle Analysis In the conventional pseudo-satellite system, time synchronization technology is usually used to broadcast pseudo-satellite signal. Like satellite positioning, the positioning accuracy of Pseudo-satellite system is directly related to the clock accuracy. Therefore, obtaining accurate clock accuracy is the basis of improving the positioning accuracy of Pseudo-satellite system. This paper analyses and experiments to improve the clock accuracy of the system. In the pseudo satellite system, the pseudo range observation equation is as follows: ρ(sGPS) = r (sGPS) + δtu,GPS − δt (sGPS) + I(sGPS) + T(sGPS) + ε(sGPS) ρ

(1.1)

Among them, s represents different satellites; u represents user receiver; δtu,GPS represents receiver clock error; δt(sGPS) represents satellite clock error; I represents ionosphere delay; T represents tropospheric delay; and ε(sGPS) is pseudo range measureρ ment noise. In the pseudo-satellite system, the influence of ionosphere can be ignored because there is no influence of ionosphere, and the factor that can improve the ranging error r (sGPS) is the clock error of the pseudo-satellite system δt(sGPS) because the tropospheric delay and pseudo range measurement noise depend on the actual environment and receiver. According to reference [6], the clock error can be expressed by Allan variance. In the conventional crystal oscillator indexes, the relative frequency accuracy is less than ±5 × 10–9 /day, the relative time accuracy is less than ±50 ns/day, and the Allan variance of short-term stability can reach ±5 × 10–9 /s. In the high precision cesium clock, the relative frequency accuracy is less than ±5 × 10–14 /day, the relative time accuracy is less than ±10 ns/day, and the Allan variance of short-term stability is less than or equal to 5 × 10–14 /s. Therefore, the system pseudo range error is raised to ns level by improving the clock index. Therefore, the pseudo range measurement errors introduced by the system clock are 10 ns * c ≈ 3 m, which can improve the positioning accuracy of the pseudo-satellite system to within 5 m.

3 Function Composition and Working Process of Pseudo-satellite System 3.1 Composition and Function In the pseudo-satellite system, the main problems include the accuracy of clock synchronization and the problem of improving the network layout of the pseudo-satellite system. In this paper, a pseudo-satellite system based on high-precision cesium clock

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GPS satellite

Beidou satellite

GPS satellite

Beidou satellite

Beidou satellite

GPS satellite

General receiver

pseudo-satellite transmitter Time service unit

Positioning service area

pseudo-satellite transmitter Time service unit

pseudo-satellite transmitter

pseudo-satellite transmitter fiber cable

fiber cable

Time service unit GNSS antenna

Time service unit

fiber cable

Cesium clock reference

fiber cable

Time synchronization unit

Fig. 1. Pseudo-satellite system composition block diagram

time synchronization is proposed. The composition of this pseudo-satellite system is shown in Fig. 1: The main characteristics of this pseudo satellite positioning system are as follows: (1) The time synchronization between pseudo-satellite system and GNSS satellite can realize the joint service of Pseudo-satellite system and GNSS system, and the user can realize positioning by using general receiver; (2) Pseudo-satellite system can locate independently when GNSS signal cannot locate; (3) The time synchronization of pseudo satellite signal generator can be realized through cesium clock networking, which can realize long-distance pseudo satellite signal networking; (4) The synchronous time network generated by high-precision cesium clock is used to improve the positioning accuracy of Pseudo-satellite system; the high-precision cesium clock uses clock source regeneration technology to realize the traceability of high-precision time-frequency reference source; the high-precision clock transfer technology is used to complete the clock transfer of optical fiber cascade network. The main components and functions of this pseudo satellite positioning system are as follows: (1) Pseudo satellite signal generator: the system needs multiple pseudo satellites as signal sources to transmit GNSS signal in standard format. The modulation mode signal format is basically consistent with that of Beidou signal, and can be received by ordinary Beidou receiver. This scheme is realized through development;

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(2) Cesium clock reference: it is the clock reference of the whole system, providing a clock with accuracy better than 1e−14 ; (3) Time synchronization unit: the cesium clock is aligned with the GNSS system to ensure the long-term stability of the pseudo-satellite system. In this system, it is actually aligned with the GPS clock to realize the time base maintenance function. In this paper, tft3001 is used to realize the function. Part of the time is purified by the local cesium clock to generate stable second pulse signal, and the phase aging of 1PPS signal is less than 8 ns/day; (4) Time service unit: receiving cesium clock reference clock through optical fiber, providing standard clock and 1PPS signal for each pseudo satellite signal generator, ensuring that the error between local clock and reference clock of pseudo satellite signal generator is less than 3 ns; optical fiber distance can reach 80 km, realizing clock transmission function; in this scheme, TFT 3001 equipment is used to trace to cesium clock and communicate with TFT 3001 Model 1002 equipment forms a star “clock transfer” system covering 80 km range; time synchronization and transfer are completed by TF protocol, so that cesium clock 1PPS signal can be stably and reliably transmitted to pseudo-satellite equipment, TF_ The relative phase accuracy of 1PPS signal is less than 5e−14 /day, and the relative phase error is less than ±10 ns/day. (5) General receiver: receiving pseudo satellite signal, pseudo range measurement, navigation message calculation and positioning; this scheme is implemented by the general receiver. 3.2 Working Process The main working process of the pseudo satellite positioning system is as follows: (1) When the system works, first run the cesium atomic clock, and the cesium atomic clock runs stably, and achieves time synchronization with GPS through the time synchronization unit. Then, the reference clock signal of cesium atomic clock is transmitted to the clock input of pseudo satellite signal generator through the time service unit. In this system design, the system clock is 10 MHz, and the system synchronization signal is 1PPS, which ensures the accuracy of pseudo satellite signal generator Time synchronization between pseudo satellite navigation signal and GPS system; (2) The receiver in the pseudo satellite signal generator receives the GNSS signal and calculates the current satellite information. At the same time, the pseudo satellite number that should be output and the pseudo range information of the pseudo satellite are calculated according to the satellite distribution; (3) After the preparation of the internal signal generation of the pseudo satellite signal generator is completed, the pseudo satellite signal is output when the rising edge of the next 1PPS arrives; the pseudo satellite signal power output by the pseudo satellite signal generator is adjustable to ensure that the signal power received by the pseudo satellite user receiver is within the normal power range; (4) The system control software can control all kinds of equipment, including pseudosatellite signal generator and clock equipment. The operation control software can

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flexibly control the transmitting state of Pseudo-satellite signal, modify the ranging code and message of Pseudo-satellite; (5) Pseudo range measurement, navigation message calculation and positioning are carried out by using general user receiver.

4 Design and Implementation of Internal Algorithm 4.1 Design and Implementation of Pseudo-satellite Signal Generator In order to carry out the pseudo satellite experiment, the pseudo satellite signal generator is specially designed. The pseudo-satellite signal generator includes ephemeris receiving module, clock module, baseband module, RF module and antenna part. It can generate customized pseudo-satellite ephemeris parameters by receiving GNSS signals, and generate pseudo-satellite RF signals of Beidou and GPS, and realize the power control and adjustment function of Pseudo-satellite. The block diagram of Pseudo-satellite signal generator is shown in Fig. 2. Transmitting antenna GNSS antenna

Main control module

GNSS Receiver

Baseband module

1PPS External clock reference

1PPS 10MHz

RF module

1PPS 10MHz

RF output

10MHz

Clock module

Fig. 2. Pseudo-satellite signal generator block diagram

The main functions of each part are as follows: (1) The receiving antenna receives the actual satellite signal and transmits the signal to the base station navigation receiver; (2) The GNSS receiver receives the ephemeris and almanac of the actual satellite, outputs the pseudo range parameters of the satellite, and sends them to the main control module through the serial port; (3) The clock module receives the second pulse signal and 10 MHz signal from cesium clock, and outputs the two signals to baseband module and RF module respectively; (4) The main control module runs related software, which is responsible for the parameter extraction of receiver, pseudo-satellite parameter simulation and pseudo-satellite baseband module control;

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(5) The baseband module generates the baseband signal corresponding to the asterisk according to the command of the control computer and the second pulse synchronization of the clock taming module; calculates the parameters required by the digital signal processing algorithm according to the data transmitted by the control computer, generates the spread spectrum code, completes the signal spread spectrum, and generates the baseband digital signal; modulates the baseband signal to the digital intermediate frequency, and uses the DAC to convert the digital signal into the digital intermediate frequency In this paper, we design a special hardware circuit, the main chips are DSP, FPGA and DAC. (6) RF module modulates IF signal of Pseudo-satellite baseband module into RF signal, outputs RF signal after filtering and amplification, receives clock of clock taming module, generates clock signal and local frequency signal required by baseband module, and finally connects RF output signal to transmitting antenna after combining; this paper realizes it through professional design. (7) The transmitting antenna transmits the satellite signal to the presupposed service area. 4.2 Time Synchronization Algorithm and Synchronization Process The system time generated by the pseudo satellite signal generator itself can be synchronized with 1PPS. The time synchronization accuracy depends on the internal sampling clock frequency and the time deviation of navigation observation message calculation. The time deviation of navigation observation and message calculation adopts mathematical calculation method, and the internal word length is 64 bits’ floating-point calculation, so the error can be ignored The sampling time and frequency inside the block is 327.36 MHz, and the conversion time is 3 ns, which can meet the requirements of the system. In order to realize the function of clock synchronization, the baseband module in this paper receives the time signal from cesium clock system, and reads the GNSS system time GPS time. When the pseudo satellite signal generator reads UTC in software, it uses 1PPS signal and 10 MHz to align in hardware synchronization. After the pseudo satellite signal generator reads the UTC time of the time service and obtains the stable 1PPS signal, it decides whether it has the condition to align with the actual time from the next second. After the judgment condition is established, it starts the signal simulation calculation and sends the time service instruction to the baseband module to calculate and generate the pseudo satellite signal of the next second. The 10 MHz clock signal output by the time service receiver is used as the pseudo satellite mode. The next 1PPS signal is used as the start signal of pseudo satellite signal generator. This mechanism ensures that the clock synchronization accuracy of multiple pseudo-satellite generators is consistent with that of cesium clock system. 4.3 Ephemeris Parameter Calculation Process In this paper, we design a set of algorithms for generating Beidou and GPS pseudosatellite signals, and transplant the algorithms to the pseudo-satellite baseband hardware platform, through which the pseudo-satellite baseband signals can be generated in real

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time; at the same time, in order to ensure that the existing receiving equipment can receive GPS and pseudo-satellite signals at the same time, the navigation message of Pseudo-satellite refers to the navigation message structure specified by GPS and Beidou standards. In addition, the pseudo-satellite coordinate position is confirmed after positioning by the receiver, and the pseudo-satellite information is written into the navigation message after real-time dynamic calculation and adding the error between the transmitting antenna and the receiving antenna. According to the different positions of pseudo-satellites, the ephemeris calculation process of the selected pseudo-satellites is as follows: as shown in Fig. 3, taking the position of the receiving antenna of the user equipment as the origin, the measurement coordinate system is established, in which the altitude angle and azimuth angle of the satellite are calculated.

Fig. 3. Altitude and azimuth of satellite.

(1) Calculate the position of the satellite rcs in the measurement coordinate system, as shown in Eq. 4.1. s u rcs = RY (−90◦ )RX (B)RZ (−90◦ + L)(rD − rD )

(4.1)

s and  u are the satellite coordinates and the user coordinates in the rD In Eq. 4.1, rD ECEF coordinate system respectively; and (L, B) are the longitude and latitude of the user.

(2) Calculate the altitude and azimuth of the satellite, as shown in Eq. 4.2. ⎧ ⎨ E = arctg(ysc /D)  0, z ≥ 0 ⎩ Az = arccos(xsc /D) + π z 0 to ensure the convergence of the algorithm, where α is a small constant [13]. In order to solve the dual problem and obtain the optimal power allocation strategy, this paper proposes a single station multi-satellite energy efficiency optimization algorithm (SM-EEOA), which updates the power allocation matrix by iteratively updating the Lagrange multiplier. The specific process is shown in Table 1.

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Table 1. Energy efficiency optimization algorithm for single station multi-satellite MIMO uplink system

Algorithm 1 SM-EEOA Initialization

while

do

for k 1: K Update , k according to equations (2.23) and (2.24) for l 1: Lk Calculate pkl according to formula (2.22) end for end for end while

3 Simulation and Result Analysis This article uses MATLAB 2019 software to simulate the single-station multi-satellite MIMO uplink method. The channel model uses the third-order Saleh-Valenzuela channel. The additive noise is Gaussian white noise. Satellite parameters refer to low-orbit satellites. The specific simulation parameters are shown in Table 2. 3.1 Energy Efficiency Under Different SNR In order to verify the energy efficiency performance of the SM-EEOA algorithm under different signal-to-noise ratios, the SM-EEOA algorithm was compared with the average power allocation algorithm and the EECP algorithm proposed in [10] under the SNR of 4–30 dB. Energy efficiency curve as shown in Fig. 2. Due to the improvement of the signal-to-noise ratio, the channel capacity under the same transmission power also increases, which brings about an improvement in the energy efficiency of the system. Since the SM-EEOA algorithm can perform dynamic power allocation based on the satellite channel state information, it can bring more energy efficiency gains compared to the EECP algorithm. The simulation results show that the SM-EEOA algorithm can effectively improve the energy efficiency of the system compared with the traditional algorithm. Even at low signal-to-noise ratio, the system energy efficiency can be about 60%, which has better performance.

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J. Zhang et al. Table 2. Parameter values in simulation Parameter

Value

Satellite altitude

800 km

Frequency

3.5 GHz

Bandwidth

20 MHz

Number of transmitting antennas 6 Number of receiving antennas

2

Modulation

QPSK

Number of satellites

3

Fixed power consumption

50 mW

Total transmit power

100 mW

Minimum transmission rate

4 Gbps

Fig. 2. Energy efficiency under different SNR

3.2 Energy Efficiency Under Different Satellite Numbers In order to verify the energy efficiency performance of the SM-EEOA algorithm under different numbers of satellites, the three algorithms are compared when the number of satellites is 3–30. Figure 3 shows the energy efficiency curve under different numbers of satellites at 20 dB. It can be seen that the effect of SM-EEOA algorithm is better than EECP algorithm and equal power allocation algorithm. As the number of satellites increases, the objects that can be controlled by the power allocation algorithm also increase. User diversity brings improvements in system energy efficiency. When a base station sends signals to 30 satellites at the same time, the system energy efficiency can be increased by about 70%. This is because the SM-EEOA algorithm can combine the channel quality of the satellites for reasonable power allocation. However, considering the situation of incomplete CSI feedback, when the number of satellites increases to a certain extent, the co-channel interference between satellites will affect the quality of data transmission. Therefore,

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Fig. 3. Energy efficiency under different SNR

the energy efficiency gain brought by the number of satellites in practical applications will not increase indefinitely. 3.3 Energy Efficiency Under Different Satellite Numbers In order to verify the energy efficiency performance of the SM-EEOA algorithm under different data transmission rate requirements, the SM-EEOA algorithm is compared with the EECP algorithm and the equal power allocation algorithm under the QOS requirements of 2–5 Gbps. Figure 4 shows the energy efficiency curve under different data transmission rate requirements at 20 dB.

Fig. 4. Energy efficiency under different QOS

Since the average power distribution algorithm does not consider the transmission rate requirements of the satellite, it does not change accordingly. When the data transmission rate requirement is small, the energy efficiency-based power allocation method

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is not obvious enough to improve the energy efficiency. This is because the channel capacity is higher than the minimum transmission rate at this time, and the constraints brought by QOS are smaller. With the increase in data transmission rate requirements, the channel capacity has been continuously improved, and the effect of the algorithm is getting better and better. Compared with the EECP algorithm, the energy efficiency is improved by about 60%. But high transmission rate means higher transmission power and circuit power consumption. When the data transmission rate reaches 4 Gbps, even if the channel capacity can continue to grow, this will bring more circuit energy consumption. Therefore, as the transmission rate increases, energy efficiency eventually reaches saturation, and the energy efficiency curve no longer grows.

4 Conclusion This paper studies the energy efficiency optimization problem in a single base station and multiple satellite uplink system. Aiming at the shortcomings of high complexity and poor performance of the original power allocation algorithm, the single-station multisatellite MIMO uplink method was accurately modeled. The Lagrange multiplier method is used to solve the dual problem, and the optimal power distribution matrix is solved iteratively. We compare with the average power allocation algorithm and the EECP algorithm respectively. The simulation verifies that the algorithm proposed in this paper can effectively improve the energy efficiency of the system and has certain application value.

References 1. Guidotti, A., Vanelli-Coralli, A., Conti, M., et al.: Architectures and key technical challenges for 5G systems incorporating satellites. IEEE Trans. Veh. Technol. 68(3), 2624–2639 (2018) 2. You, L., Li, K.-X., Wang, J., et al.: Massive MIMO transmission for LEO satellite communications. IEEE J. Sel. Areas Commun. 38(8), 1851–1865 (2020) 3. Abrol, A., Jha, R.K.: Power optimization in 5G networks: a step towards GrEEn communication. IEEE Access 4, 1355–1374 (2016) 4. Ng, D.W.K., Lo, E.S., Schober, R.: Energy-efficient resource allocation in SDMA systems with large numbers of base station antennas. IEEE Trans. Wireless Commun. 11(9), 3292– 3304 (2012) 5. Zhang, Y., Gao, H., Tan, F., et al.: Resource allocation of energy efficient multi-user massive MIMO systems. In: GC Workshops, pp. 1–6 (2017) 6. Aghashahi, S., Aghashahi, S., Tadaion, A.: Energy efficient coordinated multicell power allocation in dynamic TDD MIMO systems. In: ICEE, pp. 1523–1528 (2019) 7. Heath, R.W., González-Prelcic, N., Rangan, S., et al.: An overview of signal processing techniques for millimeter wave MIMO systems. IEEE J. Sel. Top. Sig. Process. 10(3), 436–453 (2016) 8. Richter, R., Bergel, I., Noam, Y., et al.: Downlink cooperative MIMO in LEO satellites. IEEE Access. 8, 213866–213881 (2020) 9. Deng, B., Jiang, C., Yan, J., et al.: Joint multigroup precoding and resource allocation in integrated terrestrial-satellite networks. IEEE Trans. Veh. Technol. 68(8), 8075–8090 (2019) 10. Debnath, I.P., Gupta, S.K.: The Karush–Kuhn–Tucker conditions for multiple objective fractional interval valued optimization problems. RAIRO – Oper. Res. 54(4), 1161–1188 (2020)

Unmasking Bayesian RAIM Algorithm for Identifying Simultaneous Two-Faulty Satellites Ke Chen, Xinna Li(B) , and Junzheng Li Information Engineering University, Kexue Avenue 62, Zhengzhou 450001, China

Abstract. For the problem of identifying simultaneous two-faulty satellites in global navigation satellite systems (GNSS), an unmasking Bayesian Receiver autonomous integrity monitoring (RAIM) algorithm is proposed. In order to prevent the interaction between the two faults, the posterior distribution of observation error is obtained and the posterior probabilities of the events related to the observation errors of two satellites are calculated based on Bayes statistical theory, The complex posterior probability calculation formula is transformed into sample average by using Monte Carlo method, which meets the real-time requirements of identifying method. The simulation results based on the precise ephemeris products provided by iGMAS show that the proposed algorithm can identify two satellite faults quickly and accurately, and improve the accuracy of navigation and positioning to a certain extent. Compared with the previous RANCO method, it shows that the method is feasible, not only can effectively identify the fault, but also can effectively prevent the interaction between the two faults. Keywords: Bayesian method · 3σ principle · RAIM algorithm · Posterior probability · Monte Carlo method

1 Introduction With the wide application of global navigation satellite system (GNSS), receiver autonomous integrity monitoring (RAIM) plays an increasingly important role in improving the integrity of navigation system [1]. At the same time, with the development and use of multiple satellite navigation systems, the number of visible satellites increases greatly. On the one hand, it can provide more observations, which brings opportunities to RAIM algorithm; on the other hand, it also increases the possibility of multiple satellites, especially two satellites, failing at the same time. In the process of multi satellite fault identification, due to the mutual influence between faults, if the integrity algorithm for single satellite fault is adopted, the fault cannot be detected and identified correctly due to the mutual influence between faults, which is referred to as masking [2]. For this reason, it is necessary to study the unmasking RAIM method for two-faulty and multi-faulty and satellites. At the same time, most of the existing receiver autonomous integrity monitoring algorithms dealing with satellite fault are non-Bayesian methods [3–10], which are based © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 307–315, 2021. https://doi.org/10.1007/978-981-16-3142-9_28

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on the frequency hypothesis test and ignore the extremely important prior information. The RANCO method proposed by Stanford University to deal with satellite multi fault is also gross error detection fundamentally, but it is not a traditional gross error detection method, but a new multi gross error processing method introduced from image processing [11]. In reference [12], a Bayesian method for satellite fault detection and identification is proposed based on the Bayes principle. However, when multiple faults exist, there will still be masking phenomenon. In order to solve multiple fault identification problems better, this paper uses Bayes statistical theory, makes full use of the prior information contained in historical data, and designs a new algorithm for identifying simultaneous two-faulty satellites. The proposed algorithm can also identify the faults of multiple satellites by pairwise combination.

2 Bayesian Model for Identifying Simultaneous Two-Faulty Satellites The equation of GNSS linearized pseudorange observations is as follows L = AX + 

(1)

where the number of visible satellites is n, L = (L1 , · · ·, Ln )T is the vector of pseudorange observations; A = (a1 , a2 , · · ·, an )T is the observation matrix; X is 4 × 1 unknown state parameter vector, which represents the correction number of the user’s position coordinates and the clock difference of the receiver;  = (1 , 2 , · · ·, n )T is the observation error vector, i Generally includes troposphere, ionosphere residual, receiver noise, multipath error, etc.. Supposing  ∼ Nn (0, σ02 P −1 ), σ02 is unknown unit weight variance, P = diag(p1 , · · ·, pn ) is a known weight matrix. σ2

Let σi2 = p0i = τ1pi and τ = σ0−2 , according to the 3-principle of Normal distribution, 2 and with the fact  that  the prior distribution of i is N (0, σi ), the probability of the event   {|i | > kσi , j > kσj } should be small when k ≥ 3. After obtaining pseudorange observations, under the Normal priori, the posterior probability of the event P (|i | >   kσi , j  > kσj |L ) can be calculated. If there is no fault satellite at the current time, the true errors i , j of the observed values follow the Normal distribution, then the posterior probability of the event should be very small. On the contrary, if there exist fault at the current time, the posterior probability value of the event will be very different from the prior probability value. Therefore, based on the difference   between posterior probability and the prior probability of the event {|i | > kσi , j  > kσj }, it can be an important basis for judging whether the satellite has faults.

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3 Bayesian Method of Identification for Simultaneous Two-Faulty Satellites Based on Posterior Probability 3.1 Posterior Distribution of Errors Under the Normal-Gamma prior distribution, the posterior distribution of unknown state parameters X is calculated according to Bayes formula. )f (X |τ ) ∝ f (L|X , τ )f (X |τ ) f (X |τ, L ) = f (L|Xf ,τ (L|τ )     τ (L−AX )T P(L−AX ) τ (X −X0 )T (X −X0 ) ∝ exp − exp − 2 2   T  



∝ exp −

τ X −Xˆ B

0 +AT PA X −Xˆ B 2

where Xˆ B = (0 + AT PA)−1 (0 X 0 + AT PL)

(2)

{X |τ, L } ∼ N4 (Xˆ B , τ −1 (0 + AT PA)−1 )

(3)

so

Similarly, the formulas are derived as follows ˜ τ −1 H˜ ) {|τ, L } ∼ Nn (,

(4)

{τ |L } ∼ (a1 , b1 )

(5)

˜ = L − AXˆ B 

(6)

H˜ = A(0 + AT PA)−1 AT

(7)

where

a1 = α0 +

n 2

(8)

1 b1 = α1 + [(L − AXˆ B )T PL + (X0 − Xˆ B )T 0 X0 ] 2 Further, the posterior distribution of  can be obtained  +∞ f (|L ) = 0 f (|τ, L )f (τ |L )d τ   T  

˜ H˜ −1 − ˜ τ −  +∞  −1 −1/ 2 ˜ exp − τ a1 −1 exp{−τ b1 }d τ ∝ τ H  0

∝

 +∞ 0

n

⎧ ⎨

τ 2 +a1 −1 exp − ⎩

2  ⎫ T   ˜ H˜ −1 − ˜ +2b1 ⎬ τ − 2

⎭

dτ

(9)

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The integrand function of the above formula partially conforms to the probability density function form of Gamma distribution, which is obtained by using the properties of probability density function. 

n+2a1 ⎡   ⎤−  T    2 −1 ˜ −1 − n +a  ˜ ˜ T   b H a  −   −  1 1 2 1 ⎥ ⎢ ˜ H˜ −1  −  ˜ + 2b1 f (|L ) ∝  −  ∝ ⎣1 + ⎦ 2a1



Therefore, the posterior distribution of  is a n dimensional non-central t distribution ˜ a1 b−1 H˜ −1 , 2a1 ) { |L } ∼ tn (, 1 Furthermore, the posterior distribution of the components i is one-dimensional non-central t distribution ˜ i , a1 b−1 h˜ −1 , 2a1 ) { i |L } ∼ t( 1 ii

(10)

˜ h˜ ii is the i-th diagonal element of H˜ , and the ˜ i is the i-th component of , where  meanings of other variables are shown in formulae (6)–(9). 3.2 The Formula of Posterior Probability The simultaneous use of multiple navigation systems brings opportunities to RAIM algorithm, and also leads to the possibility of multiple faults. When multiple faults exist, due to the interaction between faults, it often leads  to  recognition failure. Therefore, the posterior probability of the event {|i | > kσi , j  > kσj } is considered as   (11) pij (k) = P(|i | > kσi , j  > kσj |L ) For

  pij (k)=

 f i , j |L d i d j

|i |>kσi , |j |>kσj



  =

|i |>kσi , |j |>kσj



+∞

=

 

f (τ |L )

+∞

  f i , j |τ, L f (τ |L )d τ d i d j

0

|i |>kσi , |j |>kσj

0

  f i , j |τ, L d i d j d τ

˜ τ −1 H˜ ), so and {|τ, L } ∼ Nn (, 



i , j |τ, L ∼ N2

Then   |i |>kσi , |j |>kσj



! ˜i  h˜ , τ −1 ˜ ii ˜j hji 

 f i , j |τ, L d i d j

h˜ ij h˜ jj

"

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311

    = P i > kσi , j > kσj |τ, L + P i > kσi , j < −kσj |τ, L     + P i < −kσi , j > kσj |τ, L + P i < −kσi , j < −kσj |τ, L = p1 + p2 + p3 + p4 Combined with the formula of bivariate Normal probability, the formula is obtained   p1 = P i > kσi , j > kσj |τ, L   √ √  √ √ ⎧ ⎫ ˜i τ ˜ i τ j −  ˜j τ ˜j τ ⎨ i −  ⎬ kσi −  kσj −  |τ, L # # # # = P > , > ⎩ ⎭ h˜ jj h˜ jj h˜ ii h˜ ii  √ √ ⎛  ⎞ ˜i τ ˜j τ kσi −  kσj −  # # = B ⎝− ,− , ρij ⎠ ˜ hjj h˜ ii where B(z1 , z2 , ρ) is the distribution function of the standard two-dimensional Normal distribution with the correlation coefficient ρ and ρij =

#

h˜ ij

h˜ ii h˜ jj

.

Similarly, ⎛ 

√  √ ⎞ ˜ i τ −kσj −  ˜j τ kσi −  # # , , −ρij ⎠ p2 = B⎝− h˜ jj h˜ ii √ √  ⎛ ⎞ ˜i τ ˜j τ −kσi −  kσj −  # # p3 = B⎝ ,− , −ρij ⎠ ˜hjj ˜hii √  √ ⎛ ⎞ ˜i τ ˜j τ −kσi −  −kσj −  ⎝ # # p4 = B , , ρij ⎠ h˜ jj h˜ ii

Let √ √   ˜i τ ˜j τ kσi −  kσj −  1 −1 1 −1 − 21 −1 2 ˜ i τ 2 )h ˜ j τ 2 )h 2 , ( # z1i = − = −(kpi − = −(kpj 2 −  ii , z1j = − jj hii hjj √ √   ˜i τ ˜j τ −kσi −  −kσj −  1 −1 1 −1 −1 −1 ˜ i τ 2 )h 2 , z2j = ˜ j τ 2 )h 2 ( # z2i = = (−kpi 2 −  = (−kpj 2 −  ii jj hii hjj

and synthetically, pij (k) = =

 +∞

 +∞ 0

0

* ) f (τ |L ) p1 + p2 + p3 + p4 d τ

   * )  f (τ |L ) B z1i , z1j , ρij + B z1i , z2j , −ρij + z2i , z1j , −ρij + B z2i , z2j , ρij d τ

(12) Through formula (12) the posterior probability pij (k) can be calculated.

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3.3 The Implementation Steps of Bayesian Method for Identifying Simultaneous Two-Faulty Satellites According to the conclusions in Sects. 3.1 and 3.2, the specific implementation steps of Bayesian method for satellite multi fault detection and identification are as follows. Step 1. Determine the value  of k. Generally k = 3. At this time, the prior probability of the event {|i | > kσi , j  > kσj } is approximately 0.7e-5. Step 2. Determine the super parameters X0 , 0 , α0 , α1 . According to reference [13, 14], the super parameters of Normal-Gamma prior distribution X0 , 0 , α0 , α1 can be determined by the following formulae: +  −1 n−t + 1, α1 = (L − AX0 )T P(L − AX0 ) 2 AT PL, 0 = AT PA, α0 = X0 = AT PA 2 Step 3. Fault identification. Firstly, the posterior probability is calculated by formula (12), which involves the calculation of infinite integral. According to the characteristics of the integrand function, the Monte Carlo method is used for approximate calculation. For  +∞ * ) pij (k) = f (τ |L ) p1 + p2 + p3 + p4 d τ 0  +∞ )     * = f (τ |L ) B z1i , z1j , ρij + B z1i , z2j , −ρij +B z2i , z1j , −ρij + B z2i , z2j , ρij d τ 0 )     * = Eτ |L B z1i , z1j , ρij + B z1i , z2j , −ρij + B z2i , z1j , −ρij + B z2i , z2j , ρij and {τ |L } ∼ (a1 , b1 ), Therefore, N random numbers of Gamma distribution are generated first as τ (1) , τ (2) , ..., τ (N ) . By substituting. 1 1 1 −1 (t) ˜ i τ (t) 21 )h− 2 , z (t) = −(kp− 2 −  ˜ j τ (t) 21 )h− 2 ’ z = −(kp 2 −  1i (t) z2i

=

i −1 (−kpi 2

ii 1j 1 − 21 (t) ˜ i τ 2 )h ’ z (t) − ii 2j

=

j −1 (−kpj 2

jj 1 1 (t) ˜ j τ 2 )h− 2 , − jj

where t = 1, 2, ..., N , and the calculation formula is obtained as )     * pij (k) = Eτ |L B z1i , z1j , ρij + B z1i , z2j , −ρij + B z2i , z1j , −ρij + B z2i , z2j , ρij N       . 1 , -  (t) (t) (t) (t) (t) (t) (t) (t) B z1i , z1j , ρij + B z1i , z2j , −ρij + B z2i , z1j , −ρij + B z2i , z2j , ρij ≈ N t=1

The posterior probability can be calculated by Monte Carlo method and by generating random numbers, and the only corresponding average operation is needed, with small calculation amount is and high efficiency. The posterior probability pij (k) can be used to identify double satellite faults. If the posterior probability of a binary combinations of two satellites is much higher than that of other binary combinations (more than 105 times), the two satellites can be considered to have faults simultaneously. In this way, the fault identification of double satellites is realized at the same time. For the multi satellite fault, if the posterior probabilities of the corresponding events of several binary satellite combinations are much higher than those of other binary satellite combinations, these satellites can be considered to have faults at the same time.

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4 Example and Analysis 4.1 Verification of Fault Identification Using the ISU precise ephemeris provided by iGMAS, GPS, BDS, GLONASS and Galileo, mixed constellations are simulated and pseudo-range observations are generated. The ground station is located in Zhengzhou (Lat. 34.6836° (N), Lon. 113.533° (E), geodetic height: 0.0 m), and the observation time is 6:00:00 on November 28, 2019, to 5:45:00 on November 30, 2019, every 15 min as a epoch, a total of 192 epoch. For each epoch, all satellites with an altitude angle greater than 15 are selected as visible satellites. The designed scheme is as follows: 1 There are 36 visible satellites in the 30th epoch. The pseudorange deviations of 45 m and 30 m are added to the pseudorange observations of the 6th and 19th satellites respectively. The posterior probability pij (k) with i > j is shown in Fig. 1. 2 There are 29 visible satellites in the 50th epoch. The deviations of 30 m, 35 m, 35 m and 45 m are added to the pseudorange of the 4th, 10th, 15th and 20th satellites respectively. The posterior probability corresponding to the 4th and other satellites is calculated and is shown in Fig. 2.

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It can be clearly shown from Fig. 1 that that the posterior probability values corresponding to (6, 19) satellites are far greater than those corresponding to other normal observation values in the 30th epoch, and it can be concluded that the 6th and 19th satellites are in fault simultaneously. Similarly, It can be shown from Fig. 2 that the posterior probability values of errors corresponding to (4, 10), (4, 15) and (4, 20) satellites are also far greater than others in the 50th epoch. It shows that the new algorithm can correctly identify multiple satellite faults. It is worth noting that, through a large number of calculations, the posterior probability values corresponding to the normal observation values are near 0, while the posterior probability values corresponding to the observation

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values from fault satellites are significantly greater than 0, with the difference between orders of magnitude. 4.2 Statistics of Correct Identification Rate of Faults In order to test the effectiveness of the proposed algorithm for identifying simultaneous two-faulty satellites, the deviation is added to the pseudorange of the 6th and 19th satellites in all the 192 epochs. The proposed Bayesian method and the RANCO method proposed by Stanford University are used to identify the faulty satellites, and the correct identification rate in the 192 epochs is counted. The added deviation is increased from 5 m to 60 m by 5 m each time. The relationship between correct identification rate and pseudorange deviation is shown in Fig. 3. 100

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It can be shown from Fig. 3 that when the fault deviation is small, the identification rate of the new algorithm is higher than that of the RANCO multi fault identification algorithm, and when the deviation is large, the accuracy identification rate is stable near

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1. The proposed method shows more sensitivity to detect smaller pseudorange deviation than the RANCO method.

5 Conclusion In this paper, Bayes statistical theory is used to propose a Bayesian algorithm for on-line identification of satellite faults. The proposed method for satellite fault identification is put forward by using 3-principle. The new Bayesian algorithm makes full use of the prior information, improves the accuracy and sensitivity of identification. The calculation formulae of the posterior probability value is deduced and the Monte Carlo algorithm to calculate the posterior probability is proposed. The Monte Carlo algorithm only needs to produce enough random numbers, and the calculation efficiency is high. When determining the value of k, an empirical value 3 is used based on the 3σ principle. It is necessary to further studying the determination of the value of k with horizontal protection level (HPL) and vertical protection level (VPL).

References 1. Du, Y.J., Wang, J.L., Rizos, C., et al.: Vulnerabilities and integrity of precise point positioning for intelligent transport systems: overview and analysis. Satell. Navig. 2, 3 (2021) 2. Deb, S., Pattipati, K.R., Raghavan, V., Shakeri, M.: Multi-signal flow graphs: a novel approach for system testability analysis and fault diagnosis. IEEE Aerosp. Electron. Syst. Mag. 5, 1–13 (1994) 3. Bei, J.Z.: GNSS integrity monitoring method. Doctoral dissertation, Wuhan University, Wuhan (2010). (in Chinese). 4. Sun, S.G.: RAIM algorithm for detection of multiple fault satellites based on maximum likelihood ratio. J. Chin. Inertial Technol. 03, 312–315 (2011). (in Chinese) 5. Zhang, Q.Q., Gui, Q.M., Gong, Y.S.: Multiple satellite faults detection and identification based on the independent component analysis. Acta Geodaetica et Cartographica Sinica 46(6), 698–705 (2017). (in Chinese) 6. Gratton, L., Joerger, M., Pervan, B.: Carrier phase relative RAIM algorithms and protection level derivation. J. Navig. 63(2), 215–231 (2010) 7. Hewitson, S., Wang, J.L.: GNSS receiver autonomous intergrity monitoring for multiple outliers. J. Navig. 4(4), 47–54 (2006) 8. Ni, J., Zhu, H., Guo, W.: An improved RAIM scheme for processing multiple outliers in GNSS. In: 2007 21st International Conference on IEEE Advanced Information Networking and Applications Workshops, AINAW 2007, pp. 840–845 (2007) 9. Wang, J.L., Wang, J.: Mitigating the effect of multiple outliers on GNSS navigation with mestimation schemes. In: 2007 Symposium on Proceeding of International Global Navigation Satellite Systems Society (IGNSS), pp. 1–9 (2007) 10. Zhang, Y., Wu, F., Isshiki, H.: A new cascade method for detecting GPS multiple outliers based on total residuals of observation equations. In: 2012 IEEE Position Location & Navigation Symposium, pp. 208–215 (2012) 11. Schrothq, R.M., Ene, A., Blanch, J., Belabbas, B., Walter, T., Enge, P., Meurer, M.: Enhancements of the range consensus algorithm (RANCO). In: 2008 Conference on Proceedings of the ION GNSS, Savannah (2008) 12. Li, X.N., M CZ, G SM: Bayes algorithms of satellite faults detection and identification. J. Geomatics Sci. Technol. 37(1), 21–25 (2020) 13. Koch, K.R.: Bayesian Inference with Geodetic Appliances. Springer, Berlin (1990) 14. Koch, K.R.: Einfuhrung in Die Bayes-Statistik. Springer, Berlin (2000)

The Realization and Performance Evaluation of Real-Time Precise Point Positioning Based on BDS-3 PPP-B2b Augmentation Information Lun Ai1,2 , Jie Wu1(B) , Binbin Wang2 , and Ruwei Zhang2 1 College of Aerospace Science and Engineering, National University of Defense Technology,

Changsha 410073, China [email protected] 2 Zhang Beijing Research Institute of Telemetry, Beijing 100076, China

Abstract. BDS-3 precise point positioning (PPP) service mainly broadcasts PPPB2b augmentation information through GEO satellites, so as to realize fast and high-precision positioning for ground users. This paper first introduces PPP-B2b information and B2b ephemeris recovery method, then evaluates ephemeris accuracy, the errors in radial, tangential and normal directions of B2b orbit are 6.70 cm, 23.39 cm and 25.84 cm respectively, which are 6.0%, 22.8% and 7.3% better than broadcast ephemeris, and the equivalent distance error of satellite clock is 5.33 cm, which is 76.4% better than broadcast ephemeris. Based on this information, a realtime PPP algorithm is realized. The new BDS-3 signals B1C, B2a and B2b are used to evaluate the positioning performance. In the static positioning experiment mode, the horizontal positioning accuracy is better than 2 cm, the vertical positioning accuracy is about 4 cm, and the convergence time is 4–5 min. In the kinematic positioning experiment mode, the horizontal positioning accuracy is better than 10 cm, the vertical direction accuracy is about 10 cm, and the convergence time is 6 min. Keywords: BDS-3 · PPP-B2b · Ephemeris evaluation · Real-time PPP · Performance evaluation

1 Introduction The third generation of Chinese BeiDou Navigation Satellite System (BDS-3) provides high-quality services such as combination of navigation and positioning to global users by 2020 [1, 2]. BDS-3 constellation is composed of 24 Medium Earth Orbit (MEO) satellites, 3 Inclined Geostationary Satellite Orbit (IGSO) satellites and 3 Geostationary Earth Orbit (GEO) satellites. The BDS-3 coordinate system is Earth-Centered EarthFixed, and the time system is atomic time. BDS-3 is downward compatible with B1I and B3I signals of BDS-2, while broadcasting new signals B1C, B2a and B2b. BDS-3 provides navigation, positioning and timing, such as global short message communication, international search and rescue services all over the world, and provide satellite-based

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 316–324, 2021. https://doi.org/10.1007/978-981-16-3142-9_29

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augmentation, ground-based augmentation, precise point positioning and regional short message service in China and surrounding areas [3]. Satellite navigation augmentation system enhances the user’s positioning performance through ground stations or GEO satellites, including Ground-Based Augmentation System (GBAS) and Satellite-Based Augmentation System (SBAS) [4–8]. BDS-3 PPP service transmits PPP-B2b augmentation information to China and its surrounding areas through GEO satellites, including satellite orbit corrections, clock corrections and differential code bias. Based on this kind of augmentation information, the receiver uses carrier phase and pseudorange to achieve high-precision positioning performance. Therefore, BDS-3 PPP service has the advantages of both GBAS and SBAS, and has high research value and application prospects in intelligent transportation, internet of things, aerospace, precision agriculture, time synchronization and other fields [9–11]. This paper first describes BDS-3 and PPP-B2b augmentation information, including its data structure and ephemeris recovery method. Using final ephemeris, the PPP-B2b real-time ephemeris accuracy is evaluated. Based on the BDS-3 PPP-B2b information and the observation of B1C and B2a, a real-time precise point positioning algorithm is designed. The mathematical model and implementation process of the algorithm are discussed in detail. Using the self-developed PPP-B2b-BRIT receiver, the positioning accuracy and convergence time of the algorithm in static mode and kinematic mode are evaluated.

2 PPP-B2b Augmentation Information The BDS-3 PPP service uses the ground tracking station and inter-satellite link data to calculate State Space Representation (SSR) products such as satellite orbits, satellite clock, differential code bias. The augmentation message is modulated on the B2b signal and broadcasted to the receiver via GEO satellites. After receiving the B2b signal, the user obtains the SSR correction by demodulating, decoding and matches the broadcast ephemeris to recover it to real-time PPP-B2b ephemeris. Ground receiver use carrier phase and pseudorange, combined with PPP-B2b ephemeris, to provide users with precise point positioning services. At present, BDS-3 PPP-B2b SSR information is modulated on the I branch of B2b signal in a way of Binary Phase Shift Keying (BPSK). Each message consists of 486 bits, including information type, message data and Cyclic Redundancy Check (CRC). The message becomes 972 characters after being encoded by the Low Density Parity Check (LDPC), and combined with a synchronization header of 16 characters, a PseudoRandom Noise (PRN) number of 6 symbols, and a reserved bit of 6 symbols to make up a total of 1000 symbols. The Fig. 1 shows the basic frame structure of PPP-B2b augmentation data. After the SSR are obtained by the receiver, it needs to be matched with the broadcast ephemeris and restore to the real-time ephemeris. For the BDS, it is matching the IODN parameter in the PPP-B2b SSR with the IODC parameter in the broadcast ephemeris of B1C frequency. Ephemeris recovery is divided into three steps: (1) recovery of satellite orbit; (2) recovery of satellite clock; (3) correction of differential code bias [12]. The accuracy of satellite orbit and clock is the key factor of ephemeris products, which determine the positioning accuracy and convergence time of PPP users. When evaluating

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Fig. 1. The data structure of PPP-B2b augmentation signal

the accuracy of PPP-B2b real-time ephemeris orbit and clock, the final product is used as the reference. This paper evaluates the ephemeris accuracy by using 7 consecutive days of PPP-B2b SSR data from the day of year 275 to 281 in 2020, and compares it with the broadcast ephemeris. At present, PPP-B2b real-time ephemeris includes satellites C19 to C46, and satellites C01 to C37 are included in the final product. Therefore, the ephemeris comparison is between C19 and C37. When evaluating the accuracy of the satellite, the PPP-B2b real-time ephemeris and broadcast ephemeris orbits refers to the phase center, while the final orbit product refers to the center of mass, so it’s required to convert the PPP-B2b real-time ephemeris and broadcast ephemeris from phase center to center of mass. When evaluating the accuracy of satellite clock, the frequency of final clock product refers to B1I and B3I. Therefore, it is necessary to correct the corresponding differential code bias of the PPP-B2b clock. Figures 2 and Fig. 3 show the accuracy statistics of the BDS-3 broadcast ephemeris and PPP-B2b real-time ephemeris, respectively. It can be seen from the figure that the radial error of the broadcast ephemeris orbit is better than 10 cm, the tangential and normal error is 20–30 cm, and the satellite clock error is about 20 cm, which is similar to the result in reference [13]. The PPP-B2b real-time orbit radial error is 6.70 cm, the tangential error is 23.39 cm, the normal error is 25.84 cm, and the satellite clock error is 5.33 cm. Compared with the broadcast ephemeris, the PPP-B2b real-time ephemeris has limited improvement in the radial and tangential directions of the orbit, which are 6.0% and 7.3% respectively, the improvement in the tangential direction is more significant, which is 22.8%, and the improvement in clock is the most significant, reaching 76.4%.

Fig. 2. Accuracy statistics of Beidou-3 broadcast ephemeris

The accuracy statistics of BDS-3 broadcast ephemeris and PPP-B2b real-time ephemeris are shown in Table 1. It can be seen that the accuracy of the orbit in radial

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Fig. 3. PPP-B2b real-time ephemeris accuracy statistics of BDS-3

and satellite clock of the PPP-B2b real-time ephemeris is about 5–6 cm, which meets the requirements of precise point positioning for satellite orbit and clock. Table 1. Accuracy of BDS-3 broadcast ephemeris and PPP-B2b real-time ephemeris Ephemeris type

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Clock bias STD (cm)

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Normal

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3 Real-Time PPP Algorithm The current research hotspots of PPP mainly lie in real-time PPP, low earth orbit constellation enhanced PPP, and multi-system multi-frequency PPP-RTK [14–17]. Based on the new signal B1C, B2a and PPP-B2b augmentation information from the BDS-3, this article describes a precise point positioning method that can be accomplished through the receiver’s own navigation signals without relying on analysis center and communication networks, which is called BDS-3 B2b real-time PPP. The algorithm uses ionosphere free combination as the observation equation: ˜ ps + msr · ztdr + εP Prs = ρrs + c · δtr − c · δt s s ˜ ps + msr · ztdr + Brs + εL Lr = ρr + c · δtr − c · δt

(1.1)

In formula (1.1), Prs and Lsr are the ionosphere-free pseudorange and carrier phase observations, respectively, ρrs is the geometric distance from the receiver to the satellite, ˜ ps is the PPP-B2b satellite clock, and c is the speed of light, δtr is the receiver clock, δt s mr is the troposphere mapping function, ztdr is the zenith troposphere delay, Brs is the ambiguity of the carrier phase ionosphere-free combination, which does not have integer characteristics. εP and εL are the pseudorange and carrier phase observation noise respectively.

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On the self-developed PPP-B2b-BRIT receiver, real-time PPP based on B2b augmentation signal is realized, as shown in Fig. 4. The receiver is mainly composed of a radio frequency (RF) front-end module, a signal processing module and an information processing module. The RF front-end module receives the analog RF signal from the antenna, and obtains an intermediate frequency digital signal after down-conversion, filtering and sampling. The signal processing module demodulates the digital signal to obtain the observations, broadcast ephemeris and PPP-B2b SSR information. The information processing module mainly completes the data processing of real-time PPP, and finally outputs the receiver coordinates, receiver clock and atmospheric delay through the serial port. Information Processing

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In the PPP-B2b-BRIT receiver information processing module, the data processing flow of the PPP based on the B2b augmentation information mainly includes PPP-B2b ephemeris recovery, data preprocessing, outlier detection and Kalman filtering. PPP-B2b ephemeris recovery is based on the PPP-B2b SSR correction and broadcast ephemeris. The data preprocessing part includes cycle slip detection and systematic error modeling. The TurboEdit method is used to detect the carrier phase cycle slip without repairing it. Then, modeling receiver antenna PCO and PCV, relativistic effects, phase wind-up, earth rotation, solid tide, ocean tide, pole tide and other systematic error. Since the PPP-B2b real-time ephemeris orbit refers to the satellite antenna phase center, there is no need to perform PCO and PCV corrections on the satellite end. The Kalman filter is used to estimate the parameters of the observations of each epoch in turn. The outlier detection is based on the post-fit residuals. The outlier detection and parameter estimation run iteratively until the outlier detection of all observations is completed or the number of iterations exceeds 5 times.

4 Real-Time PPP Experiment The PPP-B2b-BRIT receiver was installed on the roof of a building in Beijing for static positioning test from day of year 275 to 281 in 2020. The receiver output positioning results in real-time, the sampling interval is 30 s, the receiver and antenna are shown in Fig. 5. During the static positioning test, the observation data, broadcast ephemeris

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and PPP-B2b SSR information are saved to files, and we simulate the kinematic test in post-processing way. The static positioning results and kinematic positioning results are compared with the previously known coordinates, and the positioning results in the two modes are analyzed, including positioning accuracy and convergence time. The criterion for the convergence time is that the coordinate bias for 10 consecutive epochs is less than the design target of the PPP service, that is 0.3 m in the horizontal direction and 0.6 m in the vertical direction.

Fig. 5. Real-time PPP experiment receiver and antenna

In the static positioning experiment, the receiver coordinates are modeled as constant model during parameter estimation. Figure 6 is the real-time static PPP coordinate bias time series in day of year 277, 2020, starting from 0:00 to 4:00. It can be seen from the figure that after about 4 min, the coordinate bias converges to 0.3 m in the horizontal direction and 0.6 m in the vertical direction. The final positioning accuracy after 4 h of filtering is better than 5 cm.

Fig. 6. Real-time PPP coordinate bias time series in static mode

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Use the same observations, broadcast ephemeris, and PPP-B2b SSR information files saved in the static positioning experiment, we simulate the kinematic positioning in post-processing way. The receiver coordinates are modeled as white noise parameters during parameter estimation. Figure 7 is the real-time kinematic PPP coordinate bias time series in day of year 277, 2020, starting from 0:00 to 4:00. It can be seen from the figure that after about 8 min, the coordinate bias has converged within the design target of the PPP-B2b system. After the filtering of few hours, the coordinate bias RMS in the N, E, and U directions are 2.42 cm, 10.4 cm, 11.28 cm, respectively.

Fig. 7. Real-time PPP coordinate bias time series in kinematic mode

In the above time period, the observation conditions of the receiver are shown in Fig. 8. Considering that the satellites supported by PPP-B2b SSR are C19 to C46, the actual processed satellite number of BDS-3 s is 6–9, with an average of 7.4. The Position Dilution of Precision (PDOP) value is distributed between 1.73 and 5.35, with a mean value of 2.41. With the continuous improvement of PPP-B2b augmentation information, the observation conditions for ground users will be further improved.

Fig. 8. Real-time PPP experiment observation conditions

We also summarize the processing results of this experiment from day of year 275 to 281 for 7 consecutive days. In static positioning mode, the positioning accuracy in the N, E, and U directions are 0.98 cm, 1.52 cm, 4.07 cm, and the average convergence time is 4.42 min. In the kinematic positioning mode, the positioning accuracy in the

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three-dimensional directions are 4.67 cm, 9.64 cm, and 10.29 cm, respectively, and the average convergence time is 5.92 min. The statistics of real-time PPP experiment are shown in Table 2. It can be concluded that the accuracy of real-time static PPP is centimeter-level, the accuracy of kinematic positioning is decimeter-level in vertical direction, the accuracy of horizontal direction is centimeter-level, and the accuracy of the E direction and the N direction are quite different. In the two modes, the convergence time is 4–6 min. Table 2. Statistical of experimental results of real time precise point positioning Positioning mode

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5 Conclusion As one of the characteristic services of BDS-3, PPP-B2b service is a SBAS method which can achieve the performance of GBAS. This paper first describes the PPP-B2b augmentation information of BDS-3, including signal constructure, signal content and so on. After that, we focus on the real-time ephemeris recovery method based on PPP-B2b SSR and broadcast ephemeris. The accuracy in radial, tangential and normal directions of PPP-B2b real-time ephemeris orbit are 6.70 cm, 23.39 cm and 25.84 cm respectively, and the improvements compared to broadcast ephemeris are 6.0%, 22.8% and 7.3% respectively. The equivalent distance accuracy of real-time ephemeris clock is 5.33 cm, which is much better than 22.29 cm of broadcast ephemeris. Centimeter level orbit radial error and satellite clock error can meet the needs of real-time PPP. On the platform of PPP-B2b-BRIT receiver, a real-time precise point positioning algorithm based on the BDS-3 PPP-B2b augmentation information is designed and implemented. The receiver includes RF front-end module, signal processing module and information processing module. The real-time PPP data processing is completed in the information processing module, which receives and processes the signals B1C, B2a and B2b of BDS, and outputs the receiver coordinates, receiver clock and atmospheric delay through the serial port. In the static positioning mode, the horizontal positioning accuracy is better than 2 cm, the vertical positioning accuracy is about 4 cm, and the convergence time is 4–5 min. In the kinematic positioning mode, the horizontal positioning accuracy is better than 10 cm, the vertical positioning accuracy is about 10 cm, and the convergence time is 6 min. The experimental results show that the real-time precise point positioning algorithm based on PPP-B2b augmentation information can meet the requirements of static centimeter level and kinematic decimeter level scientific research and engineering applications.

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Acknowledgements. This work was supported in part by the National Key Research and Development Program of China (No. 2019YFC1511504, No. 2016YFB0501900) and National Natural Science Foundation of China (No. 41774017).

References 1. Yang, Y.X., Mao, Y., Sun, B.J.: Basic performance and future developments of BeiDou global navigation satellite system. Satell. Navig. 1, 1 (2020) 2. Lu, J., Guo, X., Su, C.G.: Global capabilities of BeiDou navigation satellite system. Satell Navig. 1, 27 (2020) 3. Chinese Satellite Navigation Office. The Application Service Architecture of BeiDou Navigation Satellite System (Version 1.0), December 2019 4. Du, C.H., Gao, X.W., Ma, Y., et al.: Design and realization of service software for nationwide BDS ground based augmentation system. The 11th China Satellite Navigation Conference. (2020) 5. Chen, J.P., Yu, C., Zhou, J.H., et al.: Decimeter-level algorithm for satellite-based augmentation systems and performance analysis of BDS-2/BDS-3. Sci. Sin-Phys. Mech. Astron. 51(01), 63–71 (2021) 6. Shao, B., Ding, Q., Wu, X.B.: Estimation method of SBAS dual-frequency range error integrity parameter. Satell. Navig. 1, 11 (2020) 7. Wang, B.H., Zhou, J.H., Wang, B., et al.: Influence of the GEO satellite orbit error fluctuation correction on the BDS WADS zone correction. Satell. Navig. 1, 18 (2020) 8. Wang, Y.C., Shen, J.: Real-time integrity monitoring for a wide area precise positioning system. Satell. Navig. 1, 24 (2020) 9. Du, Y.J., Wang, J.L., Rizos, C., et al.: Vulnerabilities and integrity of precise point positioning for intelligent transport systems: overview and analysis. Satell. Navig. 2, 3 (2021) 10. Li, X.X., Zhang, X.H., Li, P.: PPP for rapid precise positioning and orbit determination with zero-difference integer ambiguity fixing. Chin. J. Geophys. 55(3), 833–840 (2012) 11. Shi, C., Zhang, D., Song, W., et al.: BeiDou wide-area precise timing prototype system. Acta Geodaetica et Cartographica Sinica 49(3), 269–277 (2020) 12. Chinese Satellite Navigation Office. BeiDou navigation satellite system signal in space interface control document, precise point positioning service signal PPP-B2b (Version 1.0), July 2020 13. Wang, H.C., Jia, X.L., Li, D., et al.: Accuracy assessment and analysis of broadcast ephemeris of BDS-3 satellites. J. Navig. Position. 7(4), 60–63 (2019) 14. Zhang, X.H., Hu, J.H., Ren, X.D.: New progress of PPP/PPP-RTK and positioning performance comparison of BDS/GNSS PPP. Acta Geodaetica et Cartographica Sinica. 49(9), 1084–1100 (2020) 15. Zhang, X.H., Zhang, Y.X., Zhu, F.: A method of improving ambiguity fixing rate for postprocessing kinematic GNSS data. Satell. Navig. 1, 20 (2020) 16. An, X.D., Meng, X.L., Jiang, W.P.: Multi-constellation GNSS precise point positioning with multi-frequency raw observations and dual-frequency observations of ionospheric-free linear combination. Satell. Navig. 1, 7 (2020) 17. Chen, X.Y.: An alternative integer recovery clock method for precise point positioning with ambiguity resolution. Satell. Navig. 1, 28 (2020)

Autonomous Navigation and Intelligent Operation

Research on Improvement Method of Systematic Deviation of Autonomous Navigation Message of BDS Qiuli Chen1(B) , Haihong Wang1(B) , Xu Zhang1(B) , Yu Ding1(B) , and Weisong Jia2(B) 1 Institute of Telecommunication and Navigation Satellites, CAST, Beijing, China 2 Beijing Institute of Spacecraft System Engineering, Beijing, China

Abstract. Beidou navigation satellite system (BDS) is a global navigation satellite system independently constructed and operated by China. An important function of BDS is to have autonomous navigation capability. Satellite autonomous navigation is a kind of satellite navigation technology that can operate autonomously without the support of ground system. Based on the inter-satellite ranging information, the navigation message information is generated independently and broadcast to users, so as to realize real-time navigation, positioning and timing. The systematic deviation of autonomous navigation message is the deviation between the calculated value of ephemeris and clock and the observed value, which is recorded as o-c. It reflects the matching degree between navigation message and inter-satellite observation. Theoretically, the smaller the better. Aiming at the systematic deviation of autonomous navigation message, this paper proposes a calculation method to eliminate the systematic deviation. Experiments show that this method can effectively reduce the message system error of autonomous navigation, that improve the performance of autonomous navigation. Keywords: BDS satellite · Autonomous navigation · Navigation message · Systematic deviation

1 Introduction Beidou navigation satellite system (BDS) is a global navigation satellite system independently constructed and operated by China. By June 2020, the BDS has been completed global networking. The space segment of the system includes 24 MEO satellites: Walker 24/3/1, 3 geo satellites and 3 IGSO satellites [1]. An important function of BDS is to have autonomous navigation capability. Satellite autonomous navigation is a kind of satellite navigation technology that can operate autonomously without the support of ground system. Based on inter satellite ranging, the navigation message is generated and transmitted to the ground, so as to realize real-time navigation and time service [2–4]. Based on the data of the inter-satellite link and data of the ground tracking station, the average RMS of the orbital radial overlap is better than 0.2 m [5]. The relationship between GEO satellite orbit error and differential positioning accuracy, and simulation © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 327–335, 2021. https://doi.org/10.1007/978-981-16-3142-9_30

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orbit determination based on inter satellite link data were also studied [6]. In this paper, a solution was given to the error of the autonomous navigation message system based on inter satellite link. The systematic deviation of autonomous navigation message based on inter-satellite link is the deviation between the calculated value and the observed value of ephemeris and clock, which is recorded as o-c. It reflects the matching degree of navigation message and inter satellite observation data. Theoretically, the smaller the systematic deviation, the higher the accuracy of navigation message. For the systematic deviation of autonomous navigation message, this paper presented a method to eliminate the systematic deviation of message. Experiments show that this method can effectively reduce the error of autonomous navigation message system, and further improve the accuracy and service performance of autonomous navigation message.

2 Source Analysis of Systematic Deviation of Message As mentioned above, the systematic deviation of autonomous navigation message not only reflects the matching between autonomous navigation broadcast message and inter-satellite observation data, but also represents the on orbit service performance of autonomous navigation. According to the principle of autonomous navigation message solution and data processing flow, the factors causing systematic deviation of navigation message include phase centroid correction, relativistic effect correction and channel delay correction [7–9]. In this section, based on the correction method of three factors, the difference between the maximum correction error and the error of autonomous navigation message system was analyzed. And the source of the error has been given. 2.1 Correction of Satellite Centroid and Antenna Phase Center The precise measurement value of the antenna phase center in the antenna single machine coordinate system, the installation position of the antenna reference point in the satellite mechanical coordinate system, and the precise value of the centroid in the mechanical coordinate system are the input of the antenna phase center and satellite centroid correction. The vector of antenna phase center in satellite body coordinate system was shown in Formula (1). rka = rp + rt + rm

(1)

Where, rp is the vector of the antenna phase center in the antenna single machine coordinate system, rt is the vector of the antenna single machine coordinate origin in the mechanical coordinate system, rm is the vector of the satellite mechanical coordinate origin in the satellite body coordinate system, rka is the vector of the antenna phase center in the satellite body coordinate system. The error of phase center correction was shown in Formula (2). 1 = rka · cos(γ + δ)

(2)

Where, γ is the theoretical value of antenna pointing angle, δ and is the pointing angle error.

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The maximum pointing error is 0.5°. According to the precision measurement, the correction error under the maximum pointing error is about 1 cm. It can be concluded that the systematic deviation of broadcast message larger than 1 cm is not caused by centroid phase center correction. 2.2 Relativistic Effect Correction The fully autonomous navigation operating mode refers to the situation where the ground operation control system, measurement and control system, and anchoring station are unable to inject the space-time reference information required for the operation of the navigation constellation. The system only relies on a working mode in which satellites automatically generate full constellation clock difference and ephemeris data. The operating mode is shown in Fig. 2. Relativistic effects in data processing include gravitational delay of electromagnetic wave and frequency variation of satellite clock caused by relativistic effects. The time delay correction of relativistic effect was shown in Formula (3) [10]. t RC =

 · V 2R c2

(3)

Where, t RC is the relativistic time delay (in seconds) caused by the non-zero eccen is the radial vector of the satellite’s orbit, V is tricity of the satellite’s elliptical orbit, R the inertial velocity vector of the satellite’s orbit, and c is the speed of vacuum light, with the value of 299792458 m/s. From the orbit and velocity accuracy of Beidou satellite, the maximum error of time delay correction of relativistic effect is equivalent to less than mm. 2.3 Channel Transmit Receive Delay Correction The transmit and receive delay of inter satellite link was measured and calculated on the ground, and then injected to the satellite as the input of channel delay correction. Measurement error, space environment change, calculation processing and other factors would lead to a certain deviation of time delay. The correction error caused by this will further cause systematic deviation of autonomous navigation message. Based on the above analysis and the actual engineering situation, this paper attempted to correct the maximum error source of the channel delay which is the worst in the system, and obtained a better result. Figure 1 showed the difference of autonomous navigation message system in a certain test period. Based on the above analysis, it was considered that the channel delay correction error is the biggest error source of the message system error of autonomous navigation.

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Fig. 1. Systematic deviation of autonomous navigation message in 2020

3 Solution of Channel Transmit and Receive Delay Correction Error Through the epoch reduction of the ephemeris and clock observations, that differs from the calculated value, the relationship between time delay correction error and systematic error could be obtained through. For any pair of two-way transmitting and receiving satellites, tot−de , tor - de , tsr - de , tst - de , was defined as the input value of the delay of other satellite transmitting, other ∗ ∗ satellite receiving, local satellite transmitting and local satellite receiving. tot - de , tor - de , ∗ ∗ tsr - de , tst - de was define the real values of the time delay of other satellite transmitting, other satellite receiving, local satellite transmitting and local satellite receiving. Furthermore, δtot−de , δtor - de , δtsr - de , δtst - de was defined as the delay error of other satellite transmitting, other satellite receiving, local satellite transmitting and local satellite receiving. Their relationships were described in the following formula. ∗ tot−de = tot−de + δtot−de

(4)

∗ tor−de = tor−de + δtor−de

(5)

∗ tsr−de = tsr−de + δtsr−de

(6)

∗ tst−−de = tst−de + δtst−de

(7)

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3.1 Epoch Reduction of Inter Satellite Distance Observations Any link satellite is a two-way transceiver link. To the transmission of this satellite and the reception of other satellites link, the transmit time of this satellite was defined as tst , and the reception time of other satellites was defined as tor . To other satellites transmit and local satellite receive link, other satellites transmit time was defined as tot and local satellite receive time was tsr . As shown in Fig. 2, L1 was the observation of the transmission of this satellite and the reception of other satellites link. And L2 was the observation of the transmission of other satellite and the reception of this satellites link. In order to calculate the difference with the calculated value of inter satellite distance, it is necessary to reduce the observed value to the specified epoch time tz . L1’ and L2’ were the observed values reduced to tz .

Fig. 2. Inter satellite observation and epoch reduction process

Observation of this satellite transmission and other satellite reception L1 (unidirectional link): ∗ st L1 = Lo,st,or = [(tor − (t∗or−de + δtor−de ) − aor 0 ) − (tst + (tst−de + δtst−de ) − a0 )] · c (8)

Where, tor is the clock time received by other satellite, a0or is the clock difference received by other satellite, tst is the clock time transmitted by this satellite, and a0st is the clock difference transmitted by this satellite. Observation of other satellite transmission and this satellite reception L2 (unidirectional link): ∗ ot L2 = Lo,ot,sr = [(tsr − (t∗sr−de + δtsr−de ) − asr 0 ) − (tot + (tot−de + δtot−de ) − a0 )] · c (9)

Where, tsr is the clock time received by this satellite, a0sr is the clock difference received by this satellite, tot is the clock time transmitted by other satellite, and a0ot is the clock difference transmitted by other satellite. Adding the two-way pseudo range measurements to the same epoch time can eliminate the satellite clock error, only including the satellite distance [11]. The calculation of the inter satellite observations lo and EP of the ephemeris is shown in Formula (10) (reduction time tz).

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Lo,ep = (L2 +L1 )/2 ∗ ∗ = {[(tsr − tsr−de − a0sr ) − (tot + tot−de − a0ot )] · c/2}(tz ) − (δtsr−de + δtot−de ) · c/2 ∗ ∗ +{[(tor − tor−de − a0or ) − (tst + tst−de − a0st )] · c/2}(tz ) − (δtor−de + δtst−de ) · c/2

= (L2 (tz ) − (δtsr−de + δtot−de ) · c + L1 (tz ) − (δtor−de + δtst−de ) · c)/2 

(10)



Where, L1 , L2 is the observed value of L1 , L2 for epoch reduction, and δtsr−de , δtot−de , δtor−de , δtst−de has nothing to do with epoch reduction. The satellite orbit can be eliminated by subtracting the two-way pseudo range measurements at the same epoch, only including the satellite clock error [12]. The observed value of clock Lo,cl_a. The calculation method of a (reduction time TZ) is shown in Formula (11). Lo,cl_a = (L2 − L1 )/2 ∗ ∗ = {[(tsr − tsr−de − a0sr ) − (tot + tot−de − a0ot )] · c/2}(tz ) − (δtsr−de + δtot−de ) · c/2 ∗ ∗ − {[(tor − tor−de − a0or ) − (tst + tst−de − a0st )] · c/2}(tz ) + (δtor−de + δtst−de ) · c/2

= (a02 (tz ) − (δtsr−de + δtot−de ) · c − a01 (tz ) + (δtor−de + δtst−de ) · c)/2

(11)

The definition of each parameter in the formula was the same as that in Formula (10). 3.2 Calculated Value of Inter Satellite Distance The ephemeris calculated value (time TZ) is shown below. Lc,ep = |r1 (tz ) − r2 (tz )|

(12)

Where, r1 (tz ), r2 (tz ) is the calculated value of inter satellite distance at epoch time. Calculated value of satellite clock error (tz time) (2)

(1)

Lc,cl_a = a0 (tz ) − a0 (tz ) (1)

(13)

(2)

Where, a0 (tz ), a0 (tz ) is the clock difference of epoch time. 3.3 Calculation of the Difference Between the Observed and Theoretical Values of Ephemeris and Clock By calculating the difference between the observed and theoretical values of ephemeris and clock, the relationship between the systematic deviation shown in Formulas (14) and (15) and the time delay error of the link building satellite was obtained. [(δtot−de + δtor−de ) + (δtst−de + δtsr−de )] ·c 2 [(δtot−de − δtor−de ) − (δtst−de − δtsr−de )] ·c LO−C,cl = Lo,cl − Lc,cl = − 2 In the formula, the meaning of parameters were the same as the above.

LO−C,ep = Lo,ep − Lc,ep = −

(14) (15)

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4 Simulation Calculation of Channel Transmit and Receive Delay Error Based on the third part of the relationship between the receiving and transmitting delay and the systematic deviation of ephemeris and clock, the systematic deviation of a fixed period was selected as the input data of simulation solution, which is recorded as the system difference matrix B. The contents of systematic deviation matrix include the code of transmitting satellite, receiving satellite, clock O-C and ephemeris O-C of two-way link. The coefficient matrix A of the time period has been constructed from the chain building relationship corresponding to the input matrix and Formulas (14) and (15), as shown in Formula (16) [13]. ⎧ [n1, n2] = size(B) ⎪ ⎪ ⎪ ⎪ ⎪ A = zeros(2 ∗ n1, 2 ∗ B(n1, 1)) ⎪ ⎪ ⎪ ⎪ ⎪ 1 ⎪ ⎪ A(2i − 1, 2 · OC(i, 1) − 1) = − ⎪ ⎪ 2 ⎪ ⎪ ⎪ ⎪ 1 ⎪ ⎪ A(2i − 1, 2 · OC(i, 2) − 1) = ⎪ ⎪ ⎪ 2 ⎪ ⎪ ⎪ 1 ⎪ ⎪ A(2i − 1, 2 · OC(i, 2) − 1) = ⎪ ⎪ ⎪ 2 ⎨ 1 (16) A(2i − 1, 2 · OC(i, 2)) = ⎪ ⎪ 2 ⎪ ⎪ ⎪ ⎪ 1 ⎪ ⎪ A(2i, 2 · OC(i, 1) − 1) = − ⎪ ⎪ 2 ⎪ ⎪ ⎪ ⎪ 1 ⎪ ⎪ A(2i, 2 · OC(i, 1)) = − ⎪ ⎪ 2 ⎪ ⎪ ⎪ ⎪ 1 ⎪ ⎪ A(2i, 2 · OC(i, 2) − 1) = − ⎪ ⎪ ⎪ 2 ⎪ ⎪ ⎪ ⎪ ⎩ A(2i, 2 · OC(i, 2)) = − 1 2 Where n1 and n2 are the number of rows and columns of input matrix B, and i = 1, n1. Using the least square method, the correction of delay difference is obtained as Formula (17). δx = (AT A)−1 AT · B

(17)

Using the above formula, we can get the channel delay difference correction of the whole constellation. The improved channel delay is shown in Formula (18). ∗ tde = tde − δtde

(18)

The centroid antenna phase center correction, relativistic correction, and the improved time delay value were replaced into the simulation software. And the navigation message, ephemeris and clock system error were carried out again. The comparison

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Fig. 3. Comparison of ephemeris O-C before and after improvement

Fig. 4. Comparison of O-C of satellite clock before and after improvement

of the improved system was shown in Fig. 3 and Fig. 4. The experimental results show that the improvement effect was still obvious in the following period of time. The mean value of O-C system difference of ephemeris before correction was −0.690 m, root mean square was 0.842 m. And the mean value after correction was −0.0926 m, root mean square was 0.371 m. The mean value of O-C system clock error before correction was −0.003 m, root mean square was 0.806 m. And the mean value after correction was − 0.003 m, root mean square was 0.404 m.

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5 Conclusion Autonomous navigation is one of the characteristics of modern GNSS system. Based on the inter satellite measurement and information interaction, the generation and broadcast of autonomous navigation message can be completed, so as to realize the autonomous operation of the system, which will greatly reduce the ground operation cost of the system. The accuracy of autonomous navigation message will directly affect the accuracy of navigation, positioning and time service during the autonomous operation of the system. For the systematic deviation of autonomous navigation message, this paper analyzes the factors that cause the systematic deviation. It is proved that the method can effectively reduce the error of autonomous navigation message system and further improve the performance of autonomous navigation.

References 1. BeiDou Navigation Satellite System. http://en.beidou.gov.cn/SYSTEMS/TheMainArchitec ture 2. Yan, Z., Yulin, Z.: Design and implementation of autonomous navigation of constellation. J. Astronaut. 24(5), P525–P528 (2003) 3. Song, X., Mao, Y., Jia, X., et al.: The distributed processing algorithm for autonomously updating the ephemeris of navigation satellite by inter-satellite links. Geomat. Inf. Sci. Wuhan Univ. 35(10), P1161–P1164 (2010) 4. Gu, Y., Chen, Z., Ping, S.: Autonomous time synchronization algorithm on different crosslink structures among navigation satellites. In: CSNC 2010 (2010) 5. Ruan, R., et al.: Orbit determination and time synchronization for BDS-3 satellites with raw inter-satellite link ranging observations. Satell. Navig. 1(1), 1–12 (2020). https://doi.org/10. 1186/s43020-020-0008-y 6. Wang, B., Zhou, J., Wang, B., Cong, D., Zhang, H.: Influence of the GEO satellite orbit error fluctuation correction on the BDS WADS zone correction. Satell. Navig. 1(1), 18 (2020). https://doi.org/10.1186/s43020-020-00020-0 7. Wang, H., Chen, Z., Chu, H., et al.: On-board autonomous orbit prediction algorithm for navigation satellites. J. Astronaut. 33(8), P1019–P1023 (2012) 8. Mao, Y., Hu, X., Song, X., et al.: Satellite autonomous navigation algorithm analysis based on broadcast ephemeris parameters. Scientia Sinica, Mechanica Astronomica 45(7), P77–P85 (2015) 9. Liu, J., Zeng, X., Xia, L., et al.: Algorithm and simulation of autonomous orbit determination for navigation satellites. Geomatics Inf. Sci. Wuhan Univ. 29(12), P1040–P1044 (2004) 10. Li, Z., Huang, J.: GPS Measurement and Data Processing. Wuhan University Press (2005) 11. Guo, R., XiaoGong, H., Tang, B., Huang, Y., Liu, L., Cheng, L., He, F.: Precise orbit determination for geostationary satellites with multiple tracking techniques. Chin. Sci. Bull. 55(8), 687–692 (2010). https://doi.org/10.1007/s11434-010-0074-x 12. Liu, J., Yang, H., Fan, J., Zhu, D.: Deformation characteristics of COMPASS satellite signals. In: Sun, J., Jiao, W., Haitao, Wu., Mingquan, Lu. (eds.) China Satellite Navigation Conference (CSNC) 2014 Proceedings: Volume II, pp. 171–179. Springer, Heidelberg (2014). https://doi. org/10.1007/978-3-642-54743-0_15 13. Matlab practical Chinese Manual.

A DBZP Acquisition Method for High-Dynamic and Weak GPS Signal Aided by SINS Junshuai Wang1,2(B) , Xinlong Wang1 , Fei Liu2 , and Xiaoming Hao2 1 School of Astronautics, Beihang University, Beijing, China

[email protected] 2 Space Star Technology Co., Ltd., Beijing, China

Abstract. In order to enhance the acquisition performance in high-dynamic and weak GPS signal conditions, a Double Block Zero Padding (DBZP) acquisition method based on SINS is presented. In the method, the GPS doppler frequency estimated by SINS decreases the range of frequency uncertainty; the doppler rate and code doppler aided from SINS overcomes the energy diffusion caused by the receiver’s dynamic, and the energy based navigation data bits estimation method expands coherent integration time. All of them make the acquisition faster and higher sensitivity in high-dynamic and weak conditions. At last, the re-acquisition experiments of weak signal in high-dynamic environment are conducted, and the simulation results show that the proposed method can acquire high-dynamic and weak signal effectively. Keywords: High-dynamic and weak signal · SINS · Signal acquisition · DBZP · Navigation bits estimation

1 Introduction With the development of satellite navigation techniques, Global Positioning System (GPS) has been widely applied in civil and military fields. Therefore, it is very important to research the GPS receiver for high-dynamic and weak signal applications such as high earth orbit satellite, ballistic missile and cruise missile, etc. [1, 2]. In these applications, the acquisition performance is limited by many factors, such as serious signal energy attenuation, large Doppler search range, frequent signal blockage caused by Line-OfSight (LOS) obstructions, and so on. Acquisition of weak GPS signals requires long coherent integration time to boost the post signal-to-noise ratio (SNR). As the increase of coherent integration time, the complexity of dealing with data bits and the computational cost of signal acquisition grow rapidly [3, 4]. Double block zero padding (DBZP) is an effective acquisition approach to process long data coherently with fewer operations [5]. At present, as an advanced weak signal acquisition algorithm, the DBZP algorithm has been used to enhance the receiver acquisition performance for weak signals by many researchers [6, 7]. But the studies of its application in high-dynamic and weak signal conditions are relatively few.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 336–346, 2021. https://doi.org/10.1007/978-981-16-3142-9_31

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When acquiring weak signals in high-dynamic conditions, the coherent integration time need to be short so as to reduce the attenuation of coherently integrated energy; however, the time should be long to acquire weak signal reliably [7]. Obviously, the requirements of acquisition weak signals and high-dynamic signals are contradictory, and it’s difficult to balance them when the stand-alone DBZP method is applied [8, 9]. In addition, once the coherent integration time of DBZP method beyond one data bit period, the effect of unknown navigation date bit transition should be taken into account. Many researches have indicated that the information from other navigation systems [10–12] such as SINS can improve the performance of signal acquisition at the same time overcoming dynamics and noise/interference. With SINS aiding, the dynamic effect on GPS signal acquisition could be mitigated effectively. Then, the acquisition algorithm only needs to deal with the issues from weak signals. Thereby, a DBZP acquisition method for high-dynamic and weak signal aided by SINS is proposed. This method can not only make full use of the DBZP advantages in acquiring weak signals but also improve the receiver acquisition speed and capability in high-dynamic environments.

2 Performance Analysis of DBZP Algorithm in High-Dynamic Environments The principles of DBZP acquisition algorithm have been introduced by many researchers in detail. It can be seen from the DBZP algorithm, the coherent integration is calculated at all the Doppler bins and all the code delays in the same processing step. Thus, DBZP requires less process compared to long data circular correlation. And it has advantages in dealing with long coherent integration, which is suitable to acquisition for weak signals. However, its acquisition performance will be greatly influenced by Doppler effect and Doppler rate when applied to acquiring high-dynamic and weak signals. Furthermore, when the DBZP algorithm is applied to acquisition of weak signal, the bit transition will seriously affect the coherent integration result once the coherent integration beyond the 20 ms date bit period. So the data wipe off technique must be considered to extend coherent integration time. Assuming there is no navigation bit sign changes during integration time, the n-th coherent integration result [5] is   (2.1) Yn = 0.54Asat Nc Rc (τ − τu )sinc(π δfd T ) exp j · (π δfd T + θ) + n where: T is the coherent integration time. Nc = T · fs is the number of sampled points in coherent integration time. Rc (τ − τu ) is C/A code autocorrelation function and τu is the code delay of the local signal. θ is the carrier phase error. δfd = fd .0 + α n + 1 2 denotes the Doppler frequency difference. For the sake of analyzing how the Doppler rate affects coherent integration, code phase, Doppler error and noise are ignored. Then, the n-th coherent integration result can be simplified as             (2.2) Yn = 0.5Asat Nc sinc π fd ,0 + α n + 1 2 T exp j · π fd ,0 + α n + 1 2 T

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The above coherent integration results are accumulated during the whole integration time, and then FFT is performed on the accumulation. Figure 1 shows the effects on the integration results with different Doppler rates, where the coherent integration time is 80 ms and the number of incoherent accumulations is 10.

Fig. 1. The effects on the integration results with different Doppler rates

It can be seen in this figure, when the Doppler rate is 0 Hz/s, a peak value appears at the frequency bin which corresponds to the true Doppler shift. However, when there is a nonzero Doppler rate, the accumulated peak energy will diffuse to adjacent frequency bins. As the Doppler rate increases, the diffusion range becomes larger and the peak value weaker. And longer the coherent integration time is more serious the effect, which will have a bad impact on the valid SNR gain. As mentioned before, it is crucial to increase the coherent time for weak signal acquisition, so it will be very difficult to acquire high-dynamic and weak signals by DBZP without external aiding. Moreover, the acquisition time is an important variable to evaluate the receiver performance. The mean acquisition time [11] is given by,



tv 2 − Pd Pfa + 1 LTNs T acq = (2.3) 2Pd T Ns =

fcov × Lc × fs fres

(2.4)

where: Pd is the probability of detection. Pfa is the probability of false alarm. tv is the false alarm search time. L is the incoherent integration time. Ns is the total search cell number. fcov is the Doppler shift search range. Lc is the length of C/A code chip. As can be inferred from Eq. (2.3), in high-dynamic environments the Doppler search range for stand-alone DBZP acquisition grows severely, which will greatly increase acquisition time.

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3 A DBZP Acquisition Method for High-Dynamic and Weak GPS Signal Aided by SINS Information To overcome the problem that the performance of DBZP acquisition method is vulnerable to the vehicle dynamics and data bit transitions, a DBZP acquisition scheme for highdynamic and weak signal aided by SINS is designed. And its structure is presented in Fig. 2.

Fig. 2. The structure of the DBZP acquisition scheme for high-dynamic and weak signal aided by SINS

In this scheme, the local Doppler frequency aided by the LOS velocity and acceleration derived from SINS and satellite ephemeris mitigate the dynamic of received signals and reduce the search frequency range, which will improve the acquisition sensitivity and speed. With the data bit edge aided by SINS, an energy-based method is utilized to estimate the unknown data bits during the DBZP coherent integration time, which will enhance the acquisition reliability for weak signals. 3.1 Calculation of Aiding Information (1) Estimation of Doppler Shift and Doppler Rate Based on the velocity and position from SINS and satellite ephemeris, the estimated Doppler shift fˆaid , which is caused by the relative movement between satellite and receiver, can be calculated as, 1 ˆ V r − Vˆ s ej fˆaid = λL1

(3.1)

where: λL1 is the wavelength of L1 carrier. Vˆ r is the SINS aiding velocity. Vˆ s is the satellite velocity provided by satellite ephemeris. ei denotes the LOS unit vector from the satellite to receiver.

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Similarly, the Doppler rate aided by SINS and satellite ephemeris can be given as, fdop =

 1  aˆ r − aˆ s ej λL1

(3.2)

where aˆ r and aˆ s are the acceleration measurement of receiver and the satellite, respectively. The search range of Doppler shift mainly depends on the velocity error of SINS information, and the influence of the satellite ephemeris error can be ignored. As the frequency aiding error reduces, the search range will be smaller and the acquisition speed faster. The estimation error variance of Doppler shift can be expressed as, 2 = σdop

1 T T ej δV r δV r ej λ2L1

(3.3)

where δVr can be expressed as,

δV r = δV r0 +

δadt

(3.4)

T

where: δVr0 is the initial velocity error. δa represents the acceleration error of the SINS with respect to the earth-centered earth-fixed (ECEF) frame. δa can be described as [12],     δa = Reb · diag kax , kay , kaz · f b + Δb − ae ·

T

    Reb · diag kwx , kwy , kwz · ωb + εb dt

(3.5)

where: Reb is the transformation matrix from the body frame to the ECEF frame. f b is the specific force measured by the accelerometer. kax , kay , kaz are the accelerometer scale factors errors. ae denotes the acceleration vector with respect to the ECEF frame. kwx , kwy , kwz are gyro’s scale factor errors. ωb is the angular rate measured by gyro. εb is the gyro’s bias. Substituting Eq. (3.4) to Eq. (3.3), the expression of velocity error can be got. Theoretically, the velocity error δV r can be forecasted by error state equations of SINS. But in practical use, when the vehicle is under high-dynamic scenarios, it is difficult to accurately model the error function of SINS. Moreover, as the signal blockage time longer, the forecasting precision of δV r will be worse. Hence, the search range of Doppler shift is set as the maximum of Doppler error estimated by SINS, and enough margin is provided to ensure the reliability of acquisition. The Doppler shift search comparison of No aiding and SINS aiding acquisition is presented in Table 1. The vehicle LOS acceleration with respect to the satellite is 7g, and the reacquisition is performed after 150 s signal blockage. Without external aiding, the total Doppler search range is set to be ±8 KHz in high-dynamic environments. While using the aiding from SINS and satellite ephemeris, the Doppler search range is sharply reduced. This range is relative to the signal blockage time and the performance of SINS inertial components. Deduced from the compared results in the table, the Doppler shift search range is greatly reduced owing to the SINS aiding. Hence the acquisition speed after signal blockage is obviously improved, that is to say, the re-acquisition capability are enhanced.

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Table 1. The search comparison between no aiding and SINS aiding acquisition. Aiding condition

Search range

Search number

Search time

Non

±8 kHz

1280

1000 ms

160

12.5 ms

SINS ±1 kHz aiding (ε = 50°/h)

(2) Determining Data Bit Edge When ignoring the relative drift among satellites clocks, the GPS signals are transmitted simultaneously. Therefore, according to GPS signal transmitted time, the data bit edge can be calculated as, D = 1 + mod(ts , 0.02)

(3.8)

where ts is the transmitted time of GPS signal. It can be calculated with the GPS time tr when the signal is received, the delay of signal transmitting from the satellite to the receiver tD and the satellite clock correction Tcorr as, ts = tr = tD + Tcorr

(3.9)

where Tcorr = a1 + a2 × (tr − toc ) + a3 × (tr − toc )2  tD = |P r − P s | c a1 , a2 and a3 are the zeroth through second-order satellite clock correction terms from navigation data message subframe 1. toc is the reference GPS time for the satellite clock correction terms. c is the velocity of light. P r and P s represent the receiver’s position aided by SINS and the satellite’s position aided by satellite ephemeris respectively. 3.2 A DBZP Acquisition Method Based on Navigation Bit Estimation A longer coherent integration time is essential to increase accumulated SNR for the weak signal acquisition. But when the coherent integration time beyond one data bit period, bit transitions must be considered. To solve this problem, with the SINS aided data bit edge, an energy-based estimation method is taken to wipe off data bits during the DBZP coherent integration time. Its specific implementation steps are given as follows: (1) DBZP Coherent Integration Based on Navigation Bit Estimation

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Align the start position of DBZP acquisition with the navigation data bit edge aided by SINS. Before performing column-wise FFT on the DBZP matrix M c , 2Ndb−1 navigation bit combinations need to be taken into account. Thus, we will obtain coherent integration matrixes M cc for a DBZP coherent integration. The number of rows in M c is 20Ndb Nstep . According to the principle of DBZP acquisition, M c can be written into Ndb sub-matrixes as, T  M c = M 1c . . . M ic . . . M Ndb (3.10) c   where M ic is a matrix of size 20Nstep × Sblock × Nstep , i = 1, 2, . . . , Ndb . Each M ic is produced by coherent integration operation with one navigation data bit. In this paper, the coherent integration time is set to 80 ms (i.e. Ndb equals to 4). When Ndb equals to 4, the total number of navigation bit combinations are 2Ndb−1 = 8. And all these combinations can be written into a matrix H as, ⎡ ⎤ I I I ... I ⎢ I −I −I . . . −I ⎥ ⎥ H = [H 1 H 2 H 3 . . . H 8 ]⎢ (3.11) ⎣ I I −I . . . −I ⎦ I I I . . . −I 20N ×(S ×N ×8) step step block   where: I is a matrix of size 20Nstep × Sblock × Nstep whose elements are 1, H i corresponds to one navigation bit combination. Then eight coherent integration matrixes M c,i , i = 1, 2, . . . , 2Ndb −1 can be obtained as, M c,i = columnwise FFT(H i · M c ), i = 1, 2, . . . , 8

(3.12)

where “·” denotes dot-multiply operation. (2) Incoherently Integrating the Resulting Coherent Integration It is hardly possible to determine the reliable navigation bit combination through only one coherent integration matrix for acquisition in high-dynamic and weak signal conditions. Thus, some coherent integration matrixes must be integrated incoherently. In the following method, the incoherent integration matrix can be got meanwhile the most reliable navigation bit combination determined. Assuming I c,i and Qc,i are real part and image part of M ic , and the incoherent integration matrix of the former c − 1 coherent integration matrixes is P nc,c−1 , the 2Ndb−1 incoherent integration matrixes Pnc,i , i = 1, 2, . . . , 2Ndb −1 of the c-th coherent integration will be got by the following equation, P nc,i (τu , fd ) = P nc,c−1 (τu , fd ) + [I c,i (τu , fd )2 + Qc,i (τu , fd )2 ], i = 1, 2, . . . , 2Ndb −1 (3.13) Then P nc,i , i = 1, 2, . . . , 2N −1 are compared cell wise. The maximum from each index forms the new incoherent integration M nc,c at that index. Thus M nc,c is the c-th incoherent integration matrix.   (3.14) M nc,c (τu , fd ) = max P nc,1 (τu , fd ), P nc,2 (τu , fd ), . . . , P nc,2Ndb −1 (τu , fd ) db

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where m, n are index of each matrix. (3) Making judgment control according to acquisition threshold In the module of judgment control, judge whether the maximum power of M nc,c exceeds the acquisition threshold or not. If exceed, the acquisition is success, and the Doppler shift fdop and code phase τˆu can be got from the following equation,  τˆu , fˆdop = arg max Mnc,c (τu , fd ) (3.15) (τu ,fd )

The final estimation of Doppler shift is fˆ dop = fˆaid + fˆdop

(3.16)

where: faid is the Doppler shift aided by SINS. fdop is the residual Doppler shift estimated by acquisition method. Then the acquisition results are delivered to tracking module.

4 Simulation Verification 4.1 Simulation Conditions The GPS IF signals in the simulation are generated by GPS signal simulator. Their parameters are set as follows. The sampling rate is 4.096 MHz. IF frequency is 1.25 MHz. The carrier to noise ratio is from 15 to 44 dB-Hz and 100 Monte Carlo simulations are performed for each C/N0. For DBZP acquisition, the coherent integration time is set to be 80 ms, and the number of incoherent integration times is 10.  A low-grade IMU is adopted. The gyro bias is 50◦ h and its scale factor is 1000 ppm. The accelerometer bias is 1mg and its scale factor The white noise standard √ is 1000 ppm. √ ◦ h and 0.1 mg Hz respectively. Simuvariations of gyros and accelerations are 1 late a reacquisition scenario after GPS signal blockage in high-dynamic and weak signal conditions. In that scenario, the receiver LOS acceleration with respect to the satellite is 7g and the signal blockage time is 150 s. When the GPS signal is recovered, the initial Doppler shift is set to be 7365 Hz and the code phase is 379.1 chips. The Doppler shift error aided by SINS is 960 Hz, which is derived from Eq. (3.3). So the Doppler shift search range of SINS aiding DBZP acquisition algorithm is set ±1 KHz, i.e. Nstep = 2. For the no aiding DBZP, the search rang is ±8 KHz (Nstep = 16). 4.2 Simulation Results and Analysis It can be seen from Fig. 3(a) that the final acquired code phase is 379.1 chips which is in accordance with the preinstalled code phase, the residual Doppler shift acquired by SINS aiding DBZP acquisition algorithm is 862.5 Hz. the Doppler shift aided by SINS fˆaid is 6.5 kHz. So the total Doppler shift is 7362.5 Hz and the Doppler shift error estimated by the new algorithm is 2.5 Hz. Figure 3 shows that proposed SINS aiding DBZP algorithm gives the correct result and the no aiding DBZP algorithm can not acquire the signal.

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Fig. 3. (a) the final incoherent integration result using SINS aiding algorithm (b) the final incoherent integration result using no aiding algorithm

Fig. 4. The probability of detection of different acquisition algorithms.

Fig. 5. The reacquisition speed of different acquisition algorithms

Figure 4 presents a comparison of the detection probability between different acquisition algorithms under high-dynamic environments. The algorithms are SINS aiding DBZP algorithm and no aiding DBZP algorithm. And the total integration time for all the two acquisition algorithm is 800 ms. It can be seen in this figure that the acquisition capability of SINS aiding DBZP algorithm is higher than the no aiding DBZP algorithm by 6 dB. The main reason is that the Doppler rate aided by SINS restrains the attenuation of integrated energy due to high-dynamic condition. Figure 5 shows the normalized reacquisition time comparison of the above two acquisition algorithms. These acquisition times are calculated according to Eq. (2.3). The acquisition time which is infinite denotes the algorithm cannot acquire signals in the C/N0. It can be seen from this figure that the acquisition speed of SINS aiding DBZP algorithm is faster 9 times than no aiding DBZP algorithm due to the Doppler shift aided by SINS.

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5 Conclusions In order to improve the acquisition sensitivity and speed of GPS receiver in high-dynamic and weak signal conditions, a SINS aided DBZP acquisition method is proposed. The following conclusions are drawn by theoretical analysis and simulation verification. (1) Under high-dynamic and weak signal environments, for traditional DBZP acquisition method, the integration gain will be seriously attenuated due to the effect of Doppler rate and the acquisition speed is largely limited due to seriously increased Doppler shift search range. (2) Utilizing navigation data bit edge aided by SINS, the energy-based DBZP navigation bit estimation method extends coherent integration time, which enhances and capability for high-dynamic and weak signals. (3) Using the information (such as positions, velocities, accelerations, etc.) aided by SINS and satellite ephemeris, Doppler rate and Doppler can be given to aid the acquisition in high-dynamic and weak signal conditions. The aiding Doppler rate effectively reduces the gain attenuation caused by vehicle dynamics and improves acquisition sensitivity. And the aiding Doppler not only improves acquisition speed through greatly reducing the Doppler shift search range, but also enhances acquisition sensitivity by transformed to code Doppler and compensating to code Doppler effect. The acquisition method proposed in this paper can effectively improve the acquisition performance in high dynamic and weak signal environments such as ballistic missile, hypersonic cruise missile and high earth orbit satellite. This method has a wide application foreground.

References 1. Lashley, M., Bevly, D.M., Hung, J.Y.: Performance analysis of vector tracking algorithms for weak GPS signals in high dynamics. IEEE J. Sel. Top. Sig. Process. 3(4), 661–673 (2009). https://doi.org/10.1109/JSTSP.2009.2023341 2. Kamel, A.M.: Design and testing of an intelligent GPS tracking loop for noise reduction and high dynamics application. In: ION GNSS 2010, Portland, OR, 21–24 September 2010, pp. 3235–3243 (2010) 3. Kaplan, E.: Understanding GPS: Principles and Applications, 2nd edn. Artech House Inc., Boston (2005) 4. Tsui, J.B.: Fundamentals of Global Positioning System Receivers: A Software Approach, 2nd edn. Wiley, New York (2004) 5. Ziedan, N.I.: GNSS Receivers for Weak Signals. Artech House Inc., Boston (2006) 6. Meng, Q., Liu, J.Y., Zeng, Q.H., et al.: BeiDou navigation receiver weak signal acquisition aided by block improved DBZP. Acta Aeronautica et Astronautica Sinica 38(8), 320833 (2017) 7. Heckler, G.W., Garrison, J.L.: Implementation and testing of an unaided method for the acquisition of weak GPS C/A code signals. Navigation 56(4), 241–259 (2009) 8. Wang, J., Lian, B., Xue, Z.: Weak GPS signal acquisition method based on DBZP. J. Syst. Eng. Electron. 29(2), 236–243 (2018)

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9. Wang, Y., Dang, C., Han, X., Han, L., Qu, B.: A fast algorithm for GNSS-R reflected signals based on dynamic phase compensation and DBZP. In: Sun, J., Yang, C., Xie, J. (eds.) CSNC 2020. LNEE, vol. 652, pp. 242–251. Springer, Singapore (2020). https://doi.org/10.1007/978981-15-3715-8_23 10. Yongkui, M., Yi, Z., Zhongzhao, Z., Guangfu, M.: Modified method of high dynamic & high sensitivity GPS signal acquisition. Syst. Eng. Electron. 31(2), 265–269 (2009) 11. Lozow, J.B.: Analysis of direct P(Y) code acquisition. J. Inst. Navig. 44(1), 89–98 (1997) 12. Wang, X.-L., Li, Y.-F.: An innovative scheme for SINS/GPS ultra-tight integration system with low-grade IMU. Aerosp. Sci. Technol. 23, 452–460 (2011). https://doi.org/10.1016/J,ast. 2011.10.004

The Dispersion Effect of Pseudo-noise Ranging and Time Delay Measurement for Ka Inter-satellite Link Jianlou Zhuang1(B) , Jie Zhang2 , Chengbin Kang1 , Zhendong Li1 , and Zhijia Liu2 1 Institute of Telecommunication and Navigation Satellites, CAST, Beijing 100094, China 2 Beijing Institute of Spacecraft System Engineering, Beijing 100094, China

Abstract. BD-3 navigation satellite system uses the Ka Inter-satellite Link (ISL) technology. The accuracy of the distances between satellites is one of important parameters for autonomous navigation, which depends on the accuracy of the time delay of devices at both ends of ISL. However, because of the dispersion effect of RF channel and antenna, it is difficult to accurately give the time delay by traditional group delay measurement. In this paper, the Phase Spectrum Integration (PSI) method for pseudorange delay testing adapted for dispersive network is given. Then, taking the Ka reflector ISL antenna as an example, the pseudorange delay of this antenna is obtained by the PSI and other methods. The result shows the PSI method improves the accuracy of pseudorange delay measurement and meets the requirements of the in orbit application directly for ISL ranging. Keywords: Inter-satellite link · ISL · Pseudo-noise ranging · Dispersion effect · Transmission function · Group delay · Pseudorange delay · Phase Spectrum Integration · PSI

1 Introduction In the realization of constellation autonomous navigation of BD-3 global navigation satellite system, one of the key points is to use Ka band Inter-satellite Link (ISL) to measure inter satellite distance [1–7], then the clock error and the pseudorange of the phase center can be solved [1, 2, 5, 7] regarding the time delay of devices (antenna, RF channel, etc.) at both ends of ISL as constants in a short time (such as 3 days [6]), which could become the main error source in ISL range. In order to improve the accuracy of ISL ranging, the popular method is the satellite and ground joint solution method [3–6, 17]. TANG Cheng Pan et al. (2017) [6] of Shanghai Astronomical Observatory (SHAO) analyzed the in orbit data of BD-3 satellite, and the delay of satellite end calculated is better than 0.4 ns within 4 months, but the variation of delay of ground anchor station is up to 4.13 ns. RUAN Rengui et al. (2020) [4, 5, 17] of Xi’an Institute of Surveying and Mapping gave the stability of the delay calculated is more than 0.5 ns when 8 BD-3 satellites, 2 anchor stations and 7 domestic iGMAS monitoring stations included. Therefore, although the satellite and ground joint solution of ISL ranging can solve the delay of each end of the ISL as an unknown value, © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 347–355, 2021. https://doi.org/10.1007/978-981-16-3142-9_32

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it needs an accurate delay (satellite end or anchor station end) as a benchmark, so it cannot avoid the problem of determining the delay of devices accurately. The delay of devices are generally considered as group delay and measured by vector network analyzer [8, 9]. However, there are many discussions that group delay cannot represent the delay of Pseudo-Noise (PN) code ranging because of the dispersion effect of the RF devices [12–14]. A solution is to calculate the pseudorange delay by numerical processing. Among them, Mike Brookes of Imperial College of Technology (2006) [14] proposed several calculation methods for group delay in speech signal processing, including DC component, average (AV), energy weighted (EW) and so on, but they are all approximate methods. ZHU Xiangwei et al. (2008) [12, 13] proposed Taylor expansion for group delay curve and took its zero order expansion term as pseudorange delay but the error is about 0.3 ns. TANG Dezhi et al. (2019) [11] of Chery Automobile Co., Ltd. analyzed the influence of dispersive network on time-domain pulse signal according to the transmission function theory, but the approximation of transmission function of this method is not suitable for the analysis of PN code signal. Based on the research of the transmission function of dispersive networks, this paper proposes the Phase Spectrum Integration (PSI) method for pseudorange delay determination. And then, taking the Ka reflector ISL antenna of BD-3 M1S satellite as an example, the pseudorange delay is calculated by PSI method. The results show its accuracy is better than EW and AV methods mentioned above.

2 Pseudorange Delay of Dispersive Networks 2.1 Group Delay and Pseudorange Delay In the propagation theory of electromagnetic waves, the concepts of phase velocity and group velocity are widely used. Phase velocity vp is defined as the moving velocity of phase plane. Group velocity vg is defined as the moving velocity of equal amplitude points on the time domain waveform which occupies a certain bandwidth. It is well known that the group velocity is related to a specific frequency. Accordingly, the time of electromagnetic wave signal passing through a dual port network is group delay. When the signal bandwidth and dispersion effect increase, the significance of group velocity and group delay will decrease. For PN code ranging signal, the delay should be defined as pseudorange delay. The general PN code ranging signal is direct sequence spread spectrum (DSSS) signal in baseband which meets the assumption of ideal code sequence correlation [15]: s(t) =

+∞ 

(−1)cn p(t − nTc )

(1)

n=−∞

Where cn is a PN code with bipolar definition, p(t) is the time domain waveform of a single chip, T c is the time width of the chip, and the code rate is fc = 1/Tc . Generally, the correlation peak method was performed for pseudorange time delay determination.

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2.2 Transmission Function of Networks Because of the dispersion effects of microwave networks are universal, it is necessary to research their delay characteristics. Now consider a general lossless dual port network as shown in Fig. 1. The input and output voltage are U 1 , U 2 , and the characteristic impedance is Z 0 , and the transfer matrix (ABCD) and scattering matrix [s] describe the characteristics of the network.

I1

I2 ⎡A B⎤ ⎢C D ⎥ or ⎣ ⎦

U1

[ s]

U2

Fig. 1. The principle of dual-port networks

According to the theory of microwave network, the transmission function H(ω) of the network is: H (ω) =

1 s21 U2 = = U1 A + B/Z0 1 + s11

(2)

When the input port matches, s11 = 0, and |s21 | = 1, and we have H(ω) = exp(jφ(ω)) (where φ(ω) is the phase of s21 ). Generally, the group delay is determined by τ g = dφ(ω)/dω, so the transmission function and group delay are related. 2.3 Frequency Conversion on Transmission Function Because the dispersive network is located in the RF channel and the PN cross-correlation operation is located in the baseband, the transmission function of the dispersive network cannot be directly used to analyze the pseudorange delay. Let P(ω) is the spectrum of the signal p(t), and let the ω is angular frequency for either baseband or RF, and let ω0 is the angular frequency of RF carrier. We define the frequency-domain process of up conversion, down conversion and transmission as functions UP(), DW() and TR(), and the corresponding time-domain process as functions up(), dw() and tr(), shown as follows: DW(P(ω)) = P(ω + ω0 ) UP(P(ω)) = P(ω − ω0 ) TR(P(ω)) = P(ω)ejφ(ω) dw(p(t)) = p(t)e−jω0 t up(p(t)) = p(t)ejω0 t tr(p(t)) = F−1 (TR(P(ω)))

(3)

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Where F−1 (·) is the inverse Fourier Transform. Therefore, the process of a single chip signal p(t) going through up conversion, through dispersion network, and then down conversion to dispersive chip signal p’(t) in time domain can be described as p’(t) = dw(tr(up(p(t)))). After a series of deduction, we can get that:   (4) dw(tr(up(p(t)))) = F−1 P(ω − ω0 )ejφ(ω) e−jω0 t Let ω’= ω – ω0 , the equation above yields:      p (t) = F−1 P ω ejφ (ω +ω0 )

(5)

Therefore, if ω is the frequency of the baseband and φ(ω) is the transmission function shifted to the baseband, then the spectrum directly acting on the baseband time domain waveform is: P  (ω) = P(ω)ejφ(ω)

(6)

This conclusion has important guiding significance for studying the influence of dispersive network on pseudorange delay. 2.4 The Numerical Calculation Methods of Pseudorange Delay On the RF channel testing conditions it is difficult to perform the correlation peak method for pseudorange delay determination, for the RF testing bandwidth BW is so narrow for sufficient time resolution t = 1/BW. According to the theory of integral transformation, the cross-correlation curve R’(t) is obtained by time-domain waveform p(t) and p’(t), which can be converted into the following operation of each spectrum, namely:    (7) R (t) = F−1 P(ω)P ∗ (ω) Where * is conjugate operator. It is assumed that the receiver takes the peak value of the autocorrelation curve as the time reference, and the self-correlation curve was as follows:   (8) R(t) = F−1 |P(ω)|2 Assuming that two curves have only time difference it could be derived by the Law of Delay that:   (9) R (t) = R(t − τ0 ) = F−1 |P(ω)|2 e−jωτ0 Where τ 0 is the pseudorange delay to be determined. Furthermore, according to Eq. (6) and Eq. (7), the ranging cross-correlation curve at the receiving end of the transceiver is as follows:   (10) R (t) = F−1 |P(ω)|2 ejφ(ω)

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It is obtained by Eq. (9):     F−1 |P(ω)|2 ejφ(ω) ≈ F−1 |P(ω)|2 e−jωτ0

(11)

And it is equivalents to:   2 jφ(ω) |P(ω)| e dω = |P(ω)|2 e−jωτ0 dω

(12)

Let:

 C=

|P(ω)|2 ejφ(ω) dω

(13)

Therefore, the problem of pseudorange delay is transformed into finding τ = τ 0 to make the formula hold:     2 −jωτ  (14) dω − C  = 0 g(τ ) =  |P(ω)| e The above equation can be further transformed into summation form and solved by numerical method. Because of the use of the phase frequency characteristics of the transmission function and the signal spectrum, this method is called Phase Spectrum Integration (PSI) in this paper. It is worth noting that the EW method [14] can also be obtained from PSI method. By transforming Eq. (12) into summation and took the derivative of this with respect to ω from both sides, it is concluded that:   2|P(ω)||P(ω)| ejφ(ω) − j|P(ω)|2 ejφ(ω) τ (ω)   (15) = 2|P(ω)||P(ω)| e−jωτ0 − j|P(ω)|2 e−jωτ0 τ0 Let all of the exp(jφ(ω)) in the left side of the above equation approximate to exp(–jωτ 0 ), it is obtained so called EW method that: |P(ω)|2 τ (ω) τ0 ≈ (16) |P(ω)|2 So, it can be seen that the EW method is an approximate method of PSI method, and is only suitable for the case of small dispersion effect. The AV method [14] could be obtained from Eq. (16) by further approximating |P(ω)| ≈ 1. Therefore, PSI method has better accuracy than EW and AV method.

3 ISL Antenna Pseudorange Delay Measurement An antenna with single feed port is generally regarded as a single port network, but can also be equivalent to a dual port network considering its phase center [10, 16] as the 2nd port. This paper takes the Ka reflector ISL antenna of BD-3 M1S satellite as an example to illustrate the measurement of pseudorange delay by PSI method. The code rate of Ka reflector ISL is f c = 10.23 Mcps, and the center frequency of the Ka reflector ISL antenna is f 0 and BW = 100 MHz (~±5f c ).

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3.1 ISL Antenna Group Delay Measurement The aperture of the Ka reflector ISL antenna is Φ0.4 m, and the far-field distance is 2D2 /λ ≈ 27 m. Therefore, this paper adopts a group delay measurement method [16]. It will get the phase frequency φ(f ) (unit: degree). The group delay can be obtained by differential processing as follows: τg (f ) = −

1 φ(f ) 360 f

(17)

4 3.5

group delay / ns

3 2.5 2 1.5 1 0.5 0 f0-5fc f0-4fc f0-3fc f0-2fc

f0-fc

f0 f0+fc f0+2fc f0+3fc f0+4fc f0+5fc frequency

Fig. 2. The group delay of the Ka reflector ISL antenna

After processing the measured data, the group delay curve of the antenna can be obtained as shown in Fig. 2. It can be seen that within the bandwidth of ±5 f c , the fluctuation range of group delay is about 0.8 ns, and shows obvious dispersion effect. Therefore, group delay is not suitable for pseudorange delay of ISL ranging, and must be converted into pseudorange delay by post processing. 3.2 Determination of Pseudorange Delay by PSI Method Because the test bandwidth is 100 MHz and the corresponding time-domain resolution is only 10 ns, the accuracy of pseudorange delay is difficult to be less than 0.1 ns when used in correlation peak analysis method. If the pseudorange delay is directly calculated according to the far-field phase frequency curve φ(f ) or group delay τ g (f ) obtained in Sect. 3.1, there are three numerical methods, one is the PSI method proposed in this paper, the other two are EW and AV method, and different to the correlation peak analysis method, these three methods do not need to calculate the time-domain waveform, so the requirement of spectrum bandwidth is greatly reduced. The spectrum of a chip signal shows in Fig. 3. After calculating the pseudorange delay in different bandwidth, the following data is obtained as Table 1.

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0.1 0.09 0.08 0.07

P(f)

0.06 0.05 0.04 0.03 0.02 0.01 0 -5fc

-4fc

-3fc

-2fc

-fc

0 fc frequency

2fc

3fc

4fc

5fc

Fig. 3. The spectrum of a chip of PN code

Table 1. The calculated pseudorange delay BW

PSI (this paper) EW [14] AV [14]

±f c

2.82

2.77

2.60

±2 f c 2.69

2.75

2.56

±3 f c 2.65

2.75

2.59

±4 f c 2.64

2.75

2.58

±5 f c 2.64

2.75

2.60

It can be seen that the PSI method converges to the result of 2.64 ns within ±5 f c , while the result of EW method is more than 0.11 ns bigger, and the result of AV method fluctuates and the result is 0.04 ns smaller. According to the conclusion in Sect. 2.4, the EW method is the approximation of the PSI method under the condition of low dispersion, and the AV method is the further approximation of the EW method under the condition of time-domain impulse waveform. Therefore, the results of the PSI method have obvious better accuracy, and eliminate the ambiguity of about 0.15 ns caused by using the EW method and the AV method, so that the measurement accuracy of the pseudorange delay is improved. However, the existing third party calibration methods are not enough to verify such high accuracy results. The error of PSI method verified by current third party calibration method is no more than 0.25 ns. In principle, PSI method is more accurate than EW and AV method. EW and AV method are different degrees of approximation of PSI method. Therefore, this paper takes PSI method as the recommended pseudorange measurement method for dispersive networks.

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4 Conclusion In this paper, a general PSI method for calculating pseudorange delay by transmission function and signal spectrum is given. Through the work of this paper, we can draw the following conclusions: 1) The pseudorange delay of dispersive network cannot be simply considered as the group delay of the center frequency point or the median value of the fluctuation range of the group delay, but should consider the influence of the transmission function of the dispersive network; 2) The influence of the transmission function (mainly the phase-frequency function) of the dispersive network working in the carrier RF band on the baseband signal can be equivalent to that the transmission function in the RF domain acts directly on the baseband signal after it is shifted to the baseband; 3) The correlation peak analysis method needs to calculate the time domain waveform. Because of the narrow RF bandwidth and low resolution in time domain when RF measure data used, it is difficult to determine the pseudorange delay accurately; 4) The PSI method proposed in this paper has better accuracy than that of the EW and AV methods. Especially for the ISL antennas with dispersion effect, using PSI method to determine its pseudorange delay can improve the accuracy of pseudorange delay, and meet the requirements of constellation ISL ranging in orbit. The PSI method can also be used to determine the pseudorange delay of the ground station antenna with dispersion effect.

References 1. Li, X.: Research on the Key Technologies of Inter-satellite Precise Ranging for Navigation Constellation. National University of Defense Technology (2015) 2. Yu, X., Li, J., Wang, D., Wu, J.: Research on high accuracy zero-value calibration method for inter-satellite send-receive equipment. In: 7th China Satellite Navigation Conference, Changsha (2016) 3. Yang, Y., Yang, Y., Hu, X., et al.: Comparison and analysis of two orbit determination methods for BDS-3 satellites. Acta Geodaetica et Cartographica Sinica 48(7), 831 (2019) 4. Ruan, R., Feng, I., Jia, X.: Equipment delay estimation for GNSS satellite combined orbit determination with satellite-ground link and inter-satellite link observations. Acta Geodaetica et Cartographica Sinica 43(2), 137–142 (2014) 5. Ruan, R., Wei, Z., Jia, X.: BDS-3 satellite orbit and clock determination with one-way intersatellite pseudorange and monitoring station data. Acta Geodaetica et Cartographica Sinica 48(3), 269 (2019) 6. Tang, C., Xiaogong, H., Zhou, S., et al.: Initial results of centralized autonomous orbit determination of the new-generation BDS satellites with inter-satellite link measurements. J. Geodesy 92, 1155–1169 (2018) 7. Wang, H.H., Xie, J., Zhuang, J.L., et al.: Performance analysis and progress of inter-satellitelink of Beidou system. In: Proceedings of the 30th International Technical Meeting of the Satellite Division of the Institute of Navigation, IONGNSS 2017, 25–29 September 2017, Portland, Oregon (2017)

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8. Chunbang, W., Wenli, Y., Bo, L.: The measurement of antenna phase center and time delay. Space Electr. Technol. 1, P92–P96 (2009) 9. Wei, H., Yu, B., Li, G., et al.: A method for the equipment time delay in satellite navigation system. In: 1st China Satellite Navigation Conference, Beijing (2010) 10. Kunysz, W.: Antenna phase center effects and measurements in GNSS ranging applications. In: 14th International Symposium on Antenna Technology and Applied Elcetromagnetics [ANTEM] and the American Electromagnetics Conference [AMEREM] (2010) 11. Tang, D., Song, T., Zhu, Z.: Research on influence of time-domain pulse signal by transmission line dispersion and discontinuity. J. Nanchang Univ. (Eng. Technol.) 41(1) (2019) 12. Zhu, X., Li, Y., Yong, S.: A new definition, measurement method of group delay and its application. Acta Electronica Sinica 36(9) (2008) 13. Zhu, X., Sun, G., Yong, S., et al.: The impact of phase nonlinear distortion to GPS pseudo-range measurement. J. Nat. Univ. Def. Technol. 30(6) (2008) 14. Brookes, M., Naylor, P.A., Gudnason, J.: A quantitative assessment of group delay methods for identifying glottal closures in voiced speech. IEEE Trans. Audio Speech Lang. Process. 14(2), 456–466 (2006) 15. Yao, Z., Lu, M.: Design Principle and Realization Technology of Signal of New Generation Satellite Navigation System, vol. 4, pp. 63–69. Electronic Industry Press (2016). Version 1 16. Zhuang, J., et al.: The Union Testing Method of Electrical Boresight and Phase Center and Delay of Antennas with Narrow Beam, ZL201710169585.3 17. Ruan, R., et al.: Orbit determination and time synchronization for BDS-3 satellites with raw inter-satellite link ranging observations. Satell. Navig. 1(1), 1–12 (2020). https://doi.org/10. 1186/s43020-020-0008-y

Research on Collision Avoidance Between UAV Flocks Using Behavior-Based Approach Changkun Wang1 , Jiqing Du2 , Lang Ruan1 , Jing Lv1 , and Shiwei Tian1(B) 1 College of Communications Engineering, Army Engineering University of PLA,

Nanjing 210000, China 2 32753 Troops, PLA, Wuhan 430010, China

Abstract. Safety is a prerequisite for the realization of UAV flocks, this article analyzes the collision problem between flocks of quadrotor UAVs. Based on the of “Boid” flock model, we use behavior rules to model flock aggregation, separation, velocity consistency, and collision avoidance behavior. We propose the collision avoidance behavior coordination mechanism between flocks. The PF (Potential Force) which is improved artificial potential field method and the DVO (Detect Velocity Obstacles) method are innovatively introduced into the collision avoidance behavior. We analyzed and compared the application of the two algorithms in the simulation experiment. The simulation results show that both algorithms can achieve collision avoidance when the flock meets together. In the results, the DVO algorithm has shorter trajectory and faster speed, but the calculations are more complicated. Then, we analyze the influence the force threshold parameters, the number of flocks and the safety radius parameters in the DVO function. Finally, the operation time of the two algorithms is analyzed and compared. Based on the analysis, the optimization directions of flight safety and computation amount are summarized as follows: 1. Create more collision avoidance space inside or outside the flock; 2. Reasonably set the number of interactions with obstacles and the size of the algorithm’s search area. Keywords: UAV flock · Collision avoidance · Behavior rule method

1 Introduction The safety of drones is an important issue that cannot be ignored in the realization of the swarm model. Determining the free space around individuals in the flock and avoiding chain collisions caused by chain reactions between individuals are the main difficulties in group collision avoidance [1]. To solve the safety problem of UAV flocks, artificial potential field method [2] and velocity obstacle method [3], are often used. The artificial potential field method realizes flight by controlling the distance between individuals. It is widely used because of the advantages of simple realization and smooth trajectory. The velocity obstacle method has excellent performance in multi-UAV scenarios and obstacle avoidance in formations, but it is less applied to avoid collisions in flocks. The document [4] verified the feasibility © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 356–365, 2021. https://doi.org/10.1007/978-981-16-3142-9_33

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of the velocity obstacle method on multiple quadrotor UAV platforms; the document [5] showed two methods, GCA (group-wise collision avoidance) and ICA (individual collision avoidance) to avoid collision, but this method is limited by the number of flock nodes. In the literature [6], the artificial potential field method maintains the safety and stability of the formation and avoids external static obstacles, but it does not analyze the dynamic obstacles. To solve the control problem of UAV flocks, Reynolds first proposed the “Boid” flock model [7], which means that individuals follow the three basic behavioral rules of separation, aggregation, and consistent velocity. In many later algorithms, the behavior rule method [8] is favored by many scholars because of its simple implementation and convenient function design. To solve the collision problem between drone swarms, this article considers the control level and designs the swarm control algorithm based on the behavior rule method. The swarm collision avoidance control is divided into four behaviors: aggregation, separation, velocity consistency and collision avoidance. In the collision avoidance behavior, the DVO (Detect Velocity Obstacles) algorithm and PF (Potential Force) algorithm [7] are introduced innovatively, and the collision avoidance coordination mechanism is proposed to control the output. The arrangement of the article is as follows: The first section introduces the background of the article; the second section introduces the basic principles and collision avoidance coordination mechanism of flock model; the third section introduces the function details of the four behaviors; the fourth section introduces the parameter settings and simulation results of the simulation experiment and analyzes the relevant parameters; the fifth section is a summary.

2 Model Introductions In this article, we study the scenario of two groups meeting in a satellite denial environment, which have the same control algorithm. There is communication between neighboring individuals within the group, and the interaction velocity, heading, ranging information: There is no communication between individuals inside and outside the group, relying on their own sensors to perceive each other’s information (distance, orientation), and the flock model adopts distributed control. The three principles of aggregation, separation, and velocity alignment are the basis of the flock model. Among them, aggregation and separation are mechanisms that regulate the distance between individuals, which can gather individuals or avoid internal collisions. This article uses the spring model to construct the aggregation and separation between individuals. The essence of the velocity alignment strategy is to constrain the velocity difference between individuals and use the braking distance to constrain the maximum velocity difference between individuals. The collision avoidance part innovatively introduces the PF algorithm and the DVO algorithm. Compared with the traditional collision avoidance algorithm, the PF algorithm solves the problem of unreasonable output of the traditional artificial potential field method at close points by setting up a “virtual agent”; and the DVO algorithm solves the “reciprocal dance” problem in the velocity obstacle algorithm.

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Fig. 1. UAV flock collision avoidance coordination mechanism

The various behaviors designed based on the behavior rule method influence each other, as shown in Fig. 1, and their different purposes lead to inconsistent output information. This article designs a new coordination mechanism for collision avoidance scenarios: if the possibility of collision is detected, individuals at risk of collision possibility inhibit their own aggregation and velocity consistency behavior, and output separation and collision avoidance information; otherwise, output aggregation, separation, and velocity consistency information. This paper adopts the topological distance interaction method [9], which means that the individual interacts with the nearest fixed number of individuals. This article hopes to use the low-level algorithm of output velocity to control the quad-rotor UAV, the PID controller based on velocity in the literature [10] is adopted. Just input the desired velocity vector to control the aircraft.

3 Flock Control Function Design 3.1 Aggregation and Separation Function Design The aggregation and separation function design between individuals uses a spring damping model. Within the communication range r com , function will be useful. When the rep distance between individuals is the force threshold r0 , the output of this is 0. When rep the distance is less than the threshold r0 , the velocity of repulsion between individuals will be generated. When the distance is greater than the threshold, it will attract attracrep tion. Expression for velocity. vij is the velocity of individual i under the influence of neighbor.  r −r rep rep prep · (r0 − rij ) irij j if rij < r0 rep rep (1) vij = r0 rep r −r rep prep · (rij − r0 ) irij j if r0 < rij < r com

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3.2 Velocity Alignment Function Design The velocity alignment function is used to control the velocity difference between frictmax individuals. The maximum allowable velocity difference νij between individuals is: frict max

vij

frict

= max(vfrict , D(rij − r0

, africt , pfrict ))

⎧ ⎪ ⎪ 0 if r < 0 ⎨ if 0 < rp < a/p D(r, a, p) = rp  ⎪ ⎪ ⎩ 2ar − a2 /p2 otherwise

(2)

(3)

The ν frict is the preset velocity difference constant and has nothing to do with distance. frict The r0 is the distance between the preset end point and the individual i, it is the preset safety distance here. africt and pfrict is the acceleration of braking curve and linear gain of braking curve. The function D(r, a, p) is an ideal braking model to limit the allowable velocity difference by range. The formula r is the distance between the agent and the expected stopping point, a is the preferred acceleration,p is the linear gain. The cfrict is the linear frict coefficient of velocity alignment. The velocity of alignment is νij :  frict max vi −vj frict max ) vij if vij > vij cfrict (vij − vij frict vij = (4) 0 otherwise

3.3 Obstacle Avoidance 3.3.1 PF Algorithm In the PF algorithm, it is assumed that a virtual entity is set on the surface of the safety threshold. There is a velocity alignment effect between the subject and the virtual entity. Also, there is a repulsive effect between the obstacle and the subject. The next obstacle avoidance action is decided by influence of repulsive effect and the alignment effect: shill max vAB = D(dAB − rcoll , ashill , pshill )

(5)

shillmax is the maximum allowable velocity difference, the distance d The νAB AB to the invading individual B (in order to distinguish from individuals in the group, A and B are used here to denote individuals), ashill is the acceleration of braking curve for obstacle, and pshill is gain of braking curve. The output of an individual i under the influence of a obs , where v single intruder is νAB AB = vA −vB . The Nobs is the set of invading individuals detected by the individual i. Collision avoidance velocity νiobs is get as follows:  shill max ) vA −vB if v shill max (vAB − vAB AB > vAB obs vAB vAB = (6) 0 otherwise

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Fig. 2. The left figure is collision area; the right figure is diagram of collision avoidance area.

3.3.2 DVO Algorithm As shown in the left figure of Fig. 2, take A as the origin and true north as the Y axis to (A) establish a relative coordinate system X (A) . The relative velocity is vAB , and XB is the current relative position of B, which τ is the predicted time, and the safety radius of them is the rA and rB . In the left figure of Fig. 2, the shaded part VOAτ / B is the collision area, as shown in Eq. (7) and (8). Equation (9) is the calculation process of collision coefficient coll , which is between A and B monomers indicates whether two individuals collide, αAB Ds(X , r) = {Q| Q − X  ≤ r }

(7)

 (A) t VOA|B = v|∃t ∈ [0, τ ] :: tv ∈ Ds(XB , rA + rB )

(8)

 coll = αAB

t 1 if vAB ∈ VOA|B 0 otherwise

(9)

The search area that can be reached in the next step is the semicircular area RtA in right figure of Fig. 2. The diagonally shaded area is the collision avoidance area CAtA|B , that is the area of RtA but not included in VOtA|B it. So, collision avoidance velocity νAobs can be get:

 RtA = vnext |vnext · tvo  :: vnext × (vpref − vnext ) > 0 (10) t CAtA|B = {v|v ∈ RtA and v ∈ / VOA|B }

Collision avoidance velocity νAobs is: vAobs = arg min v − vpref , v ∈ CAtA|B

(11)

(12)

To enable individuals to maintain a consistent state of continuous movement, the group’s expected movement velocity set in advance in this article. The expected velocity of the flock is preset to be vprefer . The final output control velocity νicommand is:

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vicommand =

N

N

N

N

N neig rep neig frict obs α coll · obs v obs + obs α coll · v pref vij + vij + j =i m=1 im j =i m=1 im m=1 im

361

(13)

4 Simulation Experiment There are many parameters in the behavior-based method, we select the value in literature [8]. These values have been verified in many simulations and physical experiments. The settings of the parameters are shown in Table 1. Table 1. Parameters of flock control Parameter Unit

Value Parameter Unit

pγ ep

1/s

0.03

ν frict

m/s

0.63

africt

m/s2 4.16

Nneig

pfrict

1/s

3.2 0.05

rep r0 r com

Value

m

–

m

100

−

–

rcoll

m

–

vprefer

m/s

4

cfrict

−

ashill

m/s2 3.02

amax

m/s2 4

pshill

1/s

3.55

vmax

m/s

6

frict r0

m

0.3

τ

s

10

Nobs

−

–

tvo

s

0.4

In this paper, MATLAB 2018 software is used to carry out simulation experiments on the Intel Core i7-8752H CPU 2.21 G HZ platform. The simulation time is set to 50 s (not the actual running time). The initial positions of the two flocks are randomly generated in an area of 20 m in length, width and height, the central position is (10, 150, –50) and (100, 150, –50). The number of the two flocks is set to 10. The initial velocity is set to 0, and the desired heading is set to be ϕ1 = 90◦ and ϕ2 = 270◦ , so the flocks will conflict during flight. The left figure of Fig. 3 is a screenshot of the simulation process of the swarms’ flight at 32.5 s, showing the three-dimensional spatial distribution of the two four-rotor drone flocks. 4.1 Algorithm Performance Comparison This paper has carried out simulation experiments using the PF algorithm and the DVO algorithm. The right figure of Fig. 3 is the trajectory diagram of the UAV flock. Under the action of self-propelling velocity, the red and blue flocks fly relative to each other in the three-dimensional space. In right figure of Fig. 3, figure (a) is the flock collision avoidance trajectory using the PF algorithm, the flock detours from the side. figure (b) is the trajectory using the

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Fig. 3. The left figure is simulation of UAV flock collision avoidance; the right figure is the trajectory of the drone to avoid collision, which contains 4 sub-pictures (a), (b), (c) and (d).

DVO algorithm without the quadrotor UAV velocity controller, the individual can pass through the gap between the flocks. figure (c) and figure (d) are the trajectory of the flock movement when the DVO algorithm is combined with the velocity controller of the quadrotor UAV, the trajectory becomes smoother. In figure (d), the angle at which the flocks meet is changed to 45°, and the length of the collision avoidance trajectory is shorter. The left figure of Fig. 4 shows the change in the average velocity of the flock in the first three scenarios in Fig. 3. DVO algorithm can complete collision avoidance faster than PF algorithm. The velocity after using the PID controller exceeds the preset velocity 4m/s at the beginning of the simulation, which is caused by the lift-off velocity of the UAV. In the simulation of the PF algorithm, the average velocity is almost 0 at about 20 s. It is because when the group meets, the individual has complex forces and gets into a predicament.

Fig. 4. The left figure is the average velocity of UAV flocks; the right figure is the order parameters of UAV flocks.

To reflect the obstacle avoidance process of the flock under the velocity controller, the order parameter ϕorder is used to reflect this process, shown in Eq. (14). it’s used to describe the correlation degree of the individual velocity in the flock, and it is 1 when

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it is completely consistent. The result is shown in the right figure of Fig. 4. From the figure we can see the obstacle avoidance process of every scenario. ϕorder =

N vi · vj 1   i=1 N (N − 1) |vi | · vj 

(14)

The above results show that the DVO algorithm is more efficient than the PF algorithm. In the experiment of the DVO algorithm, the individual searched for the safe space in the invading flock to avoid collision, but not bypass the invading flock. The obstacle avoidance path in the DVO algorithm was shorter, but the output velocity of the artificial potential field method was smoother. After adding the velocity controller, the trajectory and velocity output of the DVO algorithm have also become equally smooth. 4.2 Parameter Analysis In the following scenes using the DVO algorithm, we analyze the influence of the three parameters of the number of UAV flocks, the force threshold, and the safety radius. In the experiment of the number of UAVs, the force threshold is set to 10 m, the safety rep radius is 1 m. In the simulation of force threshold parameter r0 , the safety distance is 1 m, and the number is 10. The remaining parameters of two experiments are shown in Table 1. The experimental results are shown in Table 2 and Table 3 respectively. In the simulation, the collision time tco is the time when the shortest distance between individuals is less than the safe distance. Table 2. The influence of the number of flocks on the collision time Number of UAVs 2 4 6

8

10 20

30

Collision time tco 0 0 0.4 2.4 7.1 30.1 45.3

Table 3. Influence of force threshold parameters on collision time. rep

Threshold parameter r0

3

6

8

10 15 20 25

Collision time tco

25.3 4.1 2.1 0.1 0.1 0

0

As shown in Table 2, when the number is less than 6, there is almost no collision, and when the number rises to 20, the collision time increases significantly. The setting of force threshold and safety distance directly affects the safety space inside the flock, causing the flock to form different collision avoidance behaviors. When the safety distance rcoll is increased, the DVO algorithm appears to bypass obstacle avoidance like the PF algorithm shown in Fig. 3(a) of Fig. 3. This shows that the detour or interspersed behavior of collision avoidance is caused by the size of the safe space inside the flock. Therefore, in addition to suitable algorithms, creating more safe collision avoidance space is also

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an important auxiliary means to achieve collision avoidance. This article summarizes two measures: one is to increase the threshold parameter, and to expand more free space within the flock; the second is to reduce the flock size and create a shorter detour path outside the flock. 4.3 Operation Time Analysis The operation time of the algorithm directly affects the practicability. This article summarizes the actual operations of the two algorithms. The number of flock individuals is 10, the preset simulation time is 50 s (not the actual running time), and the number of obstacles is fully interactive. In 10 experiments, the actual running average total time of the PF algorithm part was 16.1 s, accounting for 23.8% of the total running time. The experiment of DVO algorithm sets different obstacle interaction numbers 2, 4 and 6, and the simulation running time is 65.2 s, 106.7 s and 142.5 s, respectively. The main amount of calculation is concentrated in the collision area (VOtA|B ) and the safe area (CAtA|B ) search and determination, accounting for about 62.9% and 17.8% of the collision calculation part. Compared with the DVO method, the PF algorithm in this paper is simpler. The DVO algorithm has a high computational load and is greatly affected by the number of surrounding individuals. A reasonable plan for the number of interactive dynamic obstacles can effectively reduce the amount of calculation; at the algorithm level, the optimization of the algorithm’s collision area search is also an effective way to speed up the computation.

5 Summary This paper analyzes the application of PF algorithm and DVO algorithm in the flock collision avoidance scene. Compare the trajectory, velocity changes of the flock and analyze the parameters in the DVO algorithm. Finally, the calculation time of the two algorithms is compared and analyzed. The results show that the collision avoidance trajectory of the DVO algorithm is shorter. Although the artificial potential field method is simple to calculate, individuals are prone to get into trouble during collision avoidance. The DVO algorithm is more suitable for flock dynamic collision avoidance, can better handle multiple-drone scenes, and avoid collisions more effectively. After the analysis of the results, find that creating more collision avoidance space inside, or outside the flock is an effective means to improve the efficiency of collision avoidance outside the algorithm. To better achieve the effect of flock collision avoidance, the next step is to design an adaptive force threshold function, as well as to solve two problems in the DVO algorithm: computational complexity and the choice of the number of obstacles.

References 1. Yangwang Fang, C.O., Wenxing, F., Cheng, H.: Research status and development trend of obstacle avoidance and control technology for UAV formation. Unmanned Syst. Technol. 2(02), 32–38 (2019)

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2. Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. Int. J. Robot. Res. 5(1), 90–98 (1986) 3. Berg, J.P.V.D., Lin, M.C., Manocha, D.: Reciprocal velocity obstacles for real-time multiagent navigation. In: 2008 IEEE International Conference on Robotics and Automation, ICRA 2008, 19–23 May 2008, Pasadena, California, USA (2008) 4. Coppola, M., Mcguire, K., Scheper, K.Y.W., De Croon, G.C.H.E.: On-board communicationbased relative localization for collision avoidance in micro air vehicle teams (2016) 5. Sharma, R.K., Ghose, D.: Collision avoidance between UAV clusters using swarm intelligence techniques. Int. J. Syst. Sci. 40(5), 521–538 (2009) 6. Galvez, R.L., Faelden, G.E.U., Maningo, J.M.Z., Nakano, R.C.S., Fernando, A.H.: Obstacle avoidance algorithm for swarm of quadrotor unmanned aerial vehicle using artificial potential fields. In: TENCON 2017 - 2017 IEEE Region 10 Conference (2017) 7. Reynolds, C.W.: Flocks, herds, and schools: a distributed behavioral model. ACM Siggraph Comput. Graph. 21(4), 25–34 (1987) 8. Gábor, V., Csaba, V., Gerg, S., Tamás, N., Eiben, A.E., Tamás, V.: Optimized flocking of autonomous drones in confined environments. Sci. Robot. 3(20), eaat3536- (2018) 9. Ballerini, M., Cabibbo, N., Candelier, R., Cavagna, A., Cisbani, E., Giardina, I., et al.: Interaction ruling animal collective behavior depends on topological rather than metric distance: evidence from a field study. In: Proceedings of the National Academy of Sciences (2008) 10. Soria, E., Schiano, F., Floreano, D.: SwarmLab: a Matlab Drone Swarm Simulator (2020)

Digital Track Map Aided Multi-sensor Fusion for Train Occupancy Identification in Complicated Track Sections Tao Yang1(B) , Debiao Lu1 , Baigen Cai2 , Jiang Liu1 , and Yu Xiao3 1 Beijing Engineering Research Center of EMC and GNSS Technology for Rail Transport,

School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China [email protected] 2 State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China 3 Department of Communications and Networking, School of Electrical Engineering, Aalto University, Espoo, Finland

Abstract. GNSS-based (Global Navigation Satellite System) train positioning techniques have been considered to apply in the next-generation train control system, aiming to improve transportation efficiency and reduce construction & maintenance costs. However, while adopting GNSS positioning techniques to train positioning, as GNSS is vulnerable to the environment, GNSS positioning accuracy usually cannot meet the requirements in complicated track sections in station areas. Track occupancy determination using traditional map-matching algorithm will fail. This paper proposes a track occupancy identification method in railway stations based on GNSS/INS/DTM sensor fusion results is proposed. Firstly, GNSS/INS loosely coupled model is implemented. Secondly, with GNSS/INS sensor fusion result aided with track geography and topology information, probability model based on distance and heading evidence can be implemented. Combined with track topology and train running characteristics, rule sets are constructed. Finally, dynamic Bayesian network is adopted to analyse the casual dependency of variables and recursive Bayesian estimation is applied to fuse GNSS/INS/DTM and prior information. Field experiment data gathered from a highspeed railway line has been analysed to verify the track occupancy identification method. The result shows that track occupancy identification accuracy has been apparently improved, error along the track under complicated track sections scenarios has been greatly reduced. Test result fully implies the effectiveness of the method proposed in this paper. Keywords: GNSS · Digital track map · Map matching · Coupled navigation · Recursive Bayesian estimation

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 366–374, 2021. https://doi.org/10.1007/978-981-16-3142-9_34

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1 Introduction Train positioning is of great importance in ensuring train operation safety and enhancing transportation efficiency. Global Navigation Satellite Systems (GNSS) have been developing rapidly including the Beidou 3rd generation, GPS modernization etc. GNSS-based train positioning solution (trainborne centric positioning) is applied in the Chinese Train Control System – New (CTCS-N) to reduce trackside equipment and cut the construction and maintenance cost. However, when train travels along the track, the train goes through complicated track sections where track spacing is extremely narrow, as GNSS is vulnerable to the environment and positioning error can be large enough that cannot meet the track selectivity requirement. Normally, GNSS-based train positioning solution cannot deliver positioning result which meets the safety-related GNSS performance requirements in certain railway environment and operation scenarios, for example track sections, tunnels etc. To solve this problem, other sensors are necessary to be coupled with GNSS to obtain the higher accuracy and dependability to determine the minimal track area occupied by the train when the train runs in the complicated track sections. GNSS is characterized by positioning accuracy 24/7 and low cost of user equipment, but GNSS signals can be easily blocked or interfered. Inertial Navigation System (INS) continuously provides attitude, angular, and acceleration measurement with high output bandwidth. But the inertial sensor errors are constantly integrating through the navigation equation, thus the accuracy drops over time. Digital Track Map (DTM) provides track geometry, geography, and topology information, has the characteristics of being unaffected by the environment and high stability, and can effectively reduce positioning error through map matching techniques. Aiming to achieve train borne-centric positioning, lots of research has been done. Xin Han proposed a GNSS/IMU tightly coupled scheme with weighting and FDE for rail applications [1]. A harmonious combination of Fault Detection and Exclusion (FDE) strategy and weighting observation error model strategy is proposed to achieve the availability and security requirements in railway applications with GNSS/INS tightly coupled system output. Wei Jiang proposed a BDS/INS/odometer/map-matching positioning methodology for train navigation applications [2]. The method aims to solve the problem of positioning during BDS outages when trains pass through signal obstructed areas. Jurgen Wohlfeil et al. proposed camera and LiDAR aided schemes to improve GNSSbased train positioning accuracy in challenging scenarios [3–5]. Shuxian Jiang proposed a GNSS NLOS signal propagation modelling method in the railway urban canyon environment aiming to remove errors brought by GNSS Non-Line-of-Sight (NLOS) signal in user location solutions [6]. DTM cannot be affected by complex environment, is available for track geographic/topology information and has the advantages of low cost and high accuracy. Therefore, this paper proposes GNSS/INS/DTM coupled train positioning method and evaluate the performance of identifying the exactly track occupied by the train when the train run into the railway complicated track sections.

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2 Method 2.1 GNSS/INS Coupled Algorithm The GNSS/INS coupled train positioning algorithm generates position, velocity, and attitude (PVA) solutions using a loosely coupled indirect Kalman filter (KF) with feedback correction. KF directly fuses GNSS and INS measurements to estimate the error states, and the feedback correction is finished by the KF-estimated error states. The system error state is composed of 15 states: attitude error (roll, pitch, and yaw), position error (latitude, longitude, and height), velocity error, gyroscope biases and accelerometer biases. It can be expressed as: X = [δψ δpn δvn δbg δba ]

(1)

where δψ, δpn , δvn , δbg and δba are the attitude error, position error, velocity error, gyroscope biases and accelerometer biases, respectively. The system measurement vector is:   pGNSS − pINS Z(k) = (2) vGNSS − vINS where pGNSS is the GNSS position solution, and pINS is the INS position solution. With the INS error model, system model can be developed. In this paper, the gyro sampling output is angular increment, and the accelerator output is velocity increment, in that way, the rotation vector coning compensation and the velocity rotation compensation and velocity sculling compensation is adopted. The measurement model is easily obtained with the composition of system error and measurement vector. Aided with system model and measurement model, KF can be implemented. The KF time-update step propagates the system state X and the corresponding state covariance matrix P: Xˆ (k|k − 1) = F(k − 1)Xˆ (k − 1)

(3)

P(k|k − 1) = F(k − 1)P(k − 1)F T (k − 1) + Q(k − 1)

(4)

The Kalman measurement-update step consists of the following operations: K(k) = P(k|k − 1)H T (k)[H (k)P(k|k − 1)H T (k) + R(k)]−1

(5)

Xˆ (k) = Xˆ (k|k − 1) + K(k)[Z(k) − H (k)Xˆ (k|k − 1)]−1

(6)

P(k) = [I − K(k)H (k|k − 1)]P(k|k − 1)

(7)

where F(k − 1) is the state transition matrix; Z(k) is the system measurement matrix; H (k) is the measurement matrix; W (k) and V (k) are the process noise and measurement noise, respectively, assumed to be zero-mean Gaussian noises; and the covariance matrix are Q(k) and R(k), respectively.

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2.2 Digital Track Map Generation Aiding with DTM generation tool, traditional digital track map is generated with massive route points which are sampled evenly [7]. However, it is contradictory to minimize the map storage space and enhance map accuracy. Meanwhile, traditional digital track map only contains geographical information. Distinguished with traditional digital track map, DTM adopted in this paper contains geographic, geometric, and topologic information [8]. The geographic information refers to position information. Massive route points are simplified to several control points aided with Ramer-Douglas-Peucker algorithm. The rails can be reconstructed in Clothoids line style using the control points and corresponded parameters. Testing with Heishanbei railway station map, route points sampled with 3 m interval has been reduced to 24 from 2218 and the position error of digital track map is set to no larger than 0.5 m. The geometric information refers to the parameters of clothoids and the topological information refers to the predecessor and successor relationship. Finally, Digital track map is constructed with XML format:

2 1 3 42.3456789 6.3456789 200.8 71.23 1345.85 0.01345675432 -0.00034543214

2.3 GNSS/INS/DTM Coupled Track Occupancy Identification Method in Complicated Track Sections Adopting GNSS/INS coupled train positioning algorithm can enhance GNSS-based train positioning system availability and accuracy under complicated track sections. However, the accuracy requirement under complicated track sections still cannot be achieved. With DTM and IMU measurements, GNSS/INS/DTM coupled track occupancy identification method in complicated track sections is proposed which can increase positioning accuracy furthermore and decrease the track occupancy identification incorrectness. Basically, with DTM, GNSS/INS coupled train positioning result can be projected to the rail track segments expressed in clothoids form, the positioning accuracy is improved. However, under complicated track sections, the basic map matching method fails. Considering the multi-information DTM contains, the time-relevant characteristic is hidden,

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recursive Bayesian estimation is adopted to fuse GNSS/INS coupled train positioning result and DTM. Combined with hypothesis testing, it can be expressed as: P(Hti |Z0:t ) = P(Hti , Z0:t )/P(Z0:t )

(8)

P(Hti , Z0:t ) = P(Hti |Z0:t−1 )P(Zt |Hti )

(9)

P(Hti |Z0:t−1 ) =



j

j

P(Hti |Ht−1 )P(Ht−1 |Z0:t−1 )

(10)

j Ht−1 ∈Ht−1

where Ht = {Hti , i = 1, 2, ...} represents the hypotheses set at time t, Zt represents j the GNSS/INS coupled train positioning result at time t. P(Hti |Ht−1 ) is the hypothesis transition model between last time and current time. Hypothesis can be regarded as one state of the train localization system. P(Hti |Z0:t ) in (8) refers to the posterior probability from all measurement till current time t to each hypothesis. P(Hti , Z0:t ) can be calculated by (9) and P(Z0:t ) in (8) is a constant for every hypothesis at the same time. P(Zt |Hti ) in (9) is calculated by (12) and P(Hti |Z0:t−1 ) in (9) can be calculated by (10) which is composed j j by the recursion P(Ht−1 |Z0:t−1 ) and the state transition probability P(Hti |Ht−1 ). According to the maximum a posteriori probability Principle (MAP), the most likely hypothesis at current time is selected. Thus, an iteration is finished.   (11) Ht = arg max P(Hti |Z0:t ) Hti

Using information from DTM and GNSS/INS coupled train positioning result, j P(Zt |Hti ) and P(Hti |Ht−1 ) can be obtained as followed:    P Zt |Hti = k1 Pti

 i i + k P 2 dis t heading Pt

  i P Hti |Ht−1 = Pti topo

IMU

(12) (13)

where Pdis evaluates each hypothesis from the perspective of distance between GNSS/INS localization result and track segments. Normal distribution N (μ, σ 2 ) where μ = 0, σ = 2.5 is assumed to be described the distribution of distance between GNSS/INS localization result and track segments. σ = 2.5 is determined because BDS horizontal positioning accuracy standard (95% confidence level) in the most of AsiaPacific area is no larger than 5m [9]. Pheading evaluate each hypothesis from the perspective of heading difference between the calculated result from GNSS/INS localization result and DTM. Ptopo represents the linkage relationship between each hypothesis and DTM’s topology. Pti IMU is map-matching probability according to IMU angular velocity information. k1 , k2 are the distance, heading weight factor.

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3 Experiment and Result Analysis A field experiment has been conducted in Beijing-Shenyang high-speed railway line in 2018. The SPAN IMU-FSAS inertial system consists of a multi-constellation and multifrequency GNSS receiver and an inertial measurement unit IMU-FSAS was installed on the locomotive [10]. Heishanbei railway station is chosen, and DTM of Heishanbei railway station is shown in Fig. 2 where the blue lines are rail track, the short black vertical lines distinguish different segments, segment ID is marked in red, and SW refers to switches. Position error of DTM is below 0.5 m. Applying GNSS/INS coupled train positioning algorithm, comparing with the SPAN GNSS inertial system position output whose accuracy is assumed to be at the centimeterlevel. Dataset collected on 08/23/2018 where the train has once stopped at Heishanbei railway station is chosen to analyze the performance of GNSS/INS coupled train positioning algorithm. Table 1 shows the analysis result (Fig. 1).

Fig. 1. SPAN IMU-FSAS inertial system

SW1

SW5 SW3 SW7

SW6

SW2

SW8 SW4

Fig. 2. Switches in Heishanbei railway station

The real challenging part is achieving track occupancy identification in high correctness in complicated track sections. With recursive Bayesian estimation based GNSS/INS/DTM coupled train track occupancy identification method, the performance is verified in complicated track sections. Four levels are set to evaluate the track occupancy identification confidence as listed in Table 2.

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Standard deviation (m)

DRMS (m)

North error

1.0733

0.1870

0.3740

East error

0.0750

0.0498

0.0996

−0.4861

0.9855

1.9710

Down error

In complicated track sections, comparing to the basic vertical map matching method, verification result of map matching based on recursive Bayesian estimation (MRBE) is shown as follows. Figure 3 illustrates the comparison of confidence probability where confidence probability has been greatly increased, and Fig. 4 statistics the result that proportion of level 1 “ ++” has been increased from 64.88% to 99.17% which means the correctness and confidence of train track occupancy identification has been greatly improved. Table 3 gives a summary where maximum error along the track in complex track sections has been reduced from 113.50 m to 3.26 m. It means the ambiguous track occupancy identification has been greatly improved in complicated sections.

Fig. 3. Confidence probability comparison between basic map matching algorithm and MRBE

Table 2. Evaluation levels of track occupancy identification result Quality

Max p(Hti |Z0:t )

Level 1: ++

Identification result is right and confidence probability is greater than 0.95

Level 2: +

Identification result is right and confidence probability is less than 0.95 and greater than 0.90

Level 3: O

Identification result is right and confidence probability is less than 0.90

Level 4: -

Identification result is false

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Fig. 4. Comparison of different confidence probability levels distribution between basic map matching algorithm and MRBE Table 3. Comparison of maximum error along the track L1

L2

L3

L4

Maximum error along the track

Basic

64.88%

7.05%

22.37%

5.73%

113.50

MRBE

99.17%

0.34%

0.45%

0.04%

3.26

4 Conclusion Aiming to solve the ambiguous train track occupancy identification problem, a GNSS/INS/DTM coupled track occupancy identification method in complicated track sections is proposed in this paper, and the method is divided into two parts: KF-based GNSS/INS coupled train positioning algorithm and recursive Bayesian estimation-based map matching algorithm. A real field experiment has been carried out in BeijingShenyang high-speed railway line, datasets collected in Heishanbei railway station has been chosen where 8 switches is installed at the station, and verify result shows the effectiveness of the method this paper proposed: comparing to the basic vertical mapmatching method, confidence probability of track occupancy identification has been greatly increased, from 64.88% to 99.17%. Maximum error along the track in complicated track sections has been reduced from 113.50 m to 3.26 m. In the future, GNSS/INS tightly coupled train positioning algorithm and fault detection and exclusion method under GNSS signal blocked environment are implemented which will brings a more accurate and robust track occupancy identification solution under complex track sections. Acknowledgement. This paper is supported by National Key Research and Development Program of China (2018YFB1201500), Beijing Science Program of Beijing Municipal Science and Technology (Z181100001018032), National Natural Science Foundation of China (U1934222, 61873023), Beijing Natural Science Foundation (L191014), and Beijing Nova Program of Science and Technology (Z191100001119066).

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References 1. Han, X., Kazim, S.A., Tmazirte, N.A., Marais, J., Lu, D.: GNSS/IMU tightly coupled scheme with weighting and FDE for rail applications. In: Proceedings of the 2020 International Technical Meeting of the Institute of Navigation, pp. 570–583 (2020) 2. Jiang, W., Chen, S., Cai, B., Wang, J., ShangGuan, W., Rizos, C.: A multi-sensor positioning method-based train localization system for low density line. IEEE Trans. Veh. Technol. 67(11), 10425–10437 (2018) 3. Wohlfeil, J.: Vision based rail track and switch recognition for self-localization of trains in a rail network. In: 2011 IEEE Intelligent Vehicles Symposium (IV), pp. 1025–1030. IEEE (2011) 4. Stein, D.: Mobile Laser Scanning Based Determination of Railway Network Topology and Branching Direction on Turnouts. KIT Scientific Publishing, Karlsruhe, vol. 38 (2018) 5. Guo, Z., Cai, B., Jiang, W., Lauer, M.: Frog and blade based branching direction detection in LiDAR data. In: 2019 IEEE Intelligent Transportation Systems Conference (ITSC), pp. 2687– 2692. IEEE (2019) 6. Jiang, S., Lu, D., Cai, B.: GNSS NLOS signal modelling and quantification method in railway urban canyon environment. In: 2019 IEEE Intelligent Vehicles Symposium (IV), pp. 1268– 1273. IEEE (2019) 7. Wang, J., Tao, W.J., Cai, B.G., Liu, J., Toro, F.G.: Generation and evaluation of the track map database for GNSS-based train positioning using a map-tool-chain. In: Proceedings of the 29th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2016), pp. 1914–1926 (2016) 8. Yang, T., Lu, D., Cai, B., Wang, J., Liu, J., Laviron, P.: Digital track map aided track occupancy identification method in railway stations. In: Proceedings of the 33rd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2020), pp. 2618– 2627 (2020) 9. BeiDou Navigation Satellite System Open Service Performance Standard (Version 2.0). (2018). http://www.beidou.gov.cn/xt/gfxz/201812/P020181227529449178798.pdf 10. NovAtel Corporation (2015) SPAN-FSAS product sheet. http://file.tuweia.cn/64c64f03fc33 656abbb15dffbc55439150a0122b.pdf

GNSS Multipath Detection Based on Decision Tree Algorithm in Urban Canyons Yue Wang(B) , Jiawei Xu(B) , Rong Yang(B) , and Xingqun Zhan(B) Shanghai Jiao Tong University, Shanghai 200240, China {johnld,xjw000830,rongyang,xqzhan}@sjtu.edu.cn

Abstract. Multipath detection has long been a fundamental problem in GNSS research and application especially under heavily urbanized condition. In this work, we aim to apply a machine learning algorithm to detect and classify multipath error in urban, kinematic situation based on Rinex datasets provided by the University of Texas. Correspondingly, the data samples are classified into 3 groups according to the chip length from GPS L1 and L5: Short Multipath (0– 30 m), Medium Multipath (30–90 m) and Long Multipath (>90 m). As a result, the algorithm achieves an average accuracy of 70% in the 5-folded cross validation. Furthermore, the detection result of satellites with various conditions of blockage are compared to give some angle of optimization. Keyword: GNSS · Multipath detection · Urban canyon · Machine learning · Decision tree

1 Introduction With the continuous development and improvement of GNSS (Global navigation satellite system), it gradually provides more and more accurate and reliable positioning services, making applications such as unmanned vehicles and drones possible. These applications are often applied in urban dynamic environments and have higher requirements for GNSS positioning services. In this so-called urban canyon environment, GNSS signals may be blocked by buildings around the target, creating multipath errors on the received signals, which is considered to be the main source of GNSS signal errors in this environment. Therefore, the detection and removal of multipath errors is a necessary step before the actual application of GNSS signal. To remove multipath errors, many previous studies have been done. At the antenna level, multipath errors can be reduced by upgrading the quantity or quality of the antenna [4]. At the receiver level, advanced receiver algorithms such as VDLL can improve the reliability of the signal when it is affected by multipath [3]. While at the software level, inertial navigation is used in [5] to assist GPS systems in positioning under multipath interference, and 3D building models are used in [10] and [6] to label LOS/NLOS signals. These labelled data, in turn, can be used to assist machine learning algorithms [10]. While features calculated based on pseudorange and phase observations are used in [8] and CNN is used as a model in [9]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 375–383, 2021. https://doi.org/10.1007/978-981-16-3142-9_35

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Among these methods, the machine learning algorithm shows some advantages with its flexibility and ability to respond to multiple situations or input information. In this study, we used a decision tree machine learning algorithm based on MATLAB’s Classification Learner toolbox. Considering ease of use and understanding, the input features are based on the information from Rinex files. The features include carrier-to-noise ratio, pseudorange-doppler residual, pseudorange residual, elevation angle and azimuth angle. In terms of data labelling, two labelling methods relying on Rinex files and true values were used in this study: the pseudorange positioning method and the pseudorange correction method. Considering that the pseudorange observation is not able to distinguish well between the multipath and NLOS signal, and that these 2 interferences have similar effect on pseudorange, they are collectively referred to as multipath interference in this study, For the labelled results, the chip length of GPS L1/L5 was referred (which is 300 m and 30 m separately) to make a classification of 3 categories: short multipath (0–30 m), medium multipath (30–90 m) and long multipath (>90 m). Overall, in this study, a decision tree machine learning model was trained using input from Rinex files and reference to the ground truth to detect the multipath among the dataset, and finally is able to achieve an average accuracy of 75% against its own labelled results. In addition, this paper also analyses and compares the classification results of multipath errors from the perspective of signal frequency and code rate with respect to the physical significance of multipath generation, and gives some optimization directions for current machine learning algorithms for detecting multipath effects.

2 Data Sources and Labelling 2.1 Data Sources The source data used in this study are from [7], an open dataset collected by researchers at the University of Texas on 2019/05/09 in the downtown area of Austin, during which the researchers drove from the sparsely built campus area to the heavily built-up downtown area and back when the blockage around changed in terms of height and angle. Thus, the exposure to multipath disturbances encompasses the three scenarios classified in this study. The process last about 2 h. 2.2 Data Labelling In this study, the labelling result of the data will be determined by a combination of the two methods. Since the variable that determines its final labelling result has the same physical significance (multipath error value), this variable will be averaged from the calculations of the two methods. 2.2.1 Pseudorange Positioning Method The pseudorange positioning method is calculated using the traditional least squares method [11]. For the target satellite at a certain moment, the pseudorange observations of all satellites in the same system and frequency as the target satellite at the current moment are used for the least-squares positioning. And the difference of this positioning result and

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the true value from the dataset is taken absolute value as the final considered multipath error value. Thus, this main consideration of this method would be the positioning result. The reason for using this method is that it is simple and intuitive to calculate. It contains the signal quality of all the targeted satellites of the same frequency at that moment, thus has a better performance with receiver at different positions. On the other hand, the method also has the obvious drawback that it cannot distinguish the errors resulted from different satellites, which is why we need to combine it with the second method for more accurate and targeted labelling. 2.2.2 Pseudorange Correction Method The pseudorange correction method takes a single pseudorange observation of the target satellite as the main discriminator at a given moment. First, the current position of the target satellite is solved from the ephemeris file. Then the difference between the receiver’s position from true value and the position of the target satellite is taken as the distance true value. This pseudorange observation is corrected according to the following pseudorange observation model [11]. ρ = r + δtu − δt + I + T + ∈ +M

(1)

Where ρ is the pseudorange observation, r is the satellite-receiver distance, M is the perceived multipath error value,  is the thermal noise, δtu is the receiver clock difference, δt is the satellite clock difference, I is the ionospheric error, and T is the tropospheric error. The first two clock differences are calculated from ephemeris files, and the last two atmospheric delays are calculated from the model. Finally, the difference between the true value of the satellite-receiver distance and the corrected pseudorange is taken absolute value as multipath error value for calibration. Although this method can distinguish between satellites, its reliability is not high enough in the complex urban dynamic environment. For example, clock difference calculation error, atmospheric delay error, etc. may make the result far from the real multipath error value, so it needs to be combined with the previous method. 2.3 Labelling Result The labelling results for short multipath (0−30 m), medium multipath (30−90 m) and long multipath (>90 m) are obtained according to the above methods from the selected 23555 samples of GPS L1, 21690 of GAL E1 and 19230 of E5b. The number of epochs is converted into percentages for comparison purpose (Table 1).

3 Selection and Calculation of Features All features are calculated and applied in model training or validation following two principles. One is that when the absolute value of the feature significantly exceeds the error caused by the normal multipath effect, the data at that point is considered unusable. And the second is that when one of the observations used in the signal is stumped, the data at that point is considered unusable.

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GPS L1 GAL E1 GAL E5b

Short multipath

33.43% 34.80%

21.70%

Medium multipath 33.24% 33.42%

41.00%

Long multipath

37.30%

33.33% 32.20%

1. Carrier-to-Noise Ratio: C/N 0 The carrier-to-noise ratio C/N0 is a common characteristic that indicates the strength of the signal received by the receiver. According to the characteristics of signal propagation, the signal will be significantly reduced in strength when it is reflected and blocked by walls. Therefore, the carrier-to-noise ratio is used as a feature here. The value can be read out directly from a Rinex file. 2. Pseudorange-Doppler Residuals: ρd The Doppler shift is another observation related to the multipath, which characterizes the rate of change of the pseudorange. However, it is calculated differently from the pseudorange in the receiver’s algorithm, the former given by the code tracking loop, while the latter is given by the carrier frequency. Therefore, the two observation can be considered as independent when multipath happens and the difference between the pseudorange rate of change and the Doppler shift can indicate the consistency of the internal calculations of the receiver, which in turn reflects the receiver receiving multipath interference. The calculation requires the use of both pseudorange and Doppler shift observations from the Rinex file. First, the pseudorange is differenced between epochs. Then the doppler value is converted into length. Finally, difference the two value and take absolute value to get the feature. Here, the effect of time-differenced pseudorange is ignored as the interference of multipath is considered to last for a while, namely around 10 s. 3. Pseudorange Residuals: ρ r The pseudorange residual exploits the inconsistency between the pseudorange observations of certain frequency of the target satellite and the results of the overall pseudorange positioning. According to the conclusions of [8], this feature can characterize the degree of multipath error when the number of observed satellites is sufficient. The method and principle of its calculation are almost identical to the method of calculating the multipath error by the pseudorange correction method in the labelling part (Eq. (1)), except that the true value position is replaced by the result of pseudorange positioning of the corresponding frequency at the current moment. Thus, the value of this feature is much smaller than pseudorange positioning labelling, namely 0–5 m. 4. Elevation angle The satellite elevation angle refers to the angle between the satellite and the receiver line and the horizontal plane. In the same urban environment, it is clear that satellites with low lift angles are more likely to be blocked by surrounding obstacles than satellites with high lift angles, thus generating multipath errors. In the case where

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the model considers multiple satellites with different lift angles, this value has considerable relevance to the absence of multipath errors.This value is calculated from the ephemeris data at the time during the pseudorange positioning. 5. Azimuth Angle The satellite azimuth refers to the angle turned by the receiver clockwise from the due north direction line to the horizontal direction line of the satellite. In a similar urban canyon environment, the degree of obstruction in different directions may also vary, which can lead to different levels of multipath interference for satellites at different azimuths. Although this correlation is diminished in the dynamic case, the azimuth of satellites can still play a role in model judgments in short time and small range conditions. Similarly, this value is calculated from the prevailing ephemeris data during pseudorange positioning.

4 Model Training and Classification Results In the experimental phase, we used all satellite data of GPS L1, GALILEO E1 and E5b in the dataset. 4.1 Model Training In this section, we use the Rinex files of GPS L1, GAL E1 and E5b frequencies in the dataset to perform the labelling, feature calculation and training. A total of 20,604 samples from 5 satellites were used for GPS L1and 19475, 17018 samples from 5 satellites were used for GAL E1 and E5B.The overall self-test accuracy with all the above 5 features used is shown in the table below (Table 2). Table 2. Accuracy of the model GPS L1 GAL E1 GAL E5b Model accuracy (%) 68.4%

80.3%

80.7%

To further verify the meaning of these three sets of self-test accuracies, recall rates of different labelling groups were calculated using the model predictions (Table 3). Table 3. Recall of the model of different labelling groups Recall (%)

GPS L1 GAL E1 GAL E5b

Short multipath

85%

92%

84%

Medium multipath 61%

75%

90%

Long multipath

73%

68%

59%

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From the data in the table, it can be seen that the model training results for different frequencies vary widely. For GPS L1 and GAL E1 with higher carrier frequencies, they have better distinguishing capabilities for short multipath, but poorer for medium and long multipath. For the medium and long multipaths, the model classifies these samples as two other wrong multipath cases with 20% probability respectively, leading to a lower overall accuracy. For E5b, a frequency point commonly used for multi-frequency combination analysis, its carrier frequency is lower while its level of multipath error is higher (which will be discussed in detail later). This is reflected in the prediction results as the model tends to classify samples with corresponding features as medium multipath, resulting in a higher recall rate for medium and short multipath, but long multipath cases are often misclassified as medium multipath. Thus, the E5b model has a higher overall accuracy. In order to verify the contribution of each feature, we also exclude one of the features and re-trained model to see its accuracy. The results are shown in the following Table 4. Table 4. Accuracy of the model with certain feature excluded Feature excluded

Accuracy

None (with all features)

80.7%

Carrier-to-noise ratio

81.4%

Pseudorange residual

78.5%

Pseudorange-Doppler residual 78.8% Elevation angle

76.0%

Azimuth angle

77.7%

It can be seen that all feature, except the carrier-to-noise ratio, reduce the overall accuracy after being removed. Among all features, the effect of lift angle and azimuth angle are more significant, which indicates that both of them can better distinguish the situation of multipath interference based on the previous experience in the dynamic situation of similar environment. On the contrary, the correlation between the carrierto-noise ratio and multipath interference in the dynamic environment may not be strong enough to support our machine learning model, and may produce some interference instead. 4.2 Verification of Classification Results This section focuses on the comparison of the between different frequencies, i.e., different carrier frequencies and code rates. Thus, the results of two frequencies from the same satellite system, E1 and E5b of GAL, are selected (Table 5). According to the previously labelled results, the E5b frequency point with lower carrier frequency, longer wavelength, and higher code rate suffers more long multipath and medium multipath cases than the E1 frequency point does, i.e., E5b suffers more serious multipath errors at the level of pseudorange observation than E1. This is different

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Table 5. Labelling result of GAL E1 and E5b Percentage

GAL E1 GAL E5b

Short multipath

34.80%

21.70%

Medium multipath 33.42%

41.00%

Long multipath

37.30%

32.20%

from our expected results: considering that the lower carrier frequency gives E5b a longer carrier wavelength, which makes the same multipath propagation cause a relatively larger code phase delay for E5b; the final multipath error is the code phase delay multiplied by the chip length, while the code rate of E5b is 10 times that of E1 (10.23 MHz: 1.023 MHz), and the chip length is 0.1 times (30 m: 300 m). There are several possible reasons for this error. One is the processing mode compatibility of the receiver platform with the special AltBOC (alternating binary offset carrier) modulation method for the GAL E5b frequency point. According to [12], the AltBOC modulation method, although with high tracking accuracy, requires a high RF bandwidth and sampling rate of the receiver, which may have produced a larger error at the stage of generating the code phase delay. Secondly, the steps of pseudorange positioning and correction may produce an offset. By observing the above two labelling benchmarks on E5b, it is found that the latter part of the route yields higher positioning and pseudorange errors under the same open conditions. This may be due to the fact that the positioning and correction algorithms do not apply higher-order smoothing algorithms such as carrier or Doppler smoothing, resulting in the accumulation of random errors in the moving process not covered by the observation model (Fig. 1).

Fig. 1. Increase of labelling benchmarks over time

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5 Conclusion In this study, a decision tree algorithm is applied to give a solution to the multipath classification detection problem in urban-canyon environments. A total of five feature from Rinex files output are used to train a machine learning model. As a result, the model is able to achieve an average classification accuracy of about 75% in cross-validation. While carrier-to-noise ratio may produce negative effect on accuracy, elevation and azimuth angle contribute more than other features that are applied. Compared to the existing work that shares the same method such as [6], our solution mainly deals with dynamic situations and verifies the availability of machine learning algorithm under such condition. However, the physical significance and actual effect of each feature may differ from static condition. Finally, based on the initial labelling algorithm, we analyze the reason why the E5b frequency point of the Galileo system suffers more from multipath errors than the E1 frequency point based on the physical significance of the multipath error generation. The conclusion is that the error may be generated by the hardware of the receiver or the labelling algorithm. As a pioneering study, the feasibility and reliability of machine learning algorithms for detection and rejection of multipath errors at the Rinex file level is verified in this study.

6 Future Outlook Based on this study, we have plans for more in-depth research and development. First, we plan to use a more comprehensive data labelling algorithm, combining the 3D city model, the multipath error reference values given by the receiver itself to make a weighted comprehensive labelling. Also, the least-square positioning can be modified to allocate more weight to satellites with higher elevation angle so that the result can be more validated in terms of feature calculation. Following that, we can add multi-dimensional feature variables, and conduct joint machine learning algorithm research for multipath problems. The research currently underway has machine learning algorithms based on receiver correlators as features. And in the future, we hope to apply vehicle vision signals to further improve the reliability and strain of the algorithms. Eventually, different machine learning algorithms, such as convolutional neural networks, can be applied to better integrate the impact of each feature quantity on the classification conclusion. Overall, we plan to conduct our own data-collection test to verify our method in terms of universality and apply above-mentioned improvement.

References 1. Munin, E., Blais, A., Couellan, N.: Convolutional neural network for multipath detection in GNSS receivers. In: 2020 International Conference on Artificial Intelligence and Data Analytics for Air Transportation (AIDA-AT), Singapore, pp. 1–10 (2020). https://doi.org/10. 1109/AIDA-AT48540.2020.9049188. 2. Groves, P.D.: Shadow matching: a new GNSS positioning technique for urban Canyons. J. Navig. 64(3), 417–430 (2011)

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3. Hsu, L.-T., Jan, S.-S., Groves, P.D., Kubo, N.: Multipath mitigation and NLOS detection using vector tracking in urban environments. GPS Solutions 19(2), 249–262 (2014). https:// doi.org/10.1007/s10291-014-0384-6 4. Jiang, Z., Groves, P.D.: NLOS GPS signal detection using a dual-polarisation antenna. GPS Solutions 18(1), 15–26 (2012). https://doi.org/10.1007/s10291-012-0305-5 5. Chiang, K.-W., Duong, T., Liao, J.-K.: The performance analysis of a real-time integrated INS/GPS vehicle navigation system with abnormal GPS measurement elimination. Sensors 13(8), 10599–10622 (2013) 6. Hsu, L.: GNSS multipath detection using a machine learning approach. In: 2017 IEEE 20th International Conference on Intelligent Transportation Systems (ITSC), Yokohama, pp. 1–6 (2017). https://doi.org/10.1109/ITSC.2017.8317700. 7. Narula, L., et al.: TEX-CUP: the university of texas challenge for urban positioning. In: 2020 IEEE/ION Position, Location and Navigation Symposium (PLANS), Portland, OR, USA, pp. 277–284 (2020). https://doi.org/10.1109/PLANS46316.2020.9109873. 8. Hsu, L.T., Tokura, H., Kubo, N., Gu, Y., Kamijo, S.: Multiple faulty GNSS measurement exclusion based on consistency check in Urban Canyons. IEEE Sens. J. 17(6), 1909–1917 (2017) 9. Quan, Y., Lau, L., Roberts, G.W., Meng, X., Zhang, C.: Convolutional neural network based multipath detection method for static and kinematic GPS high precision positioning. Remote Sens. 10, 2052 (2018) 10. Xu, B., Jia, Q., Luo, Y., Hsu, L.-T.: Intelligent GPS L1 LOS/Multipath/NLOS classifiers based on correlator-, RINEX- and NMEA-level measurements. Remote Sens. 11, 1851 (2019) 11. 谢钢. GPS 原理与接收机设计. 电子工业出版社 (2017) 12. 闫温合,何在民,胡永辉.伽利略E5频段信号及其性能研究[J].时间频率学报 39(01), 25– 32 (2016)

Decentralized Collaborative Localization Algorithm Based on Covariance Propagation Dongmin Wang, Dongqing Zhao(B) , Minzhi Xiang, Ziru Huang, and Jinfei Li Institute of Surveying and Mapping, PLA Information Engineering University, Zhengzhou 450001, Henan, People’s Republic of China

Abstract. We present a decentralized cooperative localization algorithm based on covariance propagation. The proposed algorithm solves the problem that decentralized collaborative localization’s accuracy. In this paper, the correlation of localization errors between different platforms is considered. The transfer equation of covariance between two cooperative localization is derived based on the Kalman filter. A method to calculate the covariance matrix based on the state recursive coefficient matrix is presented, and a decentralized cooperative localization system is designed. The simulation results show that the decentralized collaborative localization algorithm’s accuracy is equivalent to that of the centralized collaborative localization algorithm. The collaborative localization algorithm can effectively reduce distance over-correction after considering the correlation of localization errors. Keywords: Covariance matrix · Decentralized · Collaborative localization

1 Introduction In recent years, the multi-unmanned platform cooperative task execution mode has attracted more and more international attention (Kurazume et al. 1996). Multi-platform cooperation can expand surveillance, search and combat scope, and has the advantages of multiple tasks, high overall efficiency, increased system reliability, and strong stability (Fallon et al. 2010). Collaborative task execution by multiple unmanned platforms is an important trend in developing unmanned platform technology (Hirose et al. 1995; Han et al. 2020). Multi-unmanned collaborative localization is a localization method to improve the system’s localization accuracy by observing each other in movement and using the constraint relationship between platforms (Bahr et al. 2009; Hua et al. 2011). According to the data fusion structure, it can be divided into centralized, distributed, and decentralized. Compared with the other two data fusion methods, decentralized data fusion has the advantage of not relying on a separate processing center to solve the problem of unmanned platform collaborative localization (Kia et al. 2014). In this way, the system stability and reliability can be improved effectively by avoiding a single platform’s failure, leading to the collaborative system collapse (Chen et al. 2020; Han et al. 2020).

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 384–393, 2021. https://doi.org/10.1007/978-981-16-3142-9_36

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Bahr et al. (2009) proposed a suboptimal algorithm in which each robot retains a set of extended Kalman filters. Only the robot obtaining the relative measured value can update its state. Each filter in the algorithm is updated only if its state is not related to the current update equation’s state. This algorithm’s main disadvantages are high computational complexity, large memory requirements, and more information required for each update. Roumeliotis et al. (2015) proposed a distributed computing decentralized algorithm equivalent to the centralized Kalman filter. The core of the algorithm is to disperse each covariance item of the covariance matrix on each platform. In the algorithm, each platform estimates the state covariance between its state and other platforms. A data fusion center is still needed in this calculation mode, and decentralized data fusion is not achieved. Kia et al. (2014) targeted the above problems and took the robot carrying out relative measurement as the centralized processing center. The centralized processing center computes and broadcasts intermediate variables that other robots use to update their estimates to match the centralized extended Kalman filtering forecast for collaborative localization. However, when the robot’s status update frequency is high, the whole collaborative system’s communication frequency will increase, increasing the communication burden. In this paper, a decentralized data fusion algorithm based on covariance propagation is proposed, and a corresponding communication strategy is designed according to the proposed algorithm. The proposed algorithm’s accuracy is equivalent to that of the centralized collaborative location algorithm through simulation experiments.

2 Recursion Law of State Vector and Covariance Between Synergies In order to analyze the covariance transfer relationship between synergies, it is assumed that there are two platforms. Assume that for each unmanned platform, its discrete mathematical model is as follows:  X k = Φ k/k−1 X k−1 + Γ k−1 W k−1 (1) Zk = H k X k + V k The basic assumption about noise is as follows: ⎧ E[W k ] = 0, E[W k W Tj ] = Qk δkj ⎪ ⎪ ⎨ E[V k ] = 0, E[V k V Tj ] = Rk δkj ⎪ ⎪ ⎩ E[W V T ] = 0 k

(2)

j

Qk ≥ 0, Rk > 0 Suppose that the state quantity at the initial moment is Xˆ k−1 , and the covariance matrix is P k−1 . After state prediction, we can get: Xˆ k/k−1 = Φ k/k−1 Xˆ k−1 P k/k−1 = Φ k/k−1 P k−1 Φ Tk/k−1 + Γ k−1 Qk−1 Γ Tk−1

(3)

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After measurement and update, we get: Xˆ k = Xˆ k/k−1 + K k Z˜ k = Xˆ k/k−1 + K k (Zk − H k Xˆ k/k−1 ) = (I − K k H k )Xˆ k/k−1 + K k Zk

(4)

= (I − K k H k )Φ k/k−1 Xˆ k−1 + K k Zk P k = (I − K k H k )P k/k−1 (I − K k H k )T + K k Rk K Tk = (I − K k H k )Φ k/k−1 P k−1 Φ Tk/k−1 (I − K k H k )T +(I

− K k H k )Γ k−1 Qk−1 Γ Tk−1 (I

− Kk Hk )

T

(5)

+ K k Rk K Tk

For the convenience of simplification, let ξ k = (I − K k H k )Φ k/k−1 and ζ k = (I − K k H k )Γ k−1 , then: Xˆ k = ξ k Xˆ k−1 + K k Zk

(6)

P k = ξ k P k−1 ξ Tk + ζ k Qk−1 ζ Tk + K k Rk K Tk

(7)

Assume that the position covariance matrix of the two platforms A, B at the time k − 1 is:

 P A(k−1) P AB(k−1) P⎡ ⎤ = (8) P BA(k−1) P B(k−1) ⎢A⎥ ⎣ ⎦(k−1) B Since the process noise and measurement noise of the platform are not related to the state quantity of other platforms, the position covariance matrix of the two platforms A, B at the time k is:

(9)

It can be seen that the change of the covariance term of the two platforms A, B at the time k is only related to ξ A(k) and ξ B(k) , that is, exclusively related to the coefficient matrix in front of the recursive state Eq. (6). Similarly, assuming that the time of two synergies is time k and time k+n respectively, the corresponding recursive relation of covariance term can be expressed as follows:  T P AB(k+n) = ξ A(k+n) ξ A(k+n−1) . . . ξ A(k+2) ξ A(k+1) P AB(k) ξ B(k+1) ξ B(k+2) . . . ξ B(k+n−1) ξ B(k+n)

(10)

As a result, in a collaborative localization, each platform preset a state and position vector of the same dimension recursive coefficient matrix. Its initial value for the unit matrix, updated every update or time measurement, the quantity of state before the coefficient matrix of left by recursive coefficient matrix, so that when the next collaborative localization can according to the recursive coefficient matrix of each platform and collaborative covariance item after the last time to calculate the covariance of the current time.

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3 Design of Decentralized Collaborative Localization System 3.1 Problem Hypothesis Assume that the entire collaborative localization system meets the following assumptions: • The whole collaborative system has a total of M independent unmanned platforms moving in n-dimensional space. Each unmanned platform can realize dead reckoning according to the sensors carried by itself. • Through communication network connection between platforms, each platform can broadcast its state information and sensor data at corresponding time nodes, and the communication delay can be ignored. • Each platform is equipped with the corresponding ranging sensor, measuring the platform’s distance information and other platforms. 3.2 Collaborative Localization System Equation In this paper, each member’s position information and relative distance carry out collaborative localization. Instead of building the state equation of co-positioning separately, the prediction value of the state quantity involved in the measurement equation and the prediction covariance matrix is directly used to obtain each platform’s current state chain information reckoning the navigation position. Assuming at the moment k, the position error vector of the ith member is δX i (k), and the covariance matrix is P ii (k). The relative distance between this member and other N − 1 members is observed, and the corresponding position error vector is δX j (k)(j = 1, 2, . . . , N , j = i). The position covariance is P jj (k)(j = 1, 2, . . . , N , j = i), then the state vector of collaborative localization is:   X(k) = δX i (k) δX 1 (k) δX 2 (k) . . . δX N (k) Considering the position correlation among all members, the state covariance matrix is:

⎡

⎤ P ii (k) P i1 (k) P i2 (k) . . . P iN (k) ⎢ P (k) P (k) P (k) . . . P (k) ⎥ ⎢ 1i ⎥ 11 12 1N ⎢ ⎥ P(k) = ⎢ P 2i (k) P 21 (k) P 22 (k) . . . P 2N (k) ⎥ ⎢ ⎥ ⎣ ... ... ... ... ... ⎦ P Ni (k) P N 1 (k) P N 2 (k) . . . P NN (k)

In the formula, δX i (k) and P ii (k) are obtained from its state chain. δX j (k) and P jj (k)(j = 1, 2, . . . , N , j = i) are received from the state information broadcast by data link and P ij (k)(i = j) is given by the calculation method in the previous section. The observation distance between this member and the jth member is dij , and the relationship between the distance and coordinates is as follows:   (11) dij (k) = hij X i (k), X j (k) + ζij (k)

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  The function expression of hij X i (k), X j (k) is:     2  2  2 xi (k) − xj (k) + yi (k) − yj (k) + zi (k) − zj (k) hij X i (k), X j (k) = In the formula hij is the observation function of this member and the jth member. X i (k) and X j (k) are the position vector of i and j member, and ζij (k) is the ranging error. The Equation is linearized to obtain:       j dij (k) = hij Xˆ i (k), Xˆ j (k) + ∇hiij X i (k) − Xˆ i (k) +∇hij X j (k) − Xˆ j (k) + ζij (k)     j = dˆ ij (k) + ∇hiij X i (k) − Xˆ i (k) +∇hij X j (k) − Xˆ j (k) + ζij (k) j = dˆ ij (k) + ∇hiij δX i (k)+∇hij δX j (k) + ζij (k)

(12) Among them:   j  i  ∂h ∂h ij  ij  j ∇hiij = X i (k)=Xˆ i (k) , ∇hij = ˆ ∂X i (k)  ∂X j (k) X j (k)=X j (k) The corresponding observation equation is as follows: Zij (k) = H ij (k)X(k) + ζij (k)

(13)

In the formula: Zij (k) = dij (k) − dˆ ij (k)   j H ij (k) = ∇hiij . . . 0 . . . ∇hij . . . 0 According to Eq. (13), the corresponding observation N −1 equations can be written to form a complete observation equation. 3.3 System Design According to the covariance calculation formula derived in the previous section, this paper designs a decentralized filtering algorithm equivalent to the centralized filtering algorithm. Two filters are designed for each platform. A filter is used to recursion its state chain, which can be different according to different sensors. The other filter is used for collaborative localization, which contains each platform’s position state quantity in the current collaborative localization system and their covariance information, so this filter on each platform is the same. The algorithm is described after the first measurement update of collaborative localization is completed to facilitate description. Step 1 state recursion and recursion coefficient matrix recursion According to the state estimate and state covariance obtained after collaborative localization, each platform takes the initial value as the time update and measurement update according to its different sensors. For each time update or measurement update,

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the coefficient matrix in front of the state quantity is left multiplied by the recursive coefficient matrix. The recursive coefficient matrix is updated accordingly. Step 2 Ranging Each platform of the collaborative system shall conduct ranging between platforms following the agreed frequency and range rules. Step 3 Data broadcasting The data broadcast stage is divided into two parts: 1. The ranging information (including the length of the distance and the platforms’ names at both ends of the distance) is broadcast outward by the platform that conducts ranging at the agreed time point so that each platform gets the same distance information. 2. At the time node of ranging, each platform in the collaborative localization system broadcasts its current state chain information, including the estimated value of state quantity, state covariance matrix, and a recursive coefficient matrix. Step 4 Collaborative localization filter setting The state vector and covariance matrix are set as follows: • The state vector of collaborative localization is composed of combining the position state information broadcast by each platform. The dimension and value of the state vector of the collaborative localization filter for each platform are equal. • The state vector covariance matrix is composed of two parts. The covariance matrix’s diagonal block, namely the covariance item of each platform’s position, is obtained from the broadcast state covariance matrix. The covariance matrix’s non-diagonal block, namely the covariance item of the position state quantity between each platform, is calculated by the transmitted recursive coefficient matrix and the locally saved covariance item after the last collaborative localization according to Eq. (10). Step 5 Collaborative localization measurement update Based on the state vector and covariance matrix obtained in step 4, the corresponding measurement equation is constructed according to the transmitted distance information, and the measurement is updated. After the measurement update, the obtained self-state estimation and covariance information are brought back to the platform’s state chain. In contrast, the covariance items with other platforms are saved locally to use the new covariance items before the next collaborative localization. It should be noted that, in the first collaborative localization, the non-diagonal blocks of the initial covariance matrix are all zero because there is no correlation between platforms.

4 Experimental Results and Performance Analysis Digital simulation analysis is carried out to verify the effectiveness of the proposed algorithm. In the simulation, a total of three mobile land platforms were simulated for

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collaborative localization. Each platform carried out dead reckoning through inertial navigation and odometer, as shown in Table 1 for specific parameters. The simulation trajectory is shown in Fig. 1. The simulation time is 380 s in total. When comparing the accuracy of dead reckoning and collaborative localization, the ranging frequency is set at 1 Hz. Distance measurement was carried out at 1 S, 100 S, 200 S, and 300 S, respectively, when the collaborative localization algorithms’ accuracy differences were compared to observe covariance’s influence on the collaborative localization results. Table 1. Platform sensor parameters Parameter’s name

Value

Accelerometer constant deviation (μg) 500 √ Accelerometer random deviation (g · s) 100 Gyroscope constant drift (◦ /h) √ Gyroscope random drift (◦ / h)

1.2

The speed error of the odometer (m/s)

0.2

Distance measuring error (m)

0.1

3

Fig. 1. Platform trajectory diagram

Figure 2 respectively show the positioning error and heading Angle error of the platform in the co-positioning mode without covariance transmission and dead reckoning mode. It can be seen that both the positioning error and heading Angle error are significantly suppressed in the collaborative localization mode. In terms of localization error, each platform’s last localization error is 6–12 m in the single dead reckoning mode. The last localization error is up to 3 m in the collaborative localization mode, and the error is reduced by 50%–75%. In terms of heading Angle error, each platform’s final heading Angle error reached 0.5° in the single dead reckoning mode. The last heading Angle error was less than a 0.23° in the collaborative localization mode, which reduced by 54%.

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Fig. 2. Comparison diagram of dead reckoning and collaborative localization

Figure 3 is a covariance passes centralized collaborative localization algorithm and distributed collaborative localization algorithm of location error and the heading Angle error contrast figure. It can be found by comparing the location precision of the two quite, can draw based on covariance propagation of distributed collaborative localization accuracy with the centralized location on the precision are equivalent.

Fig. 3. Comparison diagram of centralized and distributed

Figure 4 shows the comparison of location errors and heading Angle errors under two different collaborative localization modes of covariance transfer and non-covariance transfer. It can be seen that under the covariance transfer mode, the effect of collaborative localization is further improved. As can be seen from the figure, after four collaborative localization times, the positioning error can be reduced by 49.3% at most, 10.3% at least, and 24.1% on average. The heading Angle is reduced by 13.6% at most, 7.1% at least, and 11.9% on average. As can be seen from the figure, when measuring collaborative localization with distance each time, the correlation between locations is taken into account in the collaborative localization mode of covariance transmission, which reduces the influence of over-correction of distance. It can be seen that with the increase of the number of collaborative localization, the accuracy of this collaborative localization mode is improved more obviously.

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Fig. 4. Comparison diagram of platform location error

5 Conclusions In this paper, based on the Kalman filter, the transfer equation of covariance between two collaborative localization methods is derived. A decentralized collaborative localization algorithm equivalent to the centralized filtering method is designed. The simulation results show that the collaborative localization algorithm based on covariance transfer can reduce the over-correction of the collaborative localization position by distance information according to the correlation of position errors between various platforms and improve the location accuracy of the collaborative localization. The improvement effect is more obvious with the increase of time. The algorithm has a certain reference value to the design of a multi-platform decentralized collaborative positioning system.

References Bahr, A., Leonard, J.J., Fallon, M.F.: Cooperative localization for autonomous underwater vehicles. Int. J. Robot. Res. 28(6), 714–728 (2009) Bahr, A., Walter, M.R., Leonard, J.J.: Consistent cooperative localization. In: IEEE International Conference on Robotics & Automation (2009) Chen, M., Xiong, Z., Liu, J., Wang, R., Xiong, J.: Cooperative navigation of unmanned aerial vehicle swarm based on cooperative dilution of precision. Int. J. Adv. Robot. Syst. 17(3), 172988142093271 (2020). https://doi.org/10.1177/1729881420932717. Fallon, M.F., Papadopoulos, G., Leonard, J.J., Patrikalakis, N.M.: Cooperative AUV navigation using a single maneuvering surface craft. Int. J. Robot. Res. 29(12), 1461–1474 (2010). https:// doi.org/10.1177/0278364910380760. Han, Y., Wei, C., Li, R., Wang, J., Yu, H.: A novel cooperative localization method based on IMU and UWB. Sensors (Basel, Switzerland) 20(2) (2020). https://doi.org/10.3390/s20020467. Hirose, S., Kurazume, R., Nagata, S.: Cooperative positioning system with multiple robots. J. Robot. Soc. Jpn. 13(6), 838–845 (1995). https://doi.org/10.7210/jrsj.13.838. Hua, M., Bailey, T., Thompson, P., Durrantwhyte, H.: Decentralised solutions to the cooperative multi-vehicle navigation problem. Aerosp. Electron. Syst. IEEE Trans. 47(2), 1433–1449 (2011) Roumeliotis, S.I., Bekey, G.A.: Distributed multirobot localization. IEEE Trans. Robot. Autom. 18(5), 781–795 (2015)

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Kurazume, R., Hirose, S., Nagata, S., Sashida, N.: Study on Cooperative Positioning System (Basic Principle and Measurement Experiment) (1996) Kia, S., Rounds, S., Martinez, S.: A centralized-equivalent decentralized implementation of extended Kalman filters for cooperative localization. In: International Conference on Intelligent Robots and Systems. Chicago. IEEE (2014)

DVT-SLAM: Deep-Learning Based Visible and Thermal Fusion SLAM Ruochen Wang1 , Ling Pei2(B) , Lei Chu1 , Qi Wu1 , Tao Li1 , Wenxian Yu1 , and Xujun Guan2 1 Shanghai Key Laboratory of Beidou Navigation and Location Services, Shanghai Jiao Tong

University, Shanghai, China 2 Shanghai Jiao Tong University, Shanghai, China

[email protected]

Abstract. The problem of visual odometry (VO) and localization in extreme illumination conditions is widely concerned. In this paper, we propose a novel SLAM algorithm namely DVT-SLAM (Deep-learning based Visible-Thermal SLAM). It focuses on the fusion of thermal infrared image and visible image which have complementary advantages in characteristics. With the contrastive learning and the measurement of mutual information between multi-modal images, the first part of DVT-SLAM is the DVT-GAN network to fuse visible-thermal images and generate pseudo visible images at night. Given the generated images, visual odometry is applied for pose estimation base. Extensive evaluations are performed on the Brno Urban Dataset, a multi-modal dataset containing different time and weather conditions in diverse scenarios. Series of experiments show that DVT-SLAM is a robustness and suitability solution for single visible camera failures, which can reduce positioning error by half and achieve superior SLAM performance. Keywords: Visual SLAM · Thermal infrared camera · Deep learning

1 Introduction In recent years, unmanned system and artificial intelligence have developed rapidly. Fast, reliable, and efficient positioning systems are the prerequisites for subsequent obstacle avoidance or decision-making tasks. Simultaneous Localization and Mapping (SLAM), as the key technology of unmanned system, would face challenges in extreme illumination conditions. Multi-modal SLAM system for complex environment has become a prevailing research topic. Compared with visible camera, the thermal camera creates an image using infrared radiation. It is less affected by changing illuminance and can be a good supplement for traditional visible camera. To make full use of the infrared imaging characteristics, researchers have carried out a series of explorations. Tarek [1] and Beauvisage [2] did similar work. They adopted multi-spectral stereo matching to find the corresponding relationship between visible image and long-wave thermal image. Then they realized the Visual Odometry (VO) for pose estimation. Poujol et al. [3] used the discrete wavelet © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 394–403, 2021. https://doi.org/10.1007/978-981-16-3142-9_37

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transform method to fuse infrared and visible images for monocular VO. In 2020, Beauvisage et al. [4] proposed a new multi-modal monocular VO method, which tracked the features of two modalities at the same time. However, only the camera which performed better is used to estimate the motion. On the other hand, some researchers struggled with deep learning for processing images of two modalities. In 2016, Choi et al. [5] introduced a convolutional neural network to enhance low-resolution thermal image quality. Sun [6] et al. proposed FuseSeg network which could integrate visible and thermal images, and then get pixel-level semantic tags. As illustrated above, some of these methods focus on the process of SLAM system, such as feature matching and keyframe extraction, which have no limitation to frame image quality. Other methods pay attention to the image fusion, without considering application in SLAM fields. The main contributions of this paper are as follows: Firstly, we propose a deep learning-based visible-thermal fusion SLAM algorithm DVT-SLAM. The traditional VO is replaced by a new VO with deep learning network to improve the positioning accuracy in low-illumination conditions. Secondly, we propose a multi-modal image fusion method based on Contrastive Learning (CL). The network uses infrared image and visible image at night to generate high-quality “pseudo visible” image, and the generated images are utilized for VO calculation. Thirdly, with mutual information, a contrastive loss function is introduced to reduce the size of network and improve the quality of generated fused images.

2 Visual SLAM The classic visual SLAM system generally includes four main parts: front-end Visual Odometry (VO), back-end optimization, loop-closure detection, and mapping. Among these, VO is the process of estimating the 6 Degrees Of Freedom (DoF) ego-motion using only the input of cameras. The back-end module solves the drift problem and corrects the trajectory error through non-linear optimization. The state-of-the-art approaches for VO can be divided into two classes, featurebased methods and direct methods. Feature-based methods minimise the geometric error between point of interest and its re-projected position in the image. Direct methods track camera poses by minimizing photometric errors. In the field of traditional visual SLAM, the ORB-SLAM [7, 8] system is one of the most prevailing monocular visual SLAM systems, which well balances the accuracy and the computational demand. It extracts ORB features to achieve the ORB dictionary for VO and loop-closure detection. Then, with tracking thread, local BA (Bundle Adjustment) thread and global loop closure optimization threads to achieve fast and robust navigation.

3 Methodology This section presents the image fusion algorithms evaluated in the DVT SLAM context. The overall framework of the DVT-SLAM system is shown in Fig. 1. It consists of two components. In the first part, the thermal and visible images generate pseudo

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visible images through the DVT-GAN network. The second part is the overall architecture of DVT-SLAM, which uses the fusion images as the input image frames. The ORB features are extracted and key frames are determined to perform pose estimation. Finally, local map construction and loop-closure detection are completed through back-end optimization.

Fig. 1. Architecture overview of DVT-SLAM

3.1 Visible-Infrared Image Fusion Network DVT-GAN 3.1.1 Mutual Information In the fields of probability and information theory, Mutual Information (MI) is a measurement of the interdependence. It estimates the correlation between two random variables or sets of events. Similarly, MI could also be used to measure the correlation between two images. The concept of MI has gradually been adapted to multi-spectral stereo matching [9], multi-modal image registration, depth map calculation and other fields. The mutual information of two random variables (X, Y ) can be defined as: MI (X , Y )=

 x∈X y∈Y

p(x, y) log(

p(x, y) ), p(x)p(y)

(1)

where p(x, y) represents the joint distribution function of X and Y, p(x) and p(y) are the marginal probability distribution functions of X and Y respectively. 3.1.2 The Architecture of DVT-GAN To establish the relationship between infrared images and visible images, MI theory is adopted in the proposed DVT-GAN network. The scheme of the DVT-GAN network is presented in Fig. 2. It is designed on the basis of CycleGAN [10] and CUT [11] architecture. The input domain X ⊂ RH ×W ×C represents the infrared image domain, and the

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output domain Y ⊂ RH ×W ×3 represents the visible image domain. The generator is composed of two parts, encoder and decoder. Then one discriminator is designed for leveraging adversarial training. Given infrared image x as input, the generated fused image can be expressed as yˆ = G(z) = Gdec (Genc (x)). DVT-GAN learns image generation relationships only in one direction, that is, from thermal image to visible image.

Fig. 2. The Architecture of DVT-GAN network

Different from CycleGAN, which contains two generators and discriminators for cyclic domain migration, the DVT-GAN network uses diverse loss functions to maximize the similarity of images between input and output domains. Adversarial Loss. The adversarial loss is used to make the generated pseudo visible image similar to the real visible image visually. The adversarial loss can be expressed as follows: LGAN (G, D, X , Y ) = Ey∼Y log D(y) + Ex∼X log(1 − D(G(x)))

(2)

Contrastive Loss. Traditionally, cycle consistency loss is used to prevent contradictions between generators, it can be defined as: Lcyc (G, F) = Ey∼Y G(F(y)) − y1 + Ex∼X F(G(x)) − x1

(3)

However, cycle consistency loss requires a reverse generator and an additional discriminator to migrate the generated images back to the input domain X , which enlarges the network and training time cost. Li et al. [12] proved that cycle consistency loss is the upper bound of conditional entropy H (X |Y ). According to the formula between MI and conditional entropy, MI (X , Y ) = H (X ) − H (X |Y ), the maximization of MI is equivalent to the minimization of conditional entropy. Generally, the problem of minimizing cycle consistency loss can be simplified as minimizing MI. Based on the method of contrast learning, noise contrastive estimation is used to maximize the MI between the input domain and the output domain. As is shown in

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Fig. 2, the infrared image and visible image are encoded into feature vectors. Multimodal image patches at the same position are taken as positive samples while others are taken as negative ones. Patch-level image loss is computed to generate a fused image as realistic as possible. 3.2 DVT-SLAM Based on the Visible-Infrared Fusion Image The front-end of SLAM estimates camera pose by iteratively optimizing the rotation and translation relationship between adjacent frames. Among these VO methods, featurebased VO, as is shown in Fig. 3, optimizes the geometric error: 2     (4) Tk−1,k = arg min ui − π(pi ) ui Ik , T

i

Fig. 3. Indirect method of visual SLAM 

where u1 is any pixel in the image Ik−1 , its projection in the space is p, u1 represents the coordinate pixel in Ik which is the projection of p. In this part, we use visible-infrared fusion images as input frames to optimize VO and realize the DVT-SLAM system based on the ORB-SLAM framework. In the tracking thread, we extract keypoints in the fused images instead of the original low-illumination visible or infrared image. Then through the back-end local mapping and loop closing thread, we achieve global BA optimization.

4 Experiments and Results 4.1 Dataset Brno Urban Dataset [14] is intentionally proposed for autonomous driving and mapping tasks. It was recorded in Brno D-Czech Republic for more than 350 km distance. The dataset provides multimodal data from sensors including WUXGA visible camera, infrared camera, LiDAR, and Inertial Measurement Unit (IMU). Ground truth was recorded by an centimetre-accuracy differential RTK GNSS receiver which produce

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an accurate pose estimate. Camera calibration parameters including their intrinsic and extrinsic parameters can also be obtained. The characteristics of visible camera and thermal infrared camera used in the experiment are shown in Table 1. Table 1. Camera characteristics of Brno datasets Model

FLIR Tau 2

Resolution

640 × 512px 1920 × 1200px

Max. frame rate 30 Hz Spectral band

WUXGA RGB camera 10 Hz

7.5–13.5 µm Visual spectrum

4.2 Visible - Thermal Image Fusion A. Experiment Implements We conducted experiments on the Brno Urban dataset. 3675 daytime infrared images and 3491 daytime visible images in different scenarios are collected to train the DVT-GAN network. Training images from visible domain and thermal domain are unpaired. After establishing the conversion relationship between infrared and high-resolution visible images, infrared images are put into the DVT-GAN network to generate pseudo visible images at night. The resolution of the generated fused image is 512 * 512. We trained the DVT-GAN network on a server with an Intel E3–1230 V2 (3.3 GHz) CPU and TITAN V graphics card, including 12-GB graphics memories. B. Fusion Results The image comparison is shown in Fig. 4. The left column depicts the origin night visible image; the thermal images of the same scenarios are shown in the middle column and the generated fused images are presented in the right column. Visually, the generated fused image realizes “pseudo visible” effect, that is, it combines the structural features of infrared image and RGB texture features. C. Evaluation Metrics We first evaluate the proposed method in terms of the fused image quality. FID (Frechet Inception Distance score) [10] is a measurement of image diversity and authenticity statistically. It calculates the distance between the generated image distribution and real image distribution to measure image similarity. The formula can be expressed as: 2   FID(x, g) = μx − μg 2 + Tr(x + g − 2 x g ),

(5)

where x is the real image and g is the generated image. µ and  respectively represent the mean value and covariance matrix of the feature vector set, generated by pre-trained

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Fig. 4. Images of DVT-GAN

Fig. 5. SIFT matching results of fused images

Inception Net-V3 network. Tr represents the trace of the matrix. Lower FID means closer distributions, thus indicates higher image generation quality and better diversity. Meanwhile, metrics of feature points characteristics is evaluated. SIFT (Scaleinvariant feature transform) is used to detect local features and find the feature matching relationship between two images. Oriented FAST and Rotated BRIEF (ORB) performs as an efficient and viable alternative to SIFT while being almost two orders of magnitude faster. The larger the number of feature points, the higher the ability for matching. The comparison results of the image quality evaluation are shown in Table 2. Table 2. Image quality evaluation Image

Visible image (night) Infrared image (night) Fused image Fused image (CycleGAN) (DVT-GAN)

FID

199.29

223.12

191.29

148.04

ORB

500

391

456

500

Matched (ORB) 84

41

31

89

SIFT

154

352

848

27

21

38

1433

Matched (SIFT) 15

As to the high noise in visible images at night, only a few keypoints can achieve good matching despite a large amount of SIFT feature points. Compared with the original image, the number of SIFT feature points and matched feature points in generated fusion images has been improved to a certain extent, as shown in Fig. 5.

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4.3 Dvt-Slam In this section, we further evaluate the position and navigation performance of DVTSLAM. We select four night-time sequences in the Brno dataset, as Table 3 shows. Each sequence contains visible images and their corresponding infrared images. Sequences 1 and 2 are collected in the urban area, while sequences 3 and 4 are collected in suburbs. Table 3. Numbers of images and distance for each sequence Seq_1 Seq_2 Seq_3 Seq_4 Number of images

280

500

100

100

Distance traveled (m) 110

133

98.8

53.8

Absolute trajectory error (ATE) calculates the Euclidean distance between each estimated camera position and the closest GPS ground truth in time. In Table 4, we calculate the Root Mean Squared Error (RMSE) of ATE. The first column in Table 4 shows that visible failure occurs in low-illumination conditions, which may be caused by insufficient feature points, mismatching, and wrong extraction of keyframes. In the last column, the pseudo images generated by DVT-GAN help DVT-SLAM perform better. Compared with thermal SLAM, RMSE reduces by half on average. This result verifies our previous conjecture. Table 4. Errors obtained from all sequences Visible SLAM

Thermal SLAM

DVT-SLAM

\

16.04

24.68

12.638

18.43

5.13

41.13

9.48

Sequence 1 RMSE(m)

\ Sequence 2

RMSE(m)

\ Sequence 3

RMSE(m)

\ Sequence 4

RMSE(m)

\

“\” represents for the failure of SLAM.

Figure 7 shows the comparison of the trajectories by DVT-SLAM on different images. The trajectories are aligned with singular values since the monocular SLAM has no scale. Even though some drift can be noticed for fused images in Fig. 7, the overall trajectories of DVT-SLAM are estimated more properly compared with Thermal SLAM. In general,

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the usage of pseudo images results in quite stable positioning effects. These results demonstrate the suitability of the proposed visible-thermal fusion approach for SLAM.

Fig. 7. The comparison of the trajectories between Thermal SLAM and DVT-SLAM

5 Conclusion This paper proposed a visible-thermal fusion SLAM algorithm called DVT-SLAM. It combined self-supervised image generation network and visual SLAM system. The DVT-GAN network is designed for generating pseudo-visible fused images in lowillumination conditions. Moreover, high-quality fused images were utilized for monocular visual SLAM. The results showed that compared with the original visible and infrared images, the quality of the generated fusion image was improved. At the same time, better positioning and navigation effects could be obtained on the DVT-SLAM algorithm, and the trajectory error of the experiment on the dataset reduced by half. In future, it is necessary to optimize the architecture of image fusion network DVTGAN. The current method may have difficulty solving the problems of pseudo visible images generation in more complicated conditions. Even if the number of datasets involved is enlarged, additional work could be carried out to highlight the benefits.

References 1. Mouats, T., Aouf, N., Sappa, A.D., et al.: Multispectral stereo odometry. IEEE Trans. Intell. Transp. Syst. 16(3), 1210–1224 (2014)

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2. Beauvisage, A., Aouf, N., Courtois, H.: Multi-spectral visual odometry for unmanned air vehicles. In: 2016 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 001994–001999 IEEE (2016) 3. Poujol, J., Aguilera, C.A., Danos, E., et al.: A visible-thermal fusion based monocular visual odometry. In: Reis, L., Moreira, A., Lima, P., Montano, L., Muñoz-Martinez, V. (eds.) Robot 2015: Second Iberian Robotics Conference. Advances in Intelligent Systems and Computing, vol. 417. Springer, Cham pp. 517–528 (2016) 4. Beauvisage, A., Ahiska, K., Aouf, N.: Multimodal tracking framework for visual odometry in challenging illumination conditions. In: 2020 IEEE International Conference on Robotics and Automation (ICRA), pp. 11133–11139. IEEE (2020) 5. Choi, Y., et al.: Thermal image enhancement using convolutional neural network. In: 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE (2016) 6. Sun, Y., Zuo, W., Yun, P., et al.: FuseSeg: semantic segmentation of urban scenes based on RGB and thermal data fusion. IEEE Trans. Autom. Sci. Eng. (2020) 7. Mur-Artal, R., Tardós, J.D.: Orb-slam2: an open-source slam system for monocular, stereo, and RGB-D cameras. IEEE Trans. Rob. 33(5), 1255–1262 (2017) 8. Campos, C., Elvira, R., Rodríguez, J.J.G., et al.: ORB-SLAM3: An accurate open-source library for visual, visual-inertial and multi-map SLAM. arXiv preprint arXiv:2007.11898, (2020) 9. Krotosky, S.J., Trivedi, M.M.: Mutual information based registration of multimodal stereo videos for person tracking. Comput. Vis. Image Underst. 106(2–3), 270–287 (2007) 10. Zhu, J.Y., Park, T., Isola, P., et al.: Unpaired image-to-image translation using cycle-consistent adversarial networks. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 2223–2232 (2017) 11. Park, T., Efros, A.A., Zhang, R., Zhu, J.: Contrastive learning for unpaired image-to-image translation. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, J.-M. (eds.) Computer Vision – ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part IX, pp. 319–345. Springer, Cham (2020) 12. Li, C., Liu, H., Chen, C., Pu, Y., Chen, L., Henao, R., Carin, L.: Alice: Towards understanding adversarial learning for joint distribution matching. In: Advances in Neural Information Processing Systems (2017) 13. Heusel, M., Ramsauer, H., Unterthiner, T., Nessler, B., Hochreiter, S.: GANs trained by a two time-scale update rule converge to a local Nash equilibrium. In: NIPSs, pp. 6626–6637 (2017) 14. Ligocki, A., Jelinek, A., Zalud, L.: Brno urban dataset-the new data for self-driving agents and mapping tasks. In: 2020 IEEE International Conference on Robotics and Automation (ICRA), pp. 3284–3290. IEEE (2020)

Satellite Thrusters’ Control Allocation and Application Used for Integrated Attitude-Orbit Control System Xiaoyue Li1,2(B) , Tao Bai1,2 , and Baojun Lin1,2 1 Innovation Academy for Microsatellites of CAS, Haikestr. 99, Shanghai 201210, China

[email protected] 2 Shanghai Engineering Center for Microsatellites, Haikestr. 99, Shanghai 201210, China

Abstract. To adapt the needs of smaller, lighter, higher load ratio of new generation of Beidou Navigation satellites, this paper innovatively presents the integrated attitude-orbit control system only by four thrusters. It highly simplifies the systems, decreases the redundancy, as well as enhances the load ratio of the whole satellite. The design solves the control allocation problem of the thrusters by using the approximation vector method. Meanwhile, the off modulation is used to attitude control in order to solve the coupling of both attitude control and orbit control. The results in this paper are applied in the new generation of Beidou Navigation Satellites. The integrated method has enhanced 8 times of the precision, and decreases the interrupt of the navigation plan furthest due to the orbit control. Keywords: Attitude control · Orbit control · Control allocation

1 Introduction The definition of control allocation of thrusters is, to choose the thrusters’ combinations which could realize the desired control force and torque, and calculate the firming time of each thruster [1]. The control allocation result affects the precision of control, the consumption of propellant and the stability of the whole control system. Previous work, such as Zhang and Fabio [2, 3] studied the attitude-orbit coupling of 12 thrusters, dealt only with full-actuated thrusters’ control allocation. Force and torque of arbitrary directions were the output, and the 6 degree of freedom model of orbit-attitude coupling was established. Especially, one domestic satellite equipped with 12 thrusters, and the attitude control and orbit control were performed using divided thrusters. Further, the amplitude and layout of the thrusters were different. The advantage of this usage is the decoupling of attitude and orbit control by the thrusters, referred in the respective work of thrusters. Nevertheless, on one hand, it becomes harder from the perspective of design and layout of the propulsion system. On the other hand, the higher redundancy of the thrusters makes the whole satellite system heavier weight and higher power dissipation. Moreover, to the control allocation of the thrusters, there exists the regular tabulation [4, 5] as well as dynamic allocation methods in the practice [6, 7]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 404–413, 2021. https://doi.org/10.1007/978-981-16-3142-9_38

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Recent years, the redundant actuators are widely used [8], including Russian Soyuz spacecraft, ESA ATV cargo spacecraft, Japanese HTV ISS cargo spacecraft and Chinese Shenzhou manned spacecraft. Among these applications, ATV designed the online control allocation algorithm, which adapts the needs of real time control allocation, and the computing resource is less occupied. In the meantime, thrusters perform efficiently. Tang built the mathematical model of the integrated attitude-orbit system on Shenzhou manned spacecraft [9], and pseudo-inverse conjunct to linear programming method were used to seek the optimal solution. The desired control commands were allocated to the redundant thrusters dynamically. However, it should be noted that the fuel consumption is of little advantage. To sum up, previous researches ignored the control allocation problem of integrated attitude-orbit control by thrusters, although the orbit control allocation was studied both on dynamic and static. On account of miniaturization, light weight, high load ratio of the new generation of Beidou Navigation Satellites, we designed the integrated attitudeorbit control by propelling system. It means we are able to control the orbit and attitude in the same control period simultaneously. Due to the limitation of fuel consumption, it is necessary to design the control allocation method on the integrated attitude and orbit control system.

2 The Integrated Attitude-Orbit Control Method Used by Thrusters 2.1 The Layout of Thrusters The layout of integrated attitude and orbit control system equipped with four chemical thrusters is shown in Fig. 1. The four incline-fixed thrusters are fixed on the Yb Ob Zb plane of the satellite. The angle between thruster vector and Xb axis of the satellite is θ = 25◦ under the nominal fixing [10]. During the orbit maneuver mode, four thrusters firm, in the meanwhile, attitude is controlled according to the control allocation result. That is the integrated attitude and orbit control system by only four thrusters. 3 4 25

+Xb

Ob 2 1

+Yb +Zb

Fig. 1. The layout of thrusters

406

X. Li et al.

2.2 The Control Allocation Problem of Thrusters The control allocation problem is to allocate the desired control sum to each of the thrusters to perform the control. That is to solve the linear equation set below.  AU = F (2.1) BU = T In the equation set, U = [u1 , u2 , ...un ]T ∈ Rn is the control sum to solve, and n is 3×n is the matrix of the control moments. F = the numberTof the3 thrusters. A ∈ R Fx , Fy , Fz ∈ R is the desired control force of the allocation method. B ∈ R3×n is the  T matrix of thrusters’ control momentum. T = Tx , Ty , Tz ∈ R3 is the matrix of x-y-z axis’s desired control moments. If thrusters are redundant, then the number of thrusters is bigger than the control dimension, so that the equation set above has non uniqueness solutions. Thus, there exists one to many allocation results after the control allocation by the thrusters. That is to say, one set of x-y-z axis’s control commands corresponds to many allocation combinations. By setting the optimization criterions, such as optimal fuel, minimal error of allocation as well as priority weights could get optimized solution. 2.3 The Vector Approximation Algorithm Under the Integrated Attitude-Orbit Control The sign of control moment of attitude control has three states, that is positive, negative and zero. Hence, the control moment combinations has 27 states owing to x-y-z three axis. According to the on or off states of the thrusters, four thrusters have 16 states. Then, how to allocate the x-y-z control moment to 4 thrusters under the orbit maneuver mode for attitude control, especially how to set the evaluation criterion for one to many allocation results, should be further studied. We set α as the angle between the desired control moment vector and the control moment vector produced by the 4 thrusters. Meanwhile, the four thrusters firm to get delta velocity under the orbit maneuver mode. OFF modulation is adopted to control the attitude. Therefore, it’s necessary to try to reduce the thrusters’ off time, and that is to say, set the number of attitude controlling thrusters, n, to be least, as the prior evaluation criteria. The criteria is set as below. J = min(α + n)

(2.2)

The efficiency of the orbit maneuver should be guaranteed firstly by using this integrated attitude and orbit control system. On condition of this, the criteria means it makes the angle between the desired control moment vector and the control moment vector produced by the allocated thrusters is minimal. There exists 27 kinds of states of the desired control moment, and the vector is written as Tc . To each of the vector, the thrusters have 16 kinds of on-off combination sets, and the vector is written as Tr . The angle between Tc and Tr is α, as the above mentioned. Further, parts of the angles of the typical examples are shown in Table 1. Among these, the 8th and 16th combinations of the thrusters all firm and all off resulting zero moments. Hence, there doesn’t exist

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the α angle. In three dimension space, the minimal angle between Tc and Tr has unique solution under some circumstances, however, the others are not. We screen out the best combination of the thrusters by the criteria referred above for the one to many solutions. For instance, in the 17th line, to get the minimal angle between the two vectors there is two combinations of the thrusters. One is No. 1,2,3 thruster, and the other one is No. 3 thruster. Based on the principle of the least time to off modulation for attitude control, we only choose No. 3 thruster to perform the attitude control. For 15th line, both No. 1,3 thrusters and No. 3,4 thrusters can make the vector angle minimal. Just like this situation, we choose the intersection of the two sets’ thrusters to control the attitude. Above all, we designed the control allocation by the thrusters’ combinations for attitude control under the orbit maneuver mode, depicted as Table 2. P is the parameter of the off time during the attitude control in one control period (One control period lasts for one second). According to the allocation results, the angle between the desired control moment vector and the allocated control moment is shown in Fig. 2. For consideration of the minimal number of the thrusters to control the attitude during the orbit maneuver mode, only 4 angles of the sets are bigger. The others are small and acute. This is important because the allocated vectors and the desired vectors are in the same direction, and the allocated results perform well. We take the example of the allocation results in the first line in Table 2, and draw the desired control moment vectors and 16 kinds of on-off states of the thrusters’ vectors in one figure. According to Table 2, we choose the No. 1,2,4 thrusters as the optimal set. As shown in Fig. 3, the angle between the desired moment vector and the No. 1,2,4 thrusters’ vector is small and in the same direction. According to Table 2, we draw the 27 kinds of desired and allocated moment vectors. The desired ones are in red, and the allocated ones are in blue. Each nine vectors are in one group, shown in Fig. 4. 2.4 The Pipeline of Control Allocation Execution Under the Integrated Attitude-Orbit Control On the basis of the desired direction of control moment, the computational resources on satellite has not been taken much. By looking up the 27-lines-table, all the possibility of the control moment has been found. Consequently, the allocated result in the table becomes the guide to the attitude control. The process could improve the efficiency of orbit maneuver even integrated with attitude control. The execution pipelines of the algorithm is as below. (1) To calculate the pulse width of command for attitude control Calculating the pulse width P of thrusters, and choose the longest pulse width of command as the pulse width P.  given  If |Tcx | ≥ Tcy  and |T  cx | ≥ |Tcz |, then P = |T  cx |; If Tcy  ≥ |Tcx | and Tcy  ≥ |Tcz |, then P = Tcy ; Else, P = |Tcz |

63.1

113.6

24.0

87.0

108.9

9

10

15

17

1

1

90.0

135.0

54.7

90.0

54.7

2

45.0

45.0

54.7

180.0

125.3

3

135.0

90.0

54.7

90.0

54.7

4

27.3

87.0

94.3

113.6

122.5

5

152.7

120.9

63.1

66.5

24.0

6

108.9

59.1

57.5

113.6

85.7

7

/

/

/

/

/

8

71.1

120.9

122.5

66.5

94.3

9

45.0

90.0

125.3

90.00

125.3

10

135.0

135.0

125.3

0

54.7

11

71.1

93.0

156.0

66.5

116.9

12

27.3

59.1

117.0

113.6

156.0

13

90.0

45.0

125.3

90.0

125.3

14

152.7

93.0

85.7

66.5

57.5

15

Table 1. Part of the angle between desired command and thrusters’ moment vectors on all conditions (in degree) 16

/

/

/

/

/

com

123 3

13 34

1

24

124

408 X. Li et al.

Satellite Thrusters’ Control Allocation

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Table 2. Thrusters’ control allocation table Control command (Tx,Ty,Tz) Control Allocation (ms) (F1,F2,F3,F4) Control command (Tx,Ty,Tz) Control Allocation (ms) (F1,F2,F3,F4) Control command (Tx,Ty,Tz) Control Allocation (ms) (F1,F2,F3,F4)

1.+++

2.++-

3.++0

4.+-+

5.+--

6.+-0

7.+0+

8.+0-

9.+00

1500 1500 1000-P 1500

1000-P 1500 1000-P 1000-P

1000-P 1500 1000-P 1000-P

1000-P 1000-P 1000-P 1500

1000-P 1500 1500 1500

1000-P 1000-P 1000-P 1500

1000-P 1000-P 1000-P 1500

1000-P 1500 1000-P 1000-P

1000-P 1500 1000-P 1500

10.-++

11.-+-

12.-+0

13.--+

14.---

15.--0

16.-0+

17.-0-

18.-00

1500 1000-P 1000-P 1000-P

1500 1500 1500 1000-P

1500 1000-P 1000-P 1000-P

1500 1000-P 1500 1500

1000-P 1000-P 1500 1000-P

1000-P 1000-P 1500 1000-P

1500 1000-P 1000-P 1000-P

1000-P 1000-P 1500 1000-P

1500 1000-P 1500 1000-P

19.0++

20.0+-

21.0+0

22.0-+

23.0--

24.0-0

25.00+

26.00-

27.000

1500 1000-P 1000-P 1000-P

1000-P 1500 1000-P 1000-P

1500 1500 1000-P 1000-P

1000-P 1000-P 1000-P 1500

1000-P 1000-P 1500 1000-P

1000-P 1000-P 1500 1500

1500 1000-P 1000-P 1500

1000-P 1500 1500 1000-P

1500 1500 1500 1500

70 Vectors' angle value 60

Allocation angle (°)

50

40

30

20

10

0 0

5

10

15 Line number

20

25

Fig. 2. The vector angles between real and desired situation

1 0 -1 0.5

1

0 Desired vector

0.5 -0.5

0

-0.5

-1

T1 T12

1

T13

1

T14

0

T123 0.5

T124 T134

0

-1 0.5

0

0

T1234 T2

-0.5

T23

-0.5

T24

1

T234 -1 1

T3

0

T34 0.5

1 0.5

0 0

-0.5

T4 000

-0.5 -1

-1

Fig. 3. Example of the vectors’ figure

-1 1

0.5

0

0 -1

-0.5

Fig. 4. The diagram of control allocation table

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(2) To calculate the pulse width under orbit maneuver mode If the satellite is under the orbit maneuver mode, four thrusters firm. If the attitude control on demand in this period, then perform the attitude control by switching off the thrusters. In detail, we set MTr as the pulse width of the thrusters and P  as the real firming time in one period. MTr = 1500 ms, P  = 1000 ms − P ; Note: The command is set to 1500 ms to avoid the lack of firming time. In practice, we make the thrusters to firm last for no more than 1000 ms during every period. (3) As Table 2 shows, the control commands are allocated to the four thrusters, along with the thrusters’ control commands. Finally, we carry on the orbit maneuver according to the allocating table. 2.5 The Stability of Integrated Attitude and Orbit Control OFF modulation is adopted to control the attitude, and the attitude controller is shown as follows. The phase plane controller aims at eliminating the error of attitude and angular velocity. 400 ms and 600 ms pulse width were taken to attitude control, and the sliding mode control model is established (Fig. 5). The control stability has been proved in our former research [11]. ω

I ω2 V

ω1

II

VII α1

III VI

α

α2 IV

ω0 V

VIII

Fig. 5. The phase plane attitude control method

3 The Simulation Results The simulation parameters are as follows. The magnitude of force is 7.5N, and the sailboard’s basic frequency is 0.4 Hz. The fix error of the thrusters is 1.0°. The mass of satellite is 850 kg. The orbit maneuver mode lasts for 1200 s. The x-y-z axis control moment commands are allocated to the four thrusters, the integrated attitude-orbit control was realized. The simulation results are shown in Fig. 6, 7, 8 and 9.

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0.6 6

X axis angular velocity 0.5

Y axis angular velocity Z axis angular velocity

0.4

4

Angular velocity(°/s)

0.3

Attitude(°)

2

0

-2

0.2 0.1 0 -0.1

X axis attitude

-0.2

Y axis attitude

-4

Z axis attitude 0

200

400

600 time(s)

800

1000

1200

-0.3 -0.4

0

200

400

600 time(s)

800

1000

1200

Fig. 6. Attitude control of simulation figure

As above, by adopting the method integrated attitude-orbit control, the attitude control during the orbit maneuver is stable, and the x-y-z commands are allocated to the four thrusters effectively. In the meanwhile, the rotation speed of the flywheels keeps stable. 1600

200

1500 1400

100 Command Allocation(ms)

Thrusters' Command(ms)

1300

0

-100

-200

1200 1100 1000 900 800

-300

-400 200

400

600 time(s)

800

1000

F4 Command 500

1200

Fig. 7. The three axis’s commands of simulation

F2 Command F3 Command

600

Z axis command 0

F1 Command

700

X axis command Y axis command

0

200

400

600 time(s)

800

1000

1200

Fig. 8. The commands allocated to thrusters

2500

2000

Speed of Wheels(rate/min)

1500

1000

Wheel X speed Wheel Y speed Wheel Z speed

500

Wheel S1 speed 0

-500 -1000

-1500 0

200

400

600 time(s)

800

1000

1200

Fig. 9. The Revolutions per minute of flywheels during orbit control

4 The on Orbit Results One Beidou Navigation Satellite took the first orbit maneuver control on Nov.14th, 2018. The mode lasts for 617 s. Semi-major axis was reduced and the attitude disturbed due to the fix error was controlled. The rotation speed of the flywheels keeps in the normal value so that the satellite keeps zero angular momentum internally. The attitude control results and thrusters’ commands are in Fig. 10, 11, and 12. The x-y-z control commands are as follows, under the sampling period of one second.

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X. Li et al. 5

0.2 X axis angular velocity

4

Y axis angular velocity Z axis angular velocity

0.15

3

X axis Attitude

Attitude(°)

1 0 -1

Angular velocity(°/s)

Y axis Attitude Z axis Attitude

2

0.1

0.05

0

-0.05

-2 -0.1

-3 -0.15

-4 -5

-0.2

0

100

200

300

400

500

600

0

100

200

300

400

500

600

time(s)

time(s)

Fig. 10. The attitude control results on orbit 600

1400 Command Allocation(ms)

Three axises' command(ms)

1600

X axis command Y axis command Z axis command

400

200

0

-200

F2 Command F3 Command F4 Command

1000

-400

-600

F1 Command

1200

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300 time(s)

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600

0

5

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Sampled points

Fig. 11. The three axis’s commands on orbit

Fig. 12. Control allocation to thrusters on orbit

The allocated results under the sampling period of 16 s on orbit is in Fig. 12. And the rotation speed of flywheels during the orbit maneuver mode under the sampling period of 16 s is in Fig. 13. 3000 2500

Speed of Wheels(rate/min)

2000 1500 1000

Wheel X's Speed Wheel Y's Speed

500

Wheel Z's Speed Wheel S1's Speed

0 -500 -1000 -1500 -2000

0

5

10

15

20

25

30

35

40

Sampled points

Fig. 13. Revolutions per minute of flywheels on orbit

5 Conclusions The integrated attitude-orbit control method was presented in this paper. By adopting the vector approximation allocation algorithm, the control allocation problem was solved under the redundant thrusters. It is effective that the x-y-z axis’s commands are allocated to the thrusters. During the orbit maneuver mode, the off modulation method was adopted to solve the coupling of the attitude and orbit control. The results are applied in the new generation of Beidou Navigation Satellites. 12 Beidou Navigation Satellites carried out the attitude control and orbit maneuver simultaneously by this correct

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and effective control allocation method. Finally, the system is simplified, and the orbit maneuver efficiency as well as precise are enhanced significantly. Also, the interrupt of the navigation plan due to the orbit control was reduced to the maximum extent. Next, we will research the method on the optimal fuel based on the algorithm in this paper.

References 1. Min, W., Yongchun, X.: A dimension-reduction algorithm for spacecraft control allocation based on the optimal thruster combination table. In: Proceedings of the 32nd Chinese Control Conference, Xi’an, China, pp. 2344–2349 (2013) 2. Haibo, Z., Jie, M., Guangfu, M.: Coupled-distributed-adaptive-coordinated control for relative orbit and attitude of multiple spacecrafts. Control Theor. Appl. 30(9),1086–1098 (2013) 3. Fabio, C., Marcello, R.: Lyapunov-based thrusters ’ selection for spacecraft control Analysis and experimentation. J. Guidance Control Dyn. 33(4),1143–1161 (2010) 4. Martel, F., Franck, M.: Optimal 6 axis command of a space vehicle with a precomputed thruster selection catalogue table. In: AAS/AIAA A Strodynamics Specialist Conference, Montana, USA, pp. 1–6 (2004) 5. Jewison, C.M.: Reconfigurable thruster selection algorithms for aggregative spacecraft systems. Doctor Thesis of Massachusetts Institute of Technology, pp. 42–60 (2014) 6. Servidia, P.A., Pena, R.S.: Spacecraft thruster control allocation problems. IEEE Trans. Autom. Control 50(2), 245–249 (2005) 7. Ankersen, F., Wu, S.F., Aleshin, A., et al.: Optimization of spacecraft thruster management function. J. Guid. Control. Dyn. 28(6), 1283–1290 (2005) 8. Chenyang, D.: Thrust Dynamic Allocaion of Spacecraft with Redundant Thrusters. Doctor Thesis of Harbin Institute of Technology (2015) 9. Shengyong, T., Shijie, Z., Min, C., et al.: Research on a thrust allocation algorithm of spacecraft in RVD. Aerosp. Control 29(4), 1120–1125 (2008) 10. Baojun, L., Xiaoyue, L., Tao, B.: The satellite integrated attitude-orbit control method based on variable structure control. Sci Sin-Phys Mech Astron 51, 019502 (2021) https://doi.org/ 10.1360/SSPMA-2020-0216 11. Xiaoyue, L., Shujie, X., Baojun, L.: Attitude control algorithm under simultaneous thruster attitude and orbit control. J. Jilin Univ. (Science Edition) 54(3), 603–608 (2016)

Real-Time Robot Localization Based on 2D Lidar Scan-to-Submap Matching Qipeng Li, Jianzhu Huai, Dong Chen, and Yuan Zhuang(B) State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan, China [email protected]

Abstract. In this paper, we propose a real-time and low-drift localization method for lidar-equipped robot in indoor environments. State-of-the-art lidar localization research mostly uses a scan-to-scan method, which produces high drifts during the localization of the robot. It is not suitable for robots to operate indoors (such as factory environment) for a long term. Besides, the mapping and localization of this method are susceptible to the dynamic objects (such as pedestrians). To solve above problems, we propose the scan-to-submap matching method for real-time localization. Currently, this method has been used for building maps, and there are few studies to use it for localization, especially for real-time localization. In our research, we build the hardware and software platform for the scan-to-submap matching method. We extensively evaluate our approach with simulations and real-world tests. Compared with the scan-to-scan method, the results demonstrate that our approach can cope with the mapping and localization problem with high localization accuracy and low drift. Keywords: Lidar mapping · Indoor localization · Scan-to-submap · Cartographer · Real-time

1 Introduction As a high-precision sensor, lidar is widely used in indoor positioning, automatic driving, robot navigation and other fields. In the field of indoor positioning, the research of indoor positioning based on lidar mainly focuses on 2D or 3D mapping using laser sensors. Among them, the main SLAM mapping methods are Hector SLAM [1], gmapping [2] and cartographer [3]. Hector SLAM uses Gauss Newton method to solve the scan matching problem, which has higher requirements for sensors, but Hector slam has higher requirements. Slam uses the least squares method to match the scanning points, and relies on high-precision lidar data. Therefore, the sensor with small scanning angle and high noise cannot match. When matching, it will fall into local points, and the map is wrong, because the Hector relies too much on scan match. Especially in the corridor problem, the error is more obvious. It is not working well for positioning in large indoor scenes. Gmapping is a widely used 2D SLAM method based on particle filter. The scan matching method is used to estimate the position of the robot. The gradient descent © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 414–423, 2021. https://doi.org/10.1007/978-981-16-3142-9_39

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method is used to estimate the initial position of the robot and the laser point in the current map. Particle filter generally needs a large number of particles to get good results at the cost of increased computational complexity. Moreover, this method relies on odometer, which cannot be applied to an uneven area. Currently, cartographer is a advanced SLAM method, which is a real-time indoor mapping program of Google [4]. Every frame of laser scan data obtained is inserted into the submap at the best estimated position by using scan match, and scan matching is only related to the current submap. After a submap is generated, a local loop closing is performed, and the global loop closure is performed after all submaps are completed by using the branch localization and pre-calculated grid [5]. The purpose of this paper is to solve the following two problems: in the complex indoor environment, remove the impact of indoor dynamic objects on robot mapping and positioning. Another point is to use low-cost lidar for high-precision real-time indoor positioning for complex large-scale areas such as factories. We use the idea of scan-tosubmap matching. Firstly, we use lidar to map the indoor environment, then with the built prior map, match the acquired scans to the submaps of the prior map instead of the online scan-to-scan matching.

2 Related Work In recent papers [6, 7], the accuracy of mapping and trajectory of these three representative methods are evaluated, and it is concluded that cartographer method is superior to the alternatives. In addition, according to [3], although the scan-to-scan matching in the key frame based graph SLAM method is faster, it can accumulate errors quickly, while the scan to submap matching method of cartographer can reduce the error accumulation. Although the idea of cartographer’s scan to submap has been proved to have good performance in SLAM, almost all of the current researches are using it to construct the map, and few people use the scan to submap method for indoor positioning. Building a 7 days 24 h localization system is, by all means, a challenging task that has received significant attention in recent years. J. Levinson et al. [8] showed that the less reflectance caused by wet road surface can be adjusted by normalizing the brightness and standard deviation for each LiDAR scan. R. Wolcott et al. [9, 10] demonstrated a robust LiDAR localization system that can survive through road repavement and snowfall by introducing a multiresolution Gaussian mixture representation in the map. Wan et al. [11] showed that the LiDAR localization system successfully passed a challenging road section with newly built walls and repaved road by incorporating the altitude cues. There is a lot of literature addressing the LiDAR odometry or SLAM problem [3, 12, 13]. In this work, we follow Hess’s work [3] and integrate an occupancy grid based LiDAR inertial odometry into our localization framework because its map representation is similar to our global matching module and it is compatible to multiple laser scanners. Inspired by previous studies, the usage of inertial sensors and other extensions are introduced for performance improvement [14].

3 Localization with Scan-to-Submap Matching In this paper, we try to achieve two goals: building high-precision lidar indoor map, and using low-cost lidar for real-time indoor positioning. In order to achieve these two goals,

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we first select a velodyne lidar, use cartographer for indoor mapping, and then use scan to submap method for real-time indoor positioning. In the positioning process, we use a low-cost Rplidar. 3.1 Cartographer Cartographer is a set of SLAM algorithms based on graph optimization. The main goal of the algorithm is to achieve low computing resource consumption and achieve realtime SLAM. The algorithm is mainly divided into two parts, the first part is called local SLAM. This part establishes and maintains a series of submaps through a frame of laser scan, and the so-called submap is a series of scans. When there is a new laser scan, it will be inserted into the best position in the subgraph through a scan matching method. However, submap suffers from the problem of error accumulation. Therefore, the second part of the algorithm, called global SLAM, is to carry out loop closure to eliminate the accumulated error: when a submap is constructed, that is, there will be no new laser scan inserted into the submap, the algorithm will add the submap to the closed-loop detection module. The essence of closed-loop detection is also an optimization problem. Branch and bound approach is used to find the loop candidates. 3.2 Definitions Occupancy grid map: Our labeling of grid map is defined as fellow. The i-th row and j-th column of the grid, mi,j , is labeled according to its occupancy probability pi,j . The prior probability of each grid is set to 0.5 [3]. ⎧ ⎨ hit pi,j > 0.5 Label(mi,j ) = (1) miss pi,j < 0.5 ⎩ unknow pi,j = 0.5 The pose of autonomous mobile robot can be represented by ξ = (ξx , ξy , ξθ ), ξx and ξy are the translation in x and y directions, and ξθ is the rotation in two-dimensional plane. The data measured by lidar sensor is recorded as H = {hk }, k = 1 . . . K, hk R2 and the initial laser point is OR2 . the pose transformation of lidar scanning data frame mapped to sub image is recorded as Tξ , which can be mapped to sub image coordinate system by formula (2).     ξ cosξθ −sinξθ p+ x (2) Tξ p = sinξθ cosξθ ξy The continuous scanning lidar data frame in a period of time can generate a subgraph, and the subgraph adopts the map expression model of probability grid. When the new scan data is inserted into the probability grid, the state of the grid will be calculated, and each grid has hit and miss conditions. The adjacent grid maps are inserted into the hit set, and all the related points on the connecting ray between the scan center and the scan point are added to the missing set. A probability value will be set for each grid that has

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not been observed before, and a probability update will be made for the grid that has been observed according to Eqs. (3) and (4) [3]. odds(p) =

p 1−p

(3)

Mnew (x) = clamp(odds−1 (odds(Mold (x)) · odds(phit )))

(4)

Before inserting the laser scanning frame into the submap, the pose of the scanning frame and the current sub image need to be optimized by Ceres solver, and then the above problem can be transformed into solving the nonlinear least squares problem [16]. arg min

K k=1

(1 − Msmooth (Tξ hξ ))2

(5)

Submap: A small occupancy grid map composed of several consecutive laser scans (see Fig. 1). The poses of laser scans contained in each submap are stored in a local coordinate system relative to the submap. Continuous scan is used to construct submap, where submap is expressed in the form of probability grid map. When a scan is inserted into a submap, each grid has two cases: hits and miss. The grid nearest to the end of the scan is hits, and the grid intersecting between the origin and the end of the scan is miss. The previously unobserved grid is assigned a probability, and the observed grid is updated by the Bayesian rule.

(a)

(b)

Fig. 1. Is a submap composed of several continuous laser scans. (a) shows the One of the submaps generated in our simulation environment. (b) shows the One of the submaps generated in our real environment.

3.3 Ceres_Scan_Matcher Every time we get the latest scan, we need to insert it into the optimal position in the submap, so that when the pose of the point bundle in our scan is converted and falls into the submap, the reliability and accuracy of each point are the highest [15]. The least square problem is solved by scan matching, which is solved by the Ceres Solver. The reason why cartographer has high accuracy of local Slam (front-end matching) is that it finally adopts the optimized matching method, which is more accurate than raster map correlation matching. The input and output of this method are as follows:

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Input: 1. Initial estimation of the pose of the current scan; 2. Current scan point cloud (2D); 3. Local map of the probability grid;

Output: 1. Refined pose of the current scan;

4 Indoor Scan-Based Mapping Although the method of scan-to-scan has a small amount of calculation and high realtime performance, the error accumulation is large. What’s more, this method is greatly affected by the dynamic objects in complex environment. In order to solve this problem, we use the scan to submap method, which can not only meet the real-time requirements, but also effectively remove the influence of dynamic objects because we maintain the local submap in real time. In addition, we use scan to submap to reduce the error, and use the back-end optimization loop closure to correct the error, so as to solve the problem of long-term running robot drift error in the factory environment. Scan and submap are transmitted serially and saved by Protobuf [3]. We maintain two submaps in real time at any time. As shown in the Fig. 2, the laser scan (as shown in the red line) of each frame will update the two submaps. When the number of scans in a submap reaches the threshold, such as 100 frames, a new submap, old, will be created_ Submap is updated to global for loop detection. Submap is also represented as occupancy grid. In addition, we will maintain a submap-list in real time. When the initial num is less than 2, we will insert it directly without any operation. According to this method, we build 2D maps in virtual environment and real environment respectively, as shown in Fig. 3.

Fig. 2. The relationship between a laser of per frame and a series of submaps

When we built a complete environment map, we will save not only 2D maps, but also a series of sub maps. These submaps, which are composed of a series of laser scans, will be used in our real-time localization process. In the real-time localization process, when our robot with lidar moves in the test environment, the laser scan of the robot will match with the sub-map of our prior map to determine the current position of the robot.

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(a)

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(b)

Fig. 3. The two-dimensional map we built in Simulation environment and real environment. (a) Simulation environment map (b) Real environment map

5 Experimental Results We implement the proposed algorithms in C+ + and test them in two different scenarios. The first is a simulation environment, using the gazebo simulation program to establish the simulation environment map. Then we play off-line laser data packets to simulate the real-time movement of the robot and verify the localization effect of our algorithm. Secondly, in the real indoor environment, our indoor data set shows higher complexity, that is, the driving trajectory related to clutter and higher change, in addition, there are constantly dynamic pedestrians, in order to verify the robustness of our algorithm for complex environment. 5.1 Simulation Platform In order to verify the effectiveness of our algorithm, we first carry out the experimental test in the simulation environment. In the gazebo simulation environment, we add a turtlebot robot and a virtual space environment for 2D space mapping. As shown in the Fig. 4(a) below. First, we build a 2D plan of the virtual space, and then we play the recorded test rosbag package to simulate real-time lidar positioning. In the process of real-time positioning,

(a)

(b)

Fig. 4. (a) The localization trajectory in simulation environment. (b) The truth (blue points) and location trajectory (orange points) in the same environment map.

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we use our algorithm to record the positioning track in real time until the whole rosbag package is played, and finally generate the whole positioning track. By comparing the localization trajectory with truth in the same map, as shown in Fig. 4(b), we see that our proposed scan to submap localization algorithm has high positioning accuracy in the simulation environment. The localization accuracy is 2.268 cm and the total length of the track we tested was about 25 m. 5.2 Real Mobile Robot Platform Although the simulation environment has a good positioning accuracy, it does not represent the real environment which is more complex, and there will be pedestrians and other dynamic objects-, which will put forward higher requirements for mapping and positioning, so we carry out experiments in the real environment to verify the effectiveness of our algorithm. Our experiment platform is a turtlebot2, as shown in Fig. 5. The robot is driven differentially and has two auxiliary caster wheels. It is equipped with a Velodyne laser scanner (100 m range and 270° field of view), a rplidar A3 lidar scanner (15 m range and 360° field of view), and a computer with an Intel i7 processor and 16 GB RAM running ROS. With two lidars, we can verify that our algorithm can still have good robustness on low-cost equipment in complex environment.

Fig. 5. The turtlebot2-robot platform used for experiments

Firstly, we use high-precision Velodyne lidar to build indoor 2D plane map. Then, in the process of localization, we place the centers of Velodyne and Rplidar-A3 coincidentally, and use our algorithm for real-time localization test. We set the high-precision Velodyne trajectory data as true knowledge, and use low-cost rplidar A3 for positioning test. The localization process is shown in Fig. 6, the green curve represents the trajectory

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in the real-time localization process. We show three of these moments, and at the end of the trajectory is where our robot with lidar is. Finally, the coordinate points of the two trajectories are extracted, and the time synchronization is also carried out through feature points to calculate the error of the localization trajectory. For example, we use obvious corner points as feature points to align the timestamps of two trajectories synchronously. As shown in Fig. 7, blue points represent the true value, orange points represent the localization track. The localization accuracy is 3.5 cm. In addition, it should be noted that our real environment is the corridor of the teaching building, which is about 1.5 m wide. The total length of the track we tested was about 50 m.

Fig. 6. Three moments in the positioning process, Green curve is a real-time trajectory

Fig. 7. The extracted coordinate point of the localization trajectory (blue) and the true value (orange)

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Average error Trajectory total length

Simulation 2.268 cm

25 m

Real test

50 m

3.508 cm

6 Conclusion In this paper, a scan to submap matching based localization method is proposed, which aims at the real-time localization of low-cost lidar sensors in complex environment. With simulation and real world tests, we show that the method using low-cost lidar sensors can achieve high-precision real-time positioning in complex indoor environment. And the algorithm has high accuracy and low drift, as shown in Table 1, and can effectively reduce the influence of dynamic objects.

References 1. Kohlbrecher, S., Von Stryk, O., Meyer, J., Klingauf, U.: A flexible and scalable SLAM system with full 3d motion estimation. In: 2011 IEEE International Symposium on Safety, Security, and Rescue Robotics. pp. 155–160. IEEE (2011) 2. Grisetti, G., Stachniss, C., Burgard, W., et al.: Improved techniques for grid mapping with rao-blackwellized particle filters. IEEE Trans. Rob. 23(1), 34 (2007) 3. Hess, W., Kohler, D., Rapp, H., Andor, D.: Real-time loop closure in 2d lidar SLAM. In: 2016 IEEE International Conference on Robotics and Automation (ICRA), pp. 1271–1278. IEEE (2016) 4. Sun, Z., Wu, B., Xu, C.Z., et al.: Frontier detection and reachability analysis for efficient 2D graph-slam based active exploration. In: 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE (2017) 5. Zhang, J., Singh, S.: LOAM: LiDAR odometry and mapping in real-time. In: Proceedings of the Robotics: Science and Systems (RSS), vol. 2, p. 9 (2014) 6. Filipenko, M., Afanasyev, I.: Comparison of various SLAM systems for mobile robot in an indoor environment. In: 2018 International Conference on Intelligent Systems (IS), pp. 400– 407. IEEE (2018) 7. Yagfarov, R., Ivanou, M., Afanasyev, I.: Map comparison of lidarbased 2d SLAM algorithms using precise ground truth. In: 2018 15th International Conference on Control, Automation, Robotics and Vision (ICARCV), pp. 1979–1983. IEEE (2018) 8. Levinson, J., Montemerlo, M., Thrun, S.: Map-based precision vehicle localization in urban environments. In: Proceedings of the Robotics: Science and Systems (RSS), vol. 4, p. 1 (2007) 9. Wolcott, R.W., Eustice, R.M.: Fast LiDAR localization using multiresolution gaussian mixture maps. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pp. 2814–2821 (2015) 10. Wolcott, R.W., Eustice, R.M.: Robust LiDAR localization using multiresolution gaussian mixture maps for autonomous driving. Int. J. Robot. Res. (IJRR) 36(3), 292–319 (2017) 11. Wan, G., Yang, X., Cai, R., Li, H., Zhou, Y., Wang, H., Song, S.: Robust and precise vehicle localization based on multi-sensor fusion in diverse city scenes. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pp. 4670– 4677 (2018)

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12. Park, C., Kim, S., Moghadam, P., Fookes, C., Sridharan, S.: Probabilistic surfel fusion for dense LiDAR mapping. In: Proceedings of the IEEE International Conference on Computer Vision (ICCV), pp. 2418–2426 (2017) 13. Droeschel, D., Behnke, S.: Efficient continuous-time SLAM for 3D LiDAR-based online mapping. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pp. 1–9 (2018) 14. Liu, H., Ye, Q., Wang, H., Chen, L., Yang, J.: A precise and robust segmentation-based LiDAR localization system for automated urban driving. Remote Sens. 11(11), 1348 (2019) 15. Li, Q., Chen, S., Wang, C., Li, X., Wen, C., Cheng, M., Li, J.: LONet: deep real-time LiDAR odometry. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 8473–8482 (2019) 16. Hao, J.: SLAM and navigation robot design based on cartographer algorithm. Shandong University (2019)

Research on Strategy of Access Node Selection for Space-Based Relay Network Based on Navigation Satellites Lingchuan Zeng1,2,3 , Weiyi Chen4 , Bingcheng Liu3 , Yan Bai1 , Xiaochun Lu1 , and Guang Yang3(B) 1 Nation Time Service Center, Chinese Academy of Sciences, Xi’an 710600, China 2 University of Chinese Academy of Sciences, Beijing 100049, China 3 Aerospace Information Research Institute, Chinese Academy of Science,

Beijing 100094, China [email protected] 4 Electronic Science Research Institute of China, Beijing 100086, China

Abstract. At present, all next generation GNSS navigation satellites have plan to equip with laser inter satellite links for high-precision ranging and high-speed data transmission. Compared with other space systems, navigation satellites have the advantages of excellent coverage performance and high-precision space-time reference. Combined with the abundant communication bandwidth of laser inter satellite links, they naturally have the potential to become the backbone network of space-based communication relay. According to the configuration characteristics of Beidou navigation satellite constellation, this paper proposes a scheme of access node selection for space-based relay network based on Beidou navigation satellite. Firstly, the delay of navigation satellite constellation network is analyzed theoretically, then two access node selection schemes are given, and the performance of the proposed scheme, such as access node coverage and queuing delay of the whole network, is simulated and analyzed, which provides a reference for the future design of space-based relay network based on navigation satellite. Keywords: Space-based relay network · Navigation satellite · Laser inter satellite link · Queuing delay

1 Introduction With the rapid development of various types of space information systems, the spacebased backbone information network is strongly needed as hub of large capacity telemetry, scientific research and other data transmission, so that all kinds of data distributed in the vast space can be timely and reliably transmitted back to the ground gateway station [1, 2]. The implementation of the space backbone communication network should rely on a certain kind of space information system, such as communication satellites, navigation satellites, etc. Compared to the backbone communication network deployed on the ground, the space backbone communication network has the following advantages: © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 424–434, 2021. https://doi.org/10.1007/978-981-16-3142-9_40

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First, the navigation satellites or TDRSS satellites has basically cover global region [3]. Second, some satellites, such as navigation satellites, naturally have time-frequency resources with high-precision and high-stability, which will generate high-precision ephemeris and clock error autonomously to maintain the network space-time reference by achieving high-precision ranging through crosslinks [4]. Third, many satellites has equipped with laser crosslinks whose transmission rate will reaches Gbps level, providing additional communication bandwidth that would satisfy the capacity of space backbone network, and it will gradually catch up with the transmission rate of ground communication network in the future [5]. At present, many research teams have carried out the research of space-based network protocol based on navigation satellite constellation, and also have the preliminary idea of using navigation satellite constellation for data relay. However, there is no publicly reported the design scheme of access node for space-based relay network based on navigation satellite constellation. In this paper, the space-based backbone network based on the hybrid constellation of Beidou navigation satellite is taken as an example. Firstly, the queuing delay of network is analyzed theoretically, then two access node selection schemes are given, and the performance of the proposed scheme, such as the access node coverage and the queuing delay of whole network, is simulated and analyzed, which can provide a reference for the future design of space-based relay network based on navigation satellite constellation.

2 Queuing Delay Analysis of Navigation Satellite Network In order to be compatible with other space information systems and ground networks as far as possible and comprehensively consider the robustness and reliability of network transmission, the space information backbone network based on navigation satellite constellation should adopt to the packet switching system with IP over CCSDS architecture as well as realize the end-to-end transmission of IP packets based on “store and forward” [6]. Since time-delay of packet transporting through network will directly affect the design of network routing, flow control and other algorithms or protocols, it is necessary to focus on the mechanism and characteristics of network delay. The delay of packet transport network with navigation satellite as node can be classified into processing delay, queuing delay and propagation delay. Processing delay mainly includes frame splitting, framing, CRC calculation, routing information calculation, etc. Queuing delay refers to the delay between the packet entering the transmission queue and sending out, and propagation delay mainly refers to the link delay when the sending node sends the packet along the transmission link until the receiving node receives it. The processing and propagation delay can be determined by calculation, while the queuing delay can not be regarded as a determined variable due to the randomness of packet arrivaling, and it’s closely related to the design of node buffer capacity. This section analyzes the queuing delay of space-based relay network based on navigation satellite, and probability theory and queuing theory are used to analyze the queuing delay and throughput of network.

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2.1 Access Node Selection Scheme In order to cover the earth’s surface, the navigation satellite constellation is usually designed as a Walker Constellation composed of MEO satellites with an orbital altitude of about 20000 km. In addition, Beidou also includes high orbit satellites such as IGSO and GEO satellites. Due to the uniform distribution and excellent surface coverage of MEO satellites, this paper considers the selection of access satellite nodes in the network. Considering the symmetry of Walker Constellation configuration, the access node chooses two schemes as shown in Fig. 1. The first strategy is configuring all the MEO satellites as the access nodes of the network (denoted as scheme A). In this scheme, for any end-to-end path, each intermediate node has two input traffic flows, one is the composite traffic flow from all the upstream nodes (denoted as upstream traffic), and the other is the external input traffic received by the node (denoted as external traffic). The second strategy is to select partial MEO satellites as the access nodes (denoted as scheme B). In this scheme, for any end-to-end path, when the intermediate node does not belong to the access node set, it only contains upstream services; when the intermediate node belongs to another access node, it has both upstream services and external services. External services

Scheme A

External services

Scheme B

Upstream services

Upstream services

Node 1 External services

Output services

Node n

Node 2

Output services

Upstream services

Upstream services Node 1

External services

Node 2

Node n

Fig. 1. Two scheme of configuring network access nodes

2.2 Theoretical Analysis of Network Queuing Delay This section deduces the mathematical relationship between the traffic intensity to be processed and the input traffic of each node in scheme A shown in Fig. 1. It is assumed that the input service is a Poisson process with strength set as λ for each access node, the service time of each node is independent of each other and obeys the general distribution. The average service rate is μ, and the buffer capacity used for packet queuing is large enough. Considering the generality, the service time does not obey the exponential distribution, this paper does not use the birth and death process theory instead of the embedded Markov chain [7]. In scheme A of Fig. 1, Nk is set to the number of packets staying in a MEO satellite node at time k + , Ak is the number of packets sent to the node by the external at time k + , and obey the Poisson distribution with the parameter λ; Bk is the number of packets sent to the node by the upstream node at time k + , which is subject to the general distribution. If they are independent of each other, then we have formula as below:

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 Nk+1 =

Nk − 1 + Ak+1 + Bk+1 Nk ≥ 1 Nk = 0 Ak+1 + Bk+1

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(1)

The sequence of random variables {Nk , k = 1, 2, ...} is called the embedding chain of random process. It can be proved that the embedding chain has Markov property:  Nk − 1 Nk ≥ 1 Xk = 0 Nk = 0 Then formula (1) becomes Nk+1 = Xk + Ak+1 + Bk+1 =Xk + Yk+1

(2)

Due to the Xk and Yk+1 are independent of each other, then Nk+1 can be regarded as the sum of two independent random variables, By using the theory of probability generating function, we can get the following expression: GN (z) = GX (z) · GY (z)

(3)

GN (z), GX (z) and GY (z) are the generating functions of N , X and Y respectively, and we have expression as below: GX (z) = P(N = 0) + P(N = 1) + P(N = 2)z + P(N = 3)z 2 + ...  1 = p(0) + GN (z) − p(0) z

(4)

where p(0) = P(N = 0). According to the properties of probability generating function, there is a relation listed below: 1 = GN (z)|z=1 = p(0)(z − 1)GY (z)/[z − GY (z)]|z→1    p(0) GY (z) + (z − 1)GY (z) p(0) = = lim   z→1 1 − GY (z) 1 − GY (z)

(5)



According to Eq. (5), we get p(0) = 1 − GY (1) = 1 − E[Y ]. The random variable Y is the number of packets that arrive at the node within the service time of a packet. The service time is represented by C, which obeys the general distribution, then we get: P(Y = n|C = t) =

n 

P(A = m, B = n − m|C = t)

m=0

⎤ ⎡∞

n m  (λt) ⎣ e−λt fB (n − m, t)⎦fC (t)dt = m! m=0

0

(6)

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Then the GY (z) can be calculated as follows: n ∞   (λt)m ∞

GY (z) =

n=0 0 m=0

∞   ∞

=

0

∞

=

m=0

m!

(λt)m −λt m e z m!



 e−λt fB (n − m, t) fC (t)z n dt

∞ 

 fB (k, t)z

k

dFC (t)

(7)

k=0

e−λt GB (z, t)dFC (t)

0

Then we can get the following results: ⎤ ⎡∞

d⎣  GY (1) = lim e−λt(1−z) GB (z, t)dFC (t)⎦ z→1 dz 0 ⎤ ⎡

∞ ⎢ λt e−λt(1−z) GB (z, t)dFC (t)+ ⎥ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 0 = lim ⎢ ∞ ⎥ ⎥ z→1⎢

⎥ ⎢ ∂G (z, t) ⎣ e−λt(1−z) B |z=1 dFC (t)⎦ ∂z

(8)

0

∞ =λ

∞ tGB (1, t)dFC (t) +

0

0

∂GB (z, t) |z=1 dFC (t) ∂z

Where the GB (1, t) satisfy the following equations: GB (1, t) =

∞ 

PB (n, t)z |z=1 = n

n=0

∞ 

PB (n, t) = 1

(9)

n=0 ∞

 ∂GB (z, t) |z=1 = nPB (n, t) = EB (t) ∂z

(10)

n=0

Therefore, Eq. (8) can be transformed into: 

∞

GY (1) = λ

∞ tdFC (t) +

0

∞ EB (t)dFC (t) = λE(C) +

0

EB (t)dFC (t) = ρ

(11)

0

In Eq. (11), ρ is the traffic intensity, which indicates the number of packets arriving at the node within the average service time of a packet. In order to maintain the stability of the network, it needs to meet the conditions that ρ < 1. Its physical meaning is that the average processing rate of data packets by the node is greater than the arriving traffic rate, and the packets waiting for queuing will not accumulate to infinity.

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For the two schemes shown in Fig. 1, if the upstream services of a node contain a large number of branches and are independent of each other, then the Kleinrock approximation [8] can be adopted. Therefore the upstream services are set as Poisson flows in strength. In this situation the Eq. (11) can be expressed as follows: 

GY (1) = λE(C) + λ0 E(C) = (λ + λ0 )E(C) = (λ + λ0 )/μ = ρ

(12)

For scheme A, since each intermediate node contains upstream services and external services, then the more downstream the node is, the stronger the Poisson flow intensity of upstream services will be gradually accumulated and increased due to the intermediate node. When the cumulative strength of upstream traffic reaches the condition, the network will be uns Table (the average packet rate of arrival is greater than the service rate). Therefore, in scheme A in order to ensure the stability of the network, it is necessary to reduce the intensity of the input external Poisson flow of the first node in the path, and the conditions λ  μ should be need. Compared with scheme A, scheme B has less access nodes, so it can receive higher strength input Poisson flow traffic and has higher network throughput theoretically.

3 Simulation Analysis In this section, two access node selection strategies are selected for queuing delay and coverage simulation analysis based on scheme B in Fig. 1 with Beidou navigation satellite whose MEO satellites are composed of Walker Constellation. 3.1 Simulation Parameters and Scene Design In this section, the constellation parameters of Beidou navigation satellite and the topology design algorithm of laser inter satellite link network are referred to [9], and STK 11 is used for the simulation of Beidou constellation. The main parameters of Beidou navigation satellite constellation are: MEO satellites are configurated as Walker 24/3/1, with an orbit altitude of 21528 km and an orbit inclination of 55°. The IGSO satellite has an orbit altitude of 35786 km and an orbit inclination of 55°. The trajectories of the lower points of the three satellites coincide, and the longitude of the intersection is 118° east longitude. The satellites are evenly distributed in three orbit planes, and the right ascension longitude difference is 120°. Each satellite is equipped with four optical inter-satellite link terminals. The orbit operation time is set as 24 h. To facilitate the configuration of network access nodes, we numbers the satellites of IGSO and MEO satellites, as shown in Fig. 2: IGSO satellites are set as output nodes of the network to receives the data from MEO satellite through the laser inter satellite link and then transmits it to the ground through the high-speed radio link, numbered 1– 3; MEO satellites are the network access node and intermediate node. For the first orbit, the number of MEO satellites on the pavement is 4–11, and the number of MEO satellites on the second orbital plane and third orbital plane is 12–19 and 20–27. We divide the scene design of network access nodes into two situations: the first is that two satellites with symmetrical positions are selected as access nodes for each

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13

21

3 19

1

6

5 26

4

14

7 8

Earth

22 11

9

10 18

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17

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Fig. 2. Schematic diagram of satellite number

orbital surface of MEO layer. Since there are 8 MEO satellites on each orbital surface, it is subdivided into four cases. The second is that four satellites with staggered positions are selected as access nodes for each orbital surface of MEO layer, which can be subdivided into two cases. See Table 1 for the specific access node combination of the above six situations. Table 1. Combination of different access nodes sets Access node combination serial number

Satellite number of MEO first orbital plane

Satellite number of MEO first orbital plane

Satellite number of MEO first orbital plane

1

4,8

12,16

20,24

2

5,9

13,17

21,25

3

6,10

14,18

22,26

4

7,11

15,19

23,27

5

4,6,8,10

12,14,16,18

20,22,24,26

6

5,7,9,11

13,15,17,19

21,23,25,27

3.2 Simulation of Network Queuing Delay Firstly, we use Matlab R2019a to calculate the average network delay of different access node combinations listed in Table 1 in each epoch of satellite operation time. Considering that the shortest path algorithm is usually used for the routing of traffic flow, so the Dijkstra algorithm is used to get the shortest path from each access node to each output node, and then the traffic flow is generated according to Poisson distribution and input to each input node. It is assumed that the input traffic flow to each output node is equal probability, and each node sends the traffic flow to its downstream node. The simulation time is 24 h.

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The simulation results of average queuing delay under the condition of input service Poisson flow intensity λ = 0.6 and service rate μ = 9.6 of each access node in the case of access node combination 1–6 in Table 1 are shown in left of Fig. 3. It can be seen that the distribution of queuing delay for the whole network corresponding to combination 1–4 are similar with each other in the movement time of 24 h, and the average values of queuing delay are basically close to 0, and the maximum values are 0.3605 s, 0.3802 s, 0.5309 s and 0.6593 s respectively.

Fig. 3. Simulation results of network queuing delay for access node combination 1 to 4 (left) and 5 to 6 (right) at λ = 0.6 and μ = 9.6

Similarly, the simulation results of average queuing delay of access node combinations 5–6 in Table 1 are shown in fight of Fig. 3. It can be seen that the average queuing delay of the whole network corresponding to combination 5 and 6 is 0.0311s and 0.0335s respectively, and the maximum is 3.2519 s and 4.2296 s respectively. So it can be seen that the average queuing delay performance of access node combination 1–4 is better than that of access node combination 5–6, due to the number of access nodes in each track plane of MEO layer of combination 5–6 is twice as many as that of combination 1–4, according to the analysis in Sect. 2.2, the queuing delay will be longer. Next, the simulation is carried out under the condition of service rate λ = 0.6 and service rate μ = 3.6. For the case of access node combination 1–4, it can be seen from Fig. 4 that, compared with Fig. 2, the proportion of input traffic strength to the data processing rate of network nodes increases nearly 2.7 times, so the network queuing delay increases significantly, with the average value of 1.6252 s, 2.0183 s, 2.1766 s and 3.0612 s respectively, and the maximum value increases to 14.5975 s, 19.2593 s, 15.6914 s and 24.4617 s. For the combination 5 and 6, the network queuing delay shows an obvious divergence trend, which indicates that the network has been congested and in fact is no longer available. In conclusion, the simulation analysis shows that under the same input traffic Poisson flow intensity and service rate, the less access nodes in the satellite network, the lower the network queuing delay, which is consistent with the analysis results in the second section of this paper.

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Fig. 4. Simulation results of network queuing delay for access node combination 1 to 4 (left) and 5 to 6 (right) at λ = 0.6 and μ = 3.6

3.3 Access Node Coverage Simulation Access node coverage simulation in this section is analyzed by creating a coverage definition object in the above scenario with STK 11, and node coverage under the combination of each access node in Table 1 is given. From the constellation configuration of Beidou navigation satellite in Fig. 2, it can be seen that the more the number of access nodes, the better the coverage of the surface and near earth space. In the simulation, the antenna beam of each satellite relay communication receiver is assumed to be a cone beam with a width of 30° and the antenna beam is axially pointing to the earth center, covering a global area of 15000 km away from the earth center. Since the access node combinations 1–6 in Table 1 are symmetrical in the Walker Constellation configuration, then we just chose combination 1 and combination 5 for coverage simulation in this section, and the results are shown in Fig. 5 and 6 respectively.

Fig. 5. Simulation results of coverage of access node combinations 1

As shown in Figs. 5 and 6, within 24 h, the global regional coverage of access node combination 1 with 15000 km away from the center of the earth varies from 85.5 to 96%, and the global regional coverage of access node combination 5 with 15000 km from the center of the ground changes from 94.5 to 99.8%. It is shown that the combination 5 can have a larger access range of relay signal than combination 1 at a height of 15000 km from the center of the ground. Through further simulation analysis,

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Fig. 6. Simulation results of coverage of access node combinations 5

it can be seen that the global coverage of the combination 1 about 10000 km from the center of the earth can reach 99%, while the combination 5 can reach 100%. It can be seen that both combinations 1 and 5 can basically meet the data relay requirements of low orbit spacecraft with a distance of 10000 km from the earth center and the surface of the world.

4 Conclusion Most of the navigation satellites belong to the medium orbit satellites. Compared with the low orbit satellites, the frequency of inter-satellite link switching is less. Besides, the global coverage ability of the medium orbit satellites is stronger than that of the high orbit satellites. Coupled with the advantages of inter-satellite ranging, time-frequency and other resources, navigation satellite constellation has become an ideal space-based backbone information network carrier. Compared with other existing high orbit and low orbit relay communication satellite systems, due to the complex changes of navigation satellite constellation configuration and topology, it is necessary to focus on the analysis of network delay to design the schemes of backbone network. Our results of research show that only two satellites with symmetrical orbit position selected as relay communication access nodes for each MEO orbital plane of navigation satellite can basically meet the data relay requirements of LEO spacecraft with a distance of less than 10000 km from the earth’s center.

References 1. Xiaoyue, L.: Research on High Performance Routing in Space Information Networks. Xidian University, Beijing (2012) 2. Hu Jianping, X., Huizhong, L.T., et al.: Networked and integrated space-ground information system. J. Spacecraft TT C Technol. 35(4), 241–252 (2016) 3. Shanghong, Z., Yongjun, L., jili, W.: Technologies of Satellite Optical Networking. Science Press, Beijing, pp. 13–17 (2010) (China) 4. Jun, Z.: Research on Orbit determination and Time Synchornizing of Navigation Satellite Based on Crosslinks. Changsha: National University of Defense Technology (2011) 5. Longlong, L., Zuohu, L.: Study of the development of the inter-satellite links in foreign GNSS. J. Geomatics Sci. Technol. 33(2), P133–138 (2016) (China)

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6. Xiaobo, W., Jiaqi, S.: Analysis of application of IP over CCSDS in space networking. J. Spacecraft TT C Technol. 30(9), P37–40 (2011) (China) 7. Zengji, L., Minquan, B., Zhiliang, Q.: Switching Principle and Technology. Posts & Telecom Press, Beijing, pp. 149–155 (2007) (China). 8. Jiandong, L., Min, S., Zhongyan, L.: Communication Network Foundation. Higher Education Press, Beijing, pp. 89–125 (2011) (China) 9. Mingji, D., Baojun, L., Yingchun, L., et al.: Topology dynamic optimization for inter-satellite laser links of navigation satellite based on multi-objective simulated annealing method. Chin. J. Laser 045(007), 211–222 (2018) (China)

Research on Error Online Calibration Method of Inertial/Stellar Refraction Integrated Navigation System Qiaochu Lv(B) , Xueying An, Dingjie Wang, and Jie Wu College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, China

Abstract. Inertial/stellar refraction integrated navigation system can use the observation information of the refraction star sensor to correct the output of the inertial navigation system (INS), thereby effectively improving the positioning performance of the integrated navigation system. However, in practical applications, the errors of navigation system such as inertial navigation misalignment angle and star sensor installation error will affect the overall performance of the integrated navigation system to some extent, so it needs to be calibrated online. Since the carrier cannot achieve continuous observation of the refracted starlight, the system observability is weak. Therefore, a new online error calibration strategy is proposed, which is to construct observations by using the position information of the INS and the attitude and star spots information of the star sensor, and establish the relationship equations between the observations, the misalignment angle of the inertial navigation and installation error of star sensor. After linearization and decoupling, the inertial navigation misalignment angle and star sensor installation error are estimated by the least square method. Monte Carlo target practice simulation results show that, compared with the traditional filtering estimation method, the system error online calibration method proposed in this paper can more effectively estimate the inertial navigation misalignment angle and star sensor installation error, and improve the positioning and speed accuracy of the inertial/stellar refraction integrated navigation system. Keywords: Star sensor installation error · Inertial navigation misalignment angle · Error calibration · Integrated navigation

1 Introduction Inertial/starlight refraction integrated navigation is a compound guidance method supplemented by starlight correction on the basic of INS. However, the traditional inertial/starlight combination is mostly used for attitude determination. Since the error of position and speed is not very observable, so its correction effect is not ideal [1]. Recently the development of star sensor refracted star measurement technology has created conditions for the realization of indirect auxiliary positioning based on starlight refraction [2]. For near-Earth spacecraft celestial navigation, the earth is the most important celestial © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 435–444, 2021. https://doi.org/10.1007/978-981-16-3142-9_41

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body for observation. Using a high-precision star sensor to obtain the horizon indirectly by observing the refraction of starlight in the atmosphere is an important means to improve the accuracy of navigation [3]. The star sensor has a measurement accuracy of arc-second level [4]. However, the installation error of the star sensor can reach angular level, and the measurement error caused by it is much higher than the measurement error of the star sensor itself, which seriously affects the measurement information [5]. Qian H. et al. used Kalman filtering to estimate the state quantity error, but did not consider the star-sensitive installation angle error [6]. Yang et al. analysed the rank of the observation matrix, and concluded that the number of observed navigation stars and the number of attitude adjustments should be greater than 2 so that the error state quantity is observable [7]. Deng H. et al. deduced the mutual conversion matrix between the attitude error angle and the mathematical platform misalignment angle [8]. Wang R. et al. proposed a rapid calibration model and method of installation error based on the measurement information of the star sensor [9]. However, most of the above methods are only for star sensor installation errors or use traditional filtering algorithms, which is difficult to accurately estimate the system error of all navigation equipment. Because it is difficult for the star sensor to continuously observe the refracted starlight, and the observability of the integrated navigation system is weak. Therefore, a new online error calibration method is proposed, which uses the indexing information by the INS and the attitude and image point information by the star sensor to establish the equations between the observation and the INS platform misalignment angle and the star sensor installation error. The misalignment angle and the installation error are estimated by the least square method. Finally, the effectiveness of the method is verified by numerical simulation experiments.

2 Error Modeling of Inertial/Starlight Refraction Integrated Navigation System In order to facilitate the description of the initial platform misalignment angle and the star sensor installation error in this article, and to establish the relationship between them and the INS transposition information and the star sensor observation information, the coordinate system involved in the article is first defined. 2.1 Reference Coordinate System 1. Launch Inertial Coordinate System (Oi Xi Yi Zi ): The origin is located at the theoretical launch point, the Xi axis points to the target point in the launch point horizontal plane, and the Yi axis is perpendicular to the launch point horizontal plane, opposite to the local gravity direction. The Zi axis and the Xi axis and the Yi axis form a right-handed coordinate system. 2. Aircraft Body Coordinate System (Ob Xb Yb Zb ): The coordinate system is used to determine the attitude of the INS platform relative to the inertial system. The origin Ob is in the center of the aircraft, and the Xb axis points to the head along the longitudinal axis of the aircraft. The Yb axis is perpendicular to the Xb axis in the

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longitudinal symmetry plane of the aircraft and points up. The Zb axis, Xb axis and Yb axis form a right-handed rectangular coordinate system. 3. Ideal Star Sensor Body Coordinate System (OS XS YS ZS ): Regardless of installation error, the body coordinate system where the star sensor is located is fixedly connected to the star sensor. The origin OS is the center of the imaging plane of the star sensor. The ZS axis is consistent with the main optical axis of the star sensor and points to the observed star. The XS axis and the YS axis are perpendicular to each other and parallel to the imaging plane. 2.2 System Error Model 2.2.1 Initial Alignment Error The mathematical platform coordinate system of the ideal strapdown INS is parallel to the launching inertial coordinate system. Assuming that the attitude angle of the  T − → mathematical platform after initial alignment is A = α β γ , where α, β, and γ are the pitch angle, yaw angle and roll angle of the mathematical platform relative to  T the inertial coordinate system. Correspondingly, take δα δβ δγ as its initial attitude platform misalignment angle. 2.2.2 Star Sensor Installation Error The installation error of the star sensor is represented by the angle between the main optical axis S of the star sensor and the ZS axis of the ideal star sensor body coordinate system. As shown in the Fig. 1, ξA , ηA , ξB , and ηB are the star sensors A, B installation error angle between their main optical axis and ZS axis.

Fig. 1. Star sensor installation error angle

2.2.3 Accelerometer Error and Gyro Error The following two errors have the same form.

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The accelerometer is used to measure the apparent acceleration of the aircraft. Due to the small influence of the error coupling term, only the zero-order term, the first-order term and random noise are considered, and the error model is [10] ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ δax Ka0x + Ka1x ax εax ⎣ δay ⎦ = ⎣ Ka0y + Ka1y ay ⎦ + ⎣ εay ⎦ (1) δaz Ka0z + Ka1z az εaz where the left side of the formula is the three-axis measurement error of the apparent acceleration, K a0 is the zero-order coefficient, K a1 is the secondary coefficient, a is the three-axis apparent acceleration in the aircraft body coordinate system, and εa is the random noise. The gyro is used to sense the angular velocity of each axis of the aircraft. Similarly the error model is [11] ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ Kω0x + Kω1x ωx εωx δωx ⎣ δωy ⎦ = ⎣ Kω0y + Kω1y ωy ⎦ + ⎣ εωy ⎦ (2) δωz Kω0z + Kω1z ωz εωz where the left side of the formula is the three-axis measurement error of angular velocity, K ω0 is the coefficient of the zero-order term, K ω1 is the coefficient of the secondary term, ω is the three-axis rotation angular velocity of the aircraft in the aircraft body coordinate system, and εω is the random noise.

3 Error Online Calibration Method In this section, online calibration is performed for initial alignment error and star sensor installation error. First introduce the general idea of error calibration, and then introduce the calibration method. From the initial attitude, the INS rotate 90° around the x-axis. Before and after the rotation, the star sensor A performs star observations to obtain the direction vector of its main optical axis in the inertial frame i. Then by the vector, the x-axis direction can be determined. The y-axis direction can also be determined after the INS is rotated around the y-axis and the star sensor B performs observations. After the x and y axes of the INS platform are determined, the initial platform misalignment angle can be obtained. Because the direction vector of the star-sensitive main optical axis in the inertial system i is measurable, the star-sensitive installation error angle can also be obtained. T  − → Suppose the initial attitude of the INS is A tt1 = α1 β1 γ1 , where α1 , β1 , and γ1 are the pitch, yaw, and roll angles of the mathematical platform relative to the inertial coordinate system, and the rotation matrix from the inertial system i to the inertial conductor coordinate system b can be expressed as  R1i A (3) tt1 = Rx (γ1 ) · Ry (β1 ) · Rz (α1 ) where Rx , Ry , and Rz are rotation matrices that rotate the corresponding attitude angles around the x, y, and z axes.

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Suppose the ideal installation attitude angles (321 rotation sequence) of star sensor A and B are respectively. T T   o o o T   = = , AttA = = αA βA γA 90 0 90 αA βA γA A ttA  T o o o −90 −90 0 The relationship between the aircraft body coordinate system and the ideal starsensitive body coordinate system is shown in the figure below (Fig. 2).

Fig. 2. The aircraft body coordinate system and the ideal star sensor body coordinate system

The rotation matrices from the vehicle body coordinate system b to the ideal starsensitive A and B body coordinate systems are respectively   B  RAb A (4) ttA = Rx (γA ) · Ry (βA ) · Rz (αA ), Rb AttB = Rx (γB ) · Ry (βB ) · Rz (αB ) Suppose that when the INS is in the first attitude (attitude angle vector is star sensors A and B measure two stars, and get the image point coordinates  xA,1 , yA,1 , xB,1 , yB,1 . The star-sensor image point coordinates are random num bers obtained by Monte Carlo sampling and obey normal distribution N 0, σS2 , where σS = 0.5 × 10−5 m = 5 μm. The right ascension and declination of the star are known, and the unit vector of the star direction in the inertial coordinate system i can be expressed as ⎧ T   T      T i   ⎪ 1 A ⎪ ⎪ S = R A · R A · Ry (−ηA ) · Rx (−ξA ) · 0 0 0 tt1 ttA ⎨ A1 i b (5) T   T      ⎪ T i   ⎪ 1 B ⎪ ⎩S = R A · R A · R (−η ) · R (−ξ ) · 0 0 0

 ), Att1

B1

i

tt1

b

ttB

y

B

x

B

The corresponding observation equation of the star-sensor image point is       i  ⎧      xA,1 100   ⎪ A 1 ⎪ =f · · Rx (ξA ) · Ry (ηA ) · Rb AttA · Ri Att1 · S A1 + ε A1,2×1 ⎨− yA,1 010       i       ⎪ 100  x  ⎪ ⎩ − B,1 = f · · Rx (ξB ) · Ry (ηB ) · RBb AttB · R1i Att1 · S B1 + ε B1,2×1 yB,1 010 (6)

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  where f = 1 m is the focal length of the star sensor, and εA1,2×1 , εB1,2×1 are the error vector of the star-sensing measurement, andeach error component is independent of each other and obeys a normal distribution N 0, σS2 . From the initial attitude, the INS rotates 90° about the X-axis to the second attitude, and rotates 90° about the Y-axis and to the third attitude. The rotation matrix from inertial coordinate system to inertial conductor coordinate system is   3  o 1  (7) R2i = Rx 90o · R1i A tt1 , Ri = Ry 90 · Ri Att1

Similarly, the observation equation at this time can be obtained. The least square method is used to solve the observation equations of star image points simultaneously, and the initial attitude Angle α1 ,β1 , γ1 and the star sensitive installation errors ξ A , ηA , ξ B , ηB are obtained. Firstly, the linearized observation equations are  T established. Take INS first attitude error Angle δα1 δβ1 δγ1 , which is small. Then ⎤⎞ ⎡ ⎛   0 δα1 −δβ1  ⎥⎟ ⎢ ⎜ R1i A = Rx (γ1 ) · Ry (β1 ) · Rz (α1 ) ≈ Rx (γ10 ) · Ry (β10 ) · Rz (α10 ) · ⎝I3×3 − ⎣ −δα1 0 δγ1 ⎦⎠ tt1 δβ1 −δγ1 0

(8)

= R0 + Rδα · δα1 + Rδβ · δβ1 + Rδγ · δγ1

⎡

⎡ ⎤⎞ ⎛ ⎤⎞ 0 0 0 0 0 −ηA Rx (ξA ) · Ry (ηA ) ≈ ⎝I3×3 + ⎣ 0 0 ξA ⎦⎠ · ⎝I3×3 + ⎣ 0 0 0 ⎦⎠ 0 −ξA 0 ηA 0 0 = I3×3 + Rξ · ξA + Rη · ηA ⎛

(9)

The Rx (ξB ) · Ry (ηB ) is same available. The star image point observation equation set becomes linearized equation set Y12×1 = A12×7 · δX7×1 + E12×1

(10)

where δX7×1 =



δα1 δβ1 δγ1 ξA ηA ξB ηB

T (11)

⎡

⎤ ⎡ ⎤ ⎡ ⎤ Y1 A1 E1 Y = ⎣ Y2 ⎦, A = ⎣ A2 ⎦, E = ⎣ E2 ⎦ Y3 A3 E3  ⎤ ⎡  i xA,1 A·R ·S − F · R − A1 ⎥ 0 b ⎢ yA,1 ⎥ Y1 = ⎢ ⎣  xB,1  i ⎦ B − F · Rb · R0 · S B1 − yB,1

⎡ i A A ⎢ F · Rb · Rδα · S A1 , F · Rb · Rδβ A1 = ⎣ i B B F · R · Rδα · S B1 , F · R · Rδβ b b

i · S A1 , F · RA · Rδγ b i · S B1 , F · RB · Rδγ b

(12)

(13)

⎤ i i i · S A1 , F · Rξ · RA · R0 · S A1 , F · Rη · RA · R0 · S A1 , 02×1 , 02×1 ⎥ b b i i ⎦ i · S B1 , 02×1 , 02×1 , F · Rξ · RB · R0 · S B1 , F · Rη · RB · R0 · S B1 b b

(14)

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Y 2 , Y 3 , A2 and A3 can be calculated in the same way. In Eq. (10), each component in the error vector is independent and identically distributed, so the equal-weight least square method can be used. ⎧  −1 ⎪ ⎨ δX7×1 = AT A AT Y (15)  −1 ⎪ 2 T ⎩ δX ,7×7 = σS A A From Eq. (15), the initial alignment attitude angles α1 ,β1 , γ1 and the estimated values of the star-sensitive installation errors ξ A , ηA , ξ B , ηB can be obtained.

4 Simulation Analysis This chapter performs online error calibration and inertial/starlight refraction integrated navigation simulation. 4.1 Simulation Analysis of Error Online Calibration Analyze the calibrated initial misalignment angle and star sensor installation error. In the simulation, the Monte Carlo simulation sampling method is used to randomly generate the star sensor image point coordinates, 6 sets of image points are generated each time, a total of 1000 samplings. The initial values of the platform misalignment angle and the installation error of the star sensor are 0.1° and 30 arcsec. The results obtained are shown in Fig. 3. The figure and table show the estimated residuals of misalignment angle and installation error. The table shows the corresponding estimator residuals and corresponding standard deviations.

Fig. 3. Estimated residuals of platform misalignment angle and star sensor installation error

It can be seen from Fig. 3 that the method proposed in this article can effectively estimate the platform misalignment angle and the installation error of star sensor. Among them, the maximum residual error of the estimated value of the platform misalignment angle is about 11 arc seconds. The maximum residual error of the estimated value of star sensor installation error is about 5 arc seconds.

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4.2 Simulation Analysis of Strapdown Inertial/Starlight Refraction Integrated Navigation The effectiveness of the algorithm is verified by comparing the numerical simulation results of using the algorithm in this paper to perform online error calibration and then filtering other errors, and directly filtering the error state. The simulation parameters of the integrated navigation orbit are as follows: the geographic latitude and longitude of the launch point B0 = 34.53°, L0 = 112.27°. The geographic latitude longitude of the target point Be = 34.05°, Le = −118.25°. Consider the influence of initial alignment error, accelerometer error, gyroscope drift error, star sensor installation and measurement error. The values of each error are shown in Table 1. Table 1. Simulation system error and value Error

Name

Value

unit

Initial alignment δα1 δβ1 δγ1 error

0.1

(°)

Accelerometer

Zero-order term First-order term Random noise

5e−6 1e−6 5e−6

g dimensionless g

Gyro

Zero-order term First-order term Random noise

1e−3 5e−3 0.001

(°)/h dimensionless (°)/h

Star sensor installation

ξ η

30 30

arcsec

Star sensor measurement

ε

5e−6

m

The positioning accuracy obtained by the simulation experiment is as follows.

Fig. 4. Comparison of positioning accuracy of integrated navigation algorithm

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Fig. 5. Comparison of speed accuracy of integrated navigation algorithm

It can be seen from Fig. 4 and Fig. 5 that the navigation positioning and speed errors have been significantly reduced throughout the simulation process. After using the online calibration method, the positioning error at the end point is reduced from 122.1 m to 100.19 m, and the speed error is reduced from 0.119 m/s to 0.085 m/s, which improves the positioning and speed accuracy of the inertial/starlight refraction integrated navigation.

5 Conclusion Compared with the traditional filtering estimation method, the system error online calibration method proposed in this paper can effectively estimate the inertial navigation misalignment angle and the installation error of the star sensor. Through numerical simulation analysis, it is proved that this method can improve the positioning and speed accuracy of the inertial/starlight refraction integrated navigation system, and has great engineering application value.

References 1. INS/CNS complete integrated navigation algorithm aided by stellar refraction positioning. Transducer and Microsystem Technologies (2017) 2. Wang, X.H., Iqbal, M., Zhou, X.: Design and implementation of a dual-radio wireless mesh network testbed for healthcare. In: Paper presented at the International Conference on Information Technology & Applications in Biomedicine (2008) 3. Fang, J., Ning, X., Liu, J.: Principles and methods of spacecraft celestial navigation, 2nd edn. National Defense Industry Press, Beijing (2017) 4. Schmidt, U.: Astro APS - The next generation Hi-Rel star tracker based on active pixel sensor technology. In: Paper presented at the Aiaa Guidance, Navigation, & Control Conference & Exhibit (2005) 5. Zhang, H., Tian, H., Yuan, J.H., Liu, E.H.: Parameter calibration and error compensation of star sensor. Opto-electron. Eng. 32(9), 1–4 (2005) 6. Qian, H., Sun, L., Huang, W., Cai, J., University, H.E.: SINS/RCNS integrated navigation algorithm. J. Harbin Inst. Technol. 45(9), 52–56 (2013)

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7. Yang, Y., Zhang, C., Lu, J.: Local observability analysis of star sensor installation errors in a SINS/CNS integration system for near-earth flight vehicles. Sensors 17(1), 167–179 (2017) 8. Deng, H., Liu, G.B., Chen, H.M., Liu, Z.G.: Deduction and simulation of angular error relationship in ‘“SINS/CNS”’ integrated navigation system. J. Astronaut. 32(4), 781–786 (2011) 9. Wang, R., Xiong, Z., Liu, J., Zhong, L., Center, N.: Study on installation error calibration model simulation of star sensor. Syst. Simul. Technol. 9(4), 287–291, 298 (2013) 10. Zhang, C.: Study on the Hybrid Celestial-Inertial Guidance Method of Ballistic Missile. National University of Defense Technology, Changsha (2016) 11. Zhao, Y., Zhang, H., Tang, G.: Strapdown stellar-inertial composite guidance method for ballistic missile considering star sensor installation error. Acta Aeronautica et Astronautica Sinica 41(08), 114–124 (2020)

Investigation on Centralized Autonomous Orbit Determination Using Inter-satellite Ranging Jingshi Tang1(B) , Haihong Wang2(B) , Jinjun Zheng2 , Lin Liu1 , Qiuli Chen2 , Weisong Jia2 , Xu Zhang2 , and Chengbin Kang2 1 School of Astronomy and Space Science, Nanjing University, Nanjing, China

[email protected] 2 Institute of Telecommunication and Navigation Satellites, CAST, Beijing, China

Abstract. Autonomous operation capability is essential to improve the overall satellite constellation in terms of stability, reliability and timeliness. In this paper, we assume a miniature constellation based on BeiDou satellite navigation system, including Inclined Geosynchronous Orbit (IGSO) satellites and Medium Earth Satellites (MEO). The performance of autonomous orbit determination (AOD) of the constellation is investigated, with inter-satellite ranging. AOD is accomplished with Extended Kalman Filter (EKF). The process noise is considered modeled with a Gauss-Markov process. The filtering process is implemented using purely analytical state transition matrix (STM) and process noise transition matrix. The centralized orbit determination in this paper is based on the concepts of reference satellites and satellite grouping (by visibility). Within each group where member satellites are directly or indirectly linked, AOD is achieved by designating at least one reference satellite whose Right Ascension of Ascending Node (RAAN) is dynamically propagated but not filtered. Although one reference satellite is theoretically enough to sustain AOD, it may still be insufficient, from the practical point of view, to constrain the whole constellation within only one satellite. On the other hand, introducing too many reference satellites with unfiltered RAANs. In this paper, we also investigate AOD performance with one or two reference satellites. Especially how two reference satellites with different initial errors, different orbital altitudes and different geometries affect the AOD performance. Keywords: Inter-satellite ranging · Heterogeneous constellation · Centralized autonomous orbit determination

1 Introduction Many of the Global Navigation Satellite Systems (GNSS) have planned for future upgrade to improve autonomous operational capability. Autonomous orbit determination (AOD) is one of the fundamental aspects in autonomous operation, based on which more complex functions can be implemented. Although requirement on autonomous operation is not new, operational practice has always seen various challenges. To lessen the dependency on ground support, inter-satellite tracking is always preferred as a replacement of ground tracking. However, it can be theoretically proved that orbit determination using © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 445–454, 2021. https://doi.org/10.1007/978-981-16-3142-9_42

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only inter-satellite range and range-rate tracking is unobservable (Liu and Liu 2000) and connection to external terrestrial or celestial reference systems is needed to determine the orbits. Inter-satellite tracking based OD is strictly unobservable in two-body problem, while with the perturbations the constraints in OD is still so weak that the normal matrix is close to rank-deficiency. The weak constraint is in the right ascension (longitude), which causes the overall rotation in the satellite constellation (Liu and Liu 2000). As inter-satellite tracking is getting popular in major GNSS, we now focus on a more practical question. Acknowledging that using only inter-satellite tracking without external reference is incapable to sustain full AOD for the overall constellation, how much can we exploit the inter-satellite tracking to correct the orbits and contain the errors by introducing an artificial reference direction. The paper is organized as follows. In Sect. 2, we propose our centralized autonomous orbit determination strategy, explaining how we plan to contain the errors by using only the inter-satellite ranging. In Sect. 3, we introduce the simulation scenarios, including the constellation, OD models and approaches. The OD models and approaches are part of the centralized AOD that makes it practically operable onboard the satellites. Simulation results in various scenarios are demonstrated in Sect. 4, while discussions and conclusions are presented in Sect. 5.

2 Centralized Orbit Determination Centralized orbit determination in this paper is referred to as the practice of orbit determination for all the satellites which are directly or indirectly connected by inter-satellite measurements at the same epoch. All the relevant measurements need to be collected and processed together and hence the name. Since it is unobservable to determine the orbits of the full constellation, at least one of the member satellites need to be selected whose right ascension of ascending node is not estimated. The selected satellites are called reference satellites and we say the right ascensions of ascending nodes are fixed during the autonomous orbit determination, in terms that they are dynamically propagated but not corrected in the filtering process. It is obvious that if the inter-satellite tracking is processed one by one during filtering, for each pair either of the satellites needs to be the reference and excess errors will be inevitably introduced. Besides, all the directly or indirectly connected satellites are indeed correlated, and it makes good sense that their orbits should be determined together. Two additional concepts are needed to further explain the strategy. 2.1 Satellite Grouping Based on the observation geometry and the actual connection status, it is possible that not all the satellites within the constellation are connected. In such cases, the satellites are grouped by inter-satellite connections and the constellation is divided into several groups. Figure 1 illustrates one such scenario, where satellites #1, #2, #3, #6 and #8 are grouped, while satellites #4 and #5 are connected and separately grouped. Satellite #7 is not connected to any other satellites and is therefore not within any group.

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Fig. 1. Visibility and grouping of the satellites in an assumed constellation

2.2 Reference Satellite For the satellites connected by inter-satellite tracking, it is impossible to determine orbits of both satellites using only the inter-satellite ranging. Given the nature of the unobservability, the RAAN of at least one satellite must be artificially fixed and the rest 11 elements of the satellites can be estimated in orbit determination. Therefore, at least one of the satellites within each group must be selected as the reference satellite. The orphan satellite that is not connected to any other satellites has no available measurements and can only be dynamically propagated. Although one reference satellite is theoretically enough, it is possible that the geometrical constraint is not strong enough. On the other hand, introducing too many reference satellites is not the optimal, since excess errors are included when too many RAANs are not corrected. In this work, together with the grouping problem, the reference satellites at each epoch are determined as follows. • At least one primary reference satellite, within the whole constellation, is designated. A primary reference satellite is always a reference satellite, except when it is an orphan. • Other secondary reference satellites are ordered. When there is no primary reference satellite within a group, the satellite ranked top among those in the group is temporarily selected as the reference at this epoch. • When a satellite is an orphan, no matter whether it is a primary reference, its orbit is only propagated but not corrected. 2.3 Processing Procedures Following the concepts and strategies, the onboard filtering process handles intersatellite ranging measurements sequentially. At each epoch, the process is demonstrated in Fig. 2, after all relevant measurements are uploaded to a central hub. At each epoch, the role of each satellite is reset, along with the variables (estimation flag) and the covariance matrix. Extended Kalman filter (Tapley et al. 2004) is applied to sequentially determine the orbits. To adapt the onboard computing capability, the state transition matrix (STM) and the process noise transition matrix (PNTM) are calculated analytically using formulas in Tang et al. (2018).

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Fig. 2. A brief flowchart at each epoch during Centralized Autonomous Orbit Determination

3 Numerical Tests A miniaturized heterogeneous constellation resembling the BeiDou system is applied, including 6 MEO satellites (M01–M06) and 3 IGSO satellites (I01–I03). Inter-satellite ranging is assumed between MEO and IGSO satellites, when the line of sight is not obstructed and its geocentric distance is within 60°. In the best case there would be 3 × 6 = 18 inter-satellite links, but there are always multiple groups or even orphans due to limited visibility. The measurements are simulated every 5 min for 10 days. Random error is added to the measurements, assuming Gaussian noise with a mean of 1 mm and a standard deviation of 1 cm. To simulate the measurements and to filter the orbits, the dynamical model includes the EGM2008 gravity field up to d/o 12 (Pavlis et al. 2012), the lunisolar gravitation (DE405) and the solar radiation pressure. The orbits are integrated using RKF7(8) method with adaptable step size (Fehlberg 1968). Unmodeled and mismodeled perturbations are considered in the simulation. To generate simulated measurement, a periodic perturbing acceleration with an amplitude of 10–8 (normalized unit, about 10–7 m/s2 , see Liu (2000)) and an orbital period (sin f , cos f ) is included, along with a Gaussian random fluctuation with a mean of 10–9 and a standard deviation of 10–9 . In the filtering process, the errors from the dynamic model and the linearization are handled by the process noise. Gauss-Markov process is applied to dynamically model the process noise w, in the following form (Tapley et al. 2004).  d w dt = −βw(t) + u, (1) where β and u are respectively the reciprocal of the correlation time in the firstorder Markov process and the Gaussian noise. The process noise is applied in the RTN directions. Here we set β = 1/100 s−1 , E(u) = 0, σ (u) = 10–8 . Initial orbit errors are assumed as a zero-mean Gaussian noise with a standard deviation of 10–5 . For semi-major axis and angular elements, it is about 64 m and 5.7 × 10–4 degree. It is noteworthy that all matrices of partial derivatives are calculated analytically, including the state-to-state STM and the noise-to-state PNTM. It has been verified that this implementation has a consistent accuracy to numerically integrating variational equations, while reduces the CPU time by no less than 50%. The test results of the filter are shown in Tang et al. (2018) and the details are skipped here in this paper.

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4 Simulation Results It is noteworthy that with the given constellation the number of MEO satellites visible to IGSO satellites ranges from 1 to 6, while the number of IGSO visible to MEO ranges from 0 to 3. 4.1 Testing the Centralized OD Strategy We arbitrarily select M06 as the primary reference satellite. Other satellites are candidates of secondary primary reference satellites, with the following order: I01, I02, I03, M01, M02, M03, M04, M05. We notice that it happens in 10 days that M06 cannot be connected to any other satellites and becomes an orphan. Without the strategy of secondary reference satellites, other satellites will lose connection to the reference and their orbits can only be fixed or estimated anyway at the risk of rank deficiency and filter failure. With the introduction of secondary reference satellites, the groups and roles within the constellation can be adaptively adjusted, as are shown in Fig. 3.

Fig. 3. With M06 as the primary reference satellite, the number of groups (left) and role-persatellite (right) in 10 days

When M06 is orphan, three IGSO satellites are occasionally designated as the reference satellites. With this strategy, the measurement residual, ephemeris errors of MEO and IGSO are shown in Fig. 4.

Fig. 4. For centralized AOD with M06 as primary reference satellite, observation residuals (left), ephemerides error of MEO satellite (middle) and IGSO satellites (right)

Even with model error, the measurement residual can still be reduced to as small as the measurement error. For both MEO and IGSO satellites, the errors of the filtered

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ephemerides are around 20 m–30 m, except at the starting phase where M06 becomes orphan for several times. The whole filtering process is quite stable and shows no drastic change despite the frequent regrouping and role assignment. 4.2 Testing with Different Reference Satellites Selecting single reference satellite (per group) meets the minimum requirement of OD observability, although the geometric constraint may be weak. Without loss of generality, we select one IGSO satellite (I01) and one MEO satellite (M06) respectively. For each satellite, the test is run for 40 times. The filtering error is quantified using the position (ephemeris) error of last 24 h in the 10-day span, as follows.  288 2 j=1 rfilter − rtrue  , (2) δr = 288 where the subscripts filtered and true respectively stand for the filtered ephemerides and the original ephemerides without simulated errors. Summation from 1 to 288 stands for the last 24 h with a 5-min interval. Filtering errors by using I01 or M06 as primary reference satellites are shown in Fig. 5. The uncorrected initial error in RAAN of the primary reference satellite δref is the major contribution to the filtering errors and is taken as the characteristic metric to be plotted against the filtering error.

Fig. 5. Taking I01 (left) and M06 (right) as the primary reference satellite, the overall position accuracy with respect to the initial δref for all 40 runs

For either IGSO or MEO reference satellite, the filtering error is roughly linear with its initial RAAN error, with similar slopes. By zooming into the details, we can still find that even with close initial RAAN error, some tests show diverse filtering errors, suggesting errors in the other elements cannot be fully correction due to correlation and may also contribute to the filtering error. Now we test double primary reference satellites with various combinations, regarding how the selection and their initial RAAN errors affect the filtering error. First, we define the characteristic metric determined by the initial RAAN errors of both reference satellites, which reads as follows.    1 δ2ref ,1 + δ2ref ,2 , (3) δref = 2

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Table 1. Simulations using two primary reference satellites Case #

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Simulations are tested with the combinations shown in Table 1. We first investigate the observation geometry, in terms of the geocentric distance of two primary reference satellites. Cases #1 and #3 are first tested and their filtering results are show in Fig. 6. 45

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Cases #2 and #5 do not show significant difference, whereas Case #4 is slightly better than #5 in terms of error growth. Nevertheless, all three tests show larger error than Cases #1 and #3, which coincides with their respective orbital geometry. In general, the ephemeris errors reflect similar patterns of the orbital geometry of the reference satellites, suggesting that candidate reference satellites, especially primary reference satellites should avoid getting aligned for optimal performance. Previous tests show that a large proportion of the filtering error comes from the initial RAAN error of the reference satellites, while initial orbital error of other non-reference satellites may also contribute. Although fixating RAAN of the reference satellites theoretically guarantees the observability, for a practical multivariable inversion problem, correlations among estimated parameters are inevitable. To highlight the contribution from the initial RAAN error, an additional test with partial errors is carried out. By partial error, we mean that all initial RAANs are error free while other elements have initial Gaussian errors as usual. We introduce this partial error test, together with its full error counterpart, to understand how initial errors in RAAN and other elements affect the filtering performance. We select Cases #1 and #3, together with #6. Figure 6 has shown the full error results of Cases #1 and #3 while for Case #6 the filtering error from the full error test is shown in Fig. 10. Without the initial RAAN error, the filtering errors of the partial error tests of Cases #1, #3 and #6 are plotted in Fig. 11. The results are now plotted by the run numbers. The filtering errors of the partial error tests are significantly reduced, even for #3 and #6 which have less optimal results in full error tests. The filtering error of the partial error tests is generally consistent with the initial element error. The results suggest that (1) since the RAANs of the reference satellites cannot be corrected, initial RAAN errors of other satellites also affect the filtering error;

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(2) even if the initial RAANs are error free, the filtering error are still subject to initial errors of other elements and could not be fully eliminated.

5 Discussion and Conclusion In this paper, we propose a centralized autonomous orbit determination strategy that processes all inter-satellite measurements at the same epoch together. This strategy is tested from various aspects, using a small heterogeneous constellation. Tests show that the proposed centralized AOD strategy can achieve sustainable convergence with measurement residual contained in the order of magnitude of the measurement error. Even the visibility varies in a highly dynamic range, the filter still converges stably and reliably. Further tests also show that the filtering error is largely affected by the initial RAAN errors of the reference satellites. This suggests careful determination of reference satellites in practical scenarios. The orbital geometry of the primary reference satellite should guarantee optimal coverage of the constellation and thus optimal geometric constraint in orbit determination. Ill-selected reference satellites cannot sufficiently constrain the AOD process or even affect negatively. Acknowledgement. This work is supported by the National Natural Science Foundation of China (Grant No. 11873031) and the Fundamental Research Funds for the Central Universities (020114380037).

References Liu, L., Liu, Y.: On the rank deficiency in autonomous orbit determination using satellite-tosatellite relative measurement. J. Telemetry Tracking Control 19, 13–16 (2000). (in Chinese)

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Tapley, B.D., Schutz, B.E., Born, G.H.: Statistical Orbit Determination. Elsevier Academic Press, London (2004) Tang, J., et al.: A time-efficient implementation of Extended Kalman Filter for sequential orbit determination and a case study for onboard application. Adv. Space Res. 62, 343–358 (2018) Pavlis, N.K., Holmes, S.A., Kenyon, S.C., Factor, J.K.: The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). J. Geophys. Res. 117, B04406 (2012) Fehlberg, E.: Classical Fifth-, Sixth-, Seventh-, and Eighth-order Runga-Kutta Formulas with Stepsize Control, NASA Technical report TR R-287 (1968) Liu, L.: Orbit Theory of Spacecraft. National Defence Industry Press, Beijing (2000). (in Chinese)

Research on Invariant Extended Kalman Filter Based 5G/SINS Integrated Navigation Simulation Yarong Luo(B) , Mengyuan Wang, Chi Guo, and Wenfei Guo GNSS Research Center, Wuhan University, Wuhan, China [email protected]

Abstract. The construction and improvement of 5G can empower navigation and positioning. 5G/SINS integrated navigation can broaden application scenarios of the traditional GNSS/SINS integrated navigation. Extended Kalman Filter (EKF) has poor convergence when the initial error is large, resulting in poor positioning accuracy. Compared with EKF, the Invariant EKF (InEKF) constructs the system state on the matrix Lie group, and its dynamic equation can describe the motion characteristics of objects more naturally and essentially. At the same time, InEKF obtains state-independent Jacobians at any linearization point. Therefore, we propose a 5G/SINS integrated navigation system based on InEKF. Furthermore, the accuracy and convergence are compared with result of EKF. The simulation experiment is carried out from two dimensions of different accuracy levels of SINS and different initial errors. Experimental results show that the performance of InEKF is significantly better than that of EKF when the SINS accuracy level is high; When the noise is large, although the model no longer satisfies the group affine property, the performance of InEKF is still better than EKF while the advantage is not as obvious as that with small noise. In addition, the larger the initial error is, the better performance of InEKF has than EKF. Keywords: Invariant Extended Kalman Filter · Matrix Lie group · 5G/SINS integrated navigation · 5G simulation positioning

1 Introduction Positioning, Navigation and Timing (PNT) emphasizes not to rely too much on global navigation satellite system (GNSS) in the post-GNSS era, and it uses as much sensor information as possible to achieve PNT services for target in the entire airspace [1]. With the advantages of low latency and large broadband, 5G positioning will provide a unified high-precision time-space system for PNT in the post-GNSS era [2]. The 5Gbased navigation and integrated navigation system with other sensors will provide PNT basic support for carriers. 5G positioning is affected by scenes such as signal occlusion and multipath easily which is similar to GNSS positioning [3]. The strapdown inertial navigation system (SINS) only needs inertial sensors to calculate the attitude, speed and position of the carrier. Therefore, 5G/ SINS integrated navigation can improve the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 455–466, 2021. https://doi.org/10.1007/978-981-16-3142-9_43

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accuracy and robustness of 5G positioning effectively [4, 5]. Peng et al. analyzed the accuracy of the 5G/GNSS fusion system through simulation [4]. Guo et al. proposed a 5G/SINS integrated navigation based on Extended Kalman Filtering (EKF) [5]. However, EKF has problems such as dependence on state estimation and inconsistency [6]. The Invariant EKF (InEKF) [6, 7] redesigns the error state equation of the integrated navigation system and uses the invariance theory to analytically obtain the log-linear differential equation. However, literature [6] only gave theoretical derivation and proof. Although literature [7] derived the error dynamics model of the inertial sensor, it aimed at the forward dynamics measurement model merged with inertial navigation mechanization and didn’t consider the rotation of the earth. Literature [8] constructed the full state equation in the Earth-Centered-Earth-Fixed (ECEF) frame and proved that the equation satisfies the invariance, but it derived the state error dynamic equation in right-invariant for the left-invariant measurement model such as GNSS positioning. Therefore, we propose a 5G/SINS integrated navigation based on InEKF in view of the limitations of EKF. According to the left invariance of the 5G positioning measurement model, the dynamic equation of the SINS error state considering the rotation of the earth (including centrifugal force and Coriolis effect) is derived in detail, which is more suitable for SINS based on mechanization. This dynamic gives the left-invariant state error derivation for the first time.

2 Invariant Extended Kalman Filter The basic idea of InEKF is to change the definition method of state error in Euclidean space to the operation of two matrix Lie group elements in matrix Lie group space. In this way, the state transition matrix in the error state differential equation is independent of state estimation, and a uniformly convergent filter is obtained [7]. Therefore, this chapter gives the differential equation of the full state in the first, and then derives the dynamic equation of the left-invariant error state. In order to facilitate the expression physical quantities such as attitude, speed and position, the relevant coordinate frames required for navigation are summarized as earth-centered-inertial (ECI) frames (i-frame), ECEF frames (e-frame), and forward-transversal-down body frames (b-frame) [9]. 2.1 The Differential Equation of the Full State in the ECEF Frame and Its Invariance The InEKF requires the system dynamics equation to satisfy the group affine property, so the state invariant error defined in this way satisfies the autonomy, and the state invariant error dynamic equation satisfies the log-linear property. Therefore, the total differential equation of the navigation state is given first. The attitude expression adopts the direction cosine matrix Cbe from the body frame to the ECEF frame. The speed expression adopts the speed of the body frame relative to the ECI frame under the ECEF frame. The position of the body frame relative to the ECI frame is expressed under the ECEF frame [8]. The differential equation of the direction cosine matrix is •

b e Cbe = Cbe (ωib ×) − (ωie ×)Cbe

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Among them, × means the antisymmetric matrix of a three-dimensional vector. The differential equation for position is e r˙ib =

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Define the system state as the element of the matrix Lie group χ , the state and its inverse are given as ⎡

⎡ b ⎡ b e re ⎤ e −C b r e ⎤ b −r b ⎤ Cbe vib Ce −Ceb vib Ce −vib e ib ib ib χ =⎣ 01×3 1 0 ⎦, χ −1 = ⎣ 01×3 1 0 ⎦ = ⎣ 01×3 1 0 ⎦ 0 1 1 01×3 0 1 01×3 01×3 0

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It can be proved that it satisfies the group affine property [12]. Therefore, the invariant state error has an autonomous linear differential equation, that is, the left-invariant and the right-invariant error dynamic equation are independent of the state estimation. 2.2 The Left-Invariant Error State Differential Equation of the SINS in the ECEF Frame Considering that the 5G measurement model is left-invariant, the differential equation of the left-invariant state error is derived. The left-invariant state error is ⎡ b e b e ⎤ b C ˜ eb r e − r˜ b C˜ e Cb C˜ e vib − v˜ ib ib ib ⎦ ηL = χ˜ −1 χ = ⎣ 01×3 (6) 1 0 0 1 01×3 Define the state error corresponding to the attitude, velocity and position in the Lie group as expG (φ b ×) = C˜ eb Cbe ≈ I + φ b × e b e e e e − v˜ ib = C˜ eb vib − C˜ eb v˜ ib = C˜ eb (vib − v˜ ib ) J ρvb = C˜ eb vib b b e b b e b e b e e J ρr = C˜ e r − r˜ = C˜ e r − C˜ e r˜ = C˜ e (r − r˜ ) ib

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where expG (•) is the matrix exponential mapping from Lie algebra to Lie group. It can be found that the attitude matrix is coupled in the newly defined velocity error and position error, unlike the traditional velocity error and position error using vector subtraction, so that the error representation in the common coordinate frame is conducive to the real representation of the system error state [11]. Since ηL is also an element in the Lie group, according to the mapping relationship between the Lie group and the Lie algebra, the left-invariant state error ηL satisfies ⎡

⎛ ⎡ b ⎤⎞ ⎤ expG (φ b ×) J ρvb J ρrb φ

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T error, ξ b = (φ b )T (ρvb )T (ρrb )T . J is the left Jacobian matrix of Rodriguez’s formula.  b If φ  is a small angle, J can be approximated as the unit matrix, that is, J ≈ I . (•) represents the linear isomorphism that maps the vector space to the Lie algebra space. In low-cost MEMS-level SINS, the bias of gyroscope and accelerometer cannot be ignored. The first-order Gauss-Markov models are used in modelling the inertial sensor errors here. The differential equation of the attitude error is given as b b − bbg − wgb = −ω˜ ib × φ b − bbg − wgb φ˙ b = φ b × ω˜ ib

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The differential equation of the new velocity error J ρvb is derived as d d e b b (J ρvb )  (C˜ eb vib − v˜ ib ) ≈ −ω˜ ib × J ρvb + φ b × f˜ b − bba − wab (10) dt dt

where the second-order small quantity φ b × bba +wab is neglected. Since the gravitational e −G ˜ e ) also can be omitted. term can be approximated as a constant value, this term C˜ eb (Gib ib Similarly, the differential equation of the new position error J ρrb is derived as d d e b b (J ρrb )  (C˜ eb rib − r˜ib ) = −ω˜ ib × J ρrb + J ρvb dt dt

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Considering J ≈ I , the inertial error state differential equation of the integrated navigation system based on InEKF can be obtained as x˙ = Fx + Gw

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where x is the SINS error state vector, F is the system state transition matrix, G is the noise driving matrix, w is the Gaussian white noise vector, and the covariance matrix of the system noise is Qt = E[wwT ]. They are defined as follows

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⎡ ⎞ ⎤ b ×) 0 −(ω˜ ib 03×3 −I3×3 03×3 3×3 φb ⎢ −(f˜ b ×) −(ω˜ b ×) 03×3 03×3 −I3×3 ⎥ ⎜ ρb ⎟ ib ⎢ ⎥ ⎜ v⎟ b ×) 0 ⎢ ⎥ ⎜ b⎟ I3×3 −(ω˜ ib 3×3 03×3 ⎥ x = ⎜ ρr ⎟, F = ⎢ 03×3 ⎢ 0 ⎜ b⎟ 1 03×3 03×3 − τb 03×3 ⎥ ⎣ 3×3 ⎦ ⎝ bg ⎠ g bba 03×3 03×3 03×3 03×3 − τb1 a ⎡ ⎤ ⎡ b⎤ −I3×3 03×3 03×3 03×3 wg ⎢ 0 ⎥ ⎢ 3×3 −I3×3 03×3 03×3 ⎥ ⎢ wb ⎥ ⎢ ⎢ ⎥ ⎥ G = ⎢ 03×3 03×3 03×3 03×3 ⎥, w = ⎢ ba ⎥ ⎢ ⎥ ⎣ wbg ⎦ ⎣ 03×3 03×3 I3×3 03×3 ⎦ wbba 03×3 03×3 03×3 I3×3

459

⎛

(13)

It can be seen that the nonlinear left-invariant error can be accurately recovered from the time-varying error state differential equation, and the system state transition matrix does not depend on the full state estimation, but it is only related to the system input and control variables. Although the system state equation after considering the bias no longer satisfies the invariance property, it can still be proved that for such a system, the consistency can still be guaranteed [6]. Therefore, this type of system still retains the main advantages of InEKF, and its robustness and convergence will still be stronger than EKF. The one-step prediction covariance matrix that satisfies the Riccati equation can be discretized as Pt = t Pt−1 Tt + GQt G T

(14)

where t is the state transition matrix obtained by F through integrating.

3 SINS/5G Integrated Navigation In this chapter, we present the 5G positioning model firstly, then construct the measurement update equation of the integrated navigation and present the filter’s gain calculation formula and the equations of state update and covariance update. 3.1 The 5G Positioning Model and Left-Invariant Observation Equation

T Assuming that the location of the base station is ri = xi yi zi and the user receives the 5G signal from the base station at coordinate r, the horizontal departure azimuth angle azii ∈ (−π, π ], vertical departure altitude angle elei ∈ (− π2 , π2 ] and signal propagation delay of the signal ti can be extracted from the signal. Therefore, the 5G positioning observation equation is ⎤ ⎤ ⎡ i arctan y−y azii x−xi z−zi ⎥ ⎣ elei ⎦ = ⎢ arctan √ ⎦ + ri ⎣ (x−x )2 +(y−yi )2 i  cti 2 2 2 (x − xi ) + (y − yi ) + +(z − zi ) ⎡

(15)

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where c is the speed of light, (x, y, z) is the coordinate at point r, ri is the observed Gaussian white noise, and its covariance matrix is Rt . Since the current position contains 3 unknowns and the simulation experiment assumes that the clock of user and the 5G base station are synchronized, the position calculation can be performed as long as there is at least one base station. After linearizing the above formula, the three-dimensional coordinates of the current position can be obtained by solving iterative least squares method [5]. Since the 5G positioning result is expressed in the same way as the GNSS positioning result, the positioning measurement model of 5G and GNSS are consistent and they both have left-invariance property. Therefore, the 5G positioning observation model can be written as a left-invariant matrix form. ⎡ ⎤ ⎡ e e e ⎤⎡ ⎤ ⎡ ⎤ r5G 03×1 Cb vib rib ri (16) Yt = ⎣ 0 ⎦ = ⎣ 01×3 1 0 ⎦⎣ 0 ⎦ + ⎣ 0 ⎦ = χt b + Vt 1 01×3 0 1 1 0 where r5G is the positioning result calculated by using the 5G positioning model at point r. The innovation can be defined as zt = χ˜ t−1 Yt − b, then the formula (16) can be substituted into it to get that

 zt = χ˜ t−1 Yt − b ≈ I + (ξ b ) b − b + χ˜ t−1 Vt = (ξ b )b + χ˜ t−1 Vt  H ξ b + V˜ (17)  where H can be abbreviated as Hrt = 03×3 03×3 I3×3 , H is independent of the system state but only depends on the known vector b. V˜ can be abbreviated as V˜ t = C˜ eb ri =

−1 C˜ be ri = Mt ri . It can be seen that the innovation defined in this way can just construct the leftinvariant error ηL , which is an error variable that is independent of the system error state χt and its estimation χ˜ t . It can also be seen that it is consistent with the previous definition of the system state error state χ˜ −1 χ . 

3.2 SINS/5G Integrated Navigation Measurement Updating Throughout the filtering process, the attitude, velocity and position are updated with innovation in the InEKF model. However, the differential equations for the biases of gyroscope and accelerometer do not satisfy the group affine property, so they are updated according to the traditional EKF updating method. Therefore, considering the biases of gyroscope and accelerometer, the innovation becomes    ξb  + V˜ t = Ht x + Mt w5G z˜t = 03×3 03×3 I3×3 03×3 03×3 (18) ζb According to the definition of the left-invariant error ηtL = χ˜ t−1 χt , after the measurement is updated, the left-invariant error is still defined as ηtL = χ˜ t+1 χt , then

L

L

η t = χ˜ t+1 χt = χ˜ t+1 χ˜ t χ˜ t−1 χt = χ˜ t+1 χt η t

(19)

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where χ˜ t+1 χ˜ t is the difference between the states before and after updating, it can be assumed that χ˜ t+1 χ˜ t = expG ((Kt z˜t ))

(20)

where Kt is the Kalman filter gain. Therefore, the whole state update equation of InEKF can be obtained χ˜ t+ =χ˜ t expG (−(Kt z˜t ))

(21)

It is worth noting that the conclusion of the above formula is consistent with literature [10], but it is different from the whole state update equation in InEKF proposed in literature [6]. Because the error in reference [6] is defined as ηL = χ −1 χ˜ , the full state update equation is χ˜ t+ =χ˜ t expG ((Kt z˜t )). The update equation of the system error state is

L

η t = expG ((Kt z˜t ))ηtL

⇒ I + ( x) ≈ (I + (Kt z˜t ))(I + (x))

(22)

⇒ x ≈ Kt z˜t + x which neglects the second-order small quantity (x)(Kt z˜t ). It can be found that the above formula has the same way as the error state update equation in the traditional EKF, so the Kalman filter gain and covariance update have the same way as the EKF. The InEKF gain calculation formula is as follows   ξ Kt (23) = Pt HtT (Ht Pt HtT + Mt Rt MtT )−1 Kt = ζ Kt The covariance matrix update equation is as follows Pt+ = (I − Kt Ht )Pt (I − Kt Ht )T + Kt Mt Rt MtT KtT Finally, the full state of the system is updated as follows [7]:

  +  + ξ χ˜ t expG −(Kt z˜t ) χ˜ t = ζ ζ˜t+ ζ˜t+ + Kt z˜t

(24)

(25)

4 Experiment In order to compare the convergence and positioning accuracy of EKF/InEKF algorithm under the influence of inertial navigation with different precision levels and different initial attitude errors (misalignment angle), this paper uses 5G simulation data to carry out the following experiments.

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4.1 Generate Simulation Data Due to many reasons such as the construction process of 5G and data acquisition, the SINS/5G integrated navigation experiment in this paper adopts the data generated by the 5G positioning simulation platform built by Guo et al. [5] and the Sub-6G frequency band is used for simulation with (1 m, 1 m, 3 m) for the accuracy of 5G positioning. This experiment simulates the on-board experiment, that is, SINS data only changes heading angle and forward-motion speed change without lateral drift which accords with the physical law of vehicle motion. Among them, the biases of gyroscope and accelerometer can be set freely to verify the performance of EKF/InEKF algorithm under different levels of SINS. SINS data is updated at a frequency of 200 Hz while 5G positioning data is updated once per second as the filter correction value, and the preset trajectory groundtruth is used as a reference for error analysis. Figure 1 shows the experimental data trajectory, which is represented by the local navigation frame East-North-Up (ENU).

Fig. 1. Data trajectory

Fig. 2. Positioning result

4.2 Integrated Navigation Simulation Experiment The accuracy of SINS with different levels is mainly reflected in the error of the sensors which are modeled as first-order Gauss-Markov process and are given initial values. On this basis, the SINS experimental data with different precision are obtained by enlarging or reducing certain multiples. Among them, gyroscope random walk (ARW) is 0.03 deg/sqrt(h), accelerometer random walk (VRW) is 0.3 m/s/sqrt(h), gyro bias random noise is 0.3 deg/h, accelerometer bias random noise is 0.0003 m/sˆ2, and correlation time of gyro and accelerometer bias is 4 h. The initial attitude error (misalignment angle) is set at different initial heading angles, which are 0, 30, 60 and 90° respectively. Figure 2 shows the trajectory containing EKF/InEKF positioning results obtained according to the above initial noise parameter settings, in which blue represents 5G observation data, black represents real trajectory, green represents EKF calculation result, and red represents InEKF calculation result. Point A in the figure is the starting point of the trajectory, and point B/C/D are the turning point. The convergence of EKF is poor in the initial stage, and the positioning error is large in the first 30 s. However, since that InEKF’s state transition matrix in its error state differential equation is independent of the

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state estimate, the algorithm can quickly converge to the expected value. Figure 3 shows the trajectory coordinates in each direction and the corresponding integrated navigation filtering results; Fig. 4 shows the positioning errors in each direction; and the shadow bar in Fig. 5 shows the comparison of positioning standard deviations of 3 times. InEKF shows advantages over EKF in the initial positioning stage and in the turning clearly.

Fig. 3. Positioning error of each axis

Fig. 4. Positioning error

In order to emphasize the experimental comparison effect, different misalignment angles and different noise levels as shown in Table 1 are set to obtain the positioning accuracy errors of the two filtering algorithms respectively. When the misalignment angle is 0° the positioning accuracy of EKF/ InEKF is relatively high, and there is little difference between them. The positioning errors in the horizontal direction (x and y axis) are about 0.2 m, and the positioning errors in the elevation direction (z axis) are about 0.5 m. With the increase of the misalignment angle, the positioning errors of both are increasing. However, the positioning accuracy of InEKF algorithm is higher than that of EKF, and the greater the misalignment angle, the more obvious the advantage of InEKF is.

Fig. 5. Comparison of positioning 3σ

Fig. 6. Positioning comparison under large misalignment angle

For example, the noise reduction factor in the first row of Table 1 is 100, and the Xaxis positioning error of EKF algorithm is 15 m while InEKF is only 3 m in the case of a large misalignment angle of 90°. Figure 6 shows the positioning results under the above large misalignment angle. It can be found that InEKF is superior to EKF in terms of both

0.24

0.23

0.22

0.21

60

40

20

0.21

20

80

0.22

40

0.24

0.23

60

100

0.24

80

InEKF

0.24

100

EKF

0.23

0.23

0.24

0.24

0.25

0.23

0.23

0.24

0.24

0.25

0.41

0.46

0.48

0.49

0.50

0.41

0.46

0.48

0.49

0.50

0.53

0.55

0.54

0.52

0.50

5.05

4.82

4.48

4.14

3.83

2.10

2.10

2.09

2.09

2.09

4.79

4.60

4.31

4.06

3.86

y-axis rms(m)

x-axis rms(m)

z-axis rms(m)

x-axis rms(m)

y-axis rms(m)

Position error at 30° of misalignment angle

Position error at 0° of misalignment angle

Noise reduction factor

Filter

0.41

0.47

0.48

0.49

0.51

0.53

0.60

0.62

0.62

0.62

z-axis rms(m)

1.88

1.89

1.83

1.77

1.70

14.39

13.10

11.94

10.89

9.99

x-axis rms(m)

4.59

4.53

4.47

4.42

4.39

24.00

23.38

21.84

20.32

18.95

y-axis rms(m)

Position error at 60° of misalignment angle

0.44

0.50

0.52

0.52

0.53

1.17

1.39

1.40

1.36

1.30

z-axis rms(m)

4.02

3.95

3.84

3.70

3.57

27.22

21.89

19.32

17.28

15.56

x-axis rms(m)

8.14

7.86

7.63

7.46

7.34

64.58

59.62

54.95

50.71

47.00

y-axis rms(m)

Position error at 90° of misalignment angle

Table 1. Experimental error analysis under different misalignment angles and noise levels

0.50

0.56

0.57

0.57

0.57

2.61

2.97

2.84

2.63

2.44

z-axis rms(m)

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Fig. 7. Effects of misalignment angle on three axis errors

the convergence speed of large misalignment angle and the overall positioning accuracy. Figure 7 shows the influence of the three axial positioning errors by the misalignment angle and noise obtained by the two filtering algorithms. The upper side of each subgraph is InEKF’s result, and the magnitude of positioning accuracy is obviously better than the EKF’s result in the lower side. For example, for the X-axis, when the misalignment angle is fixed, as the noise level changes, the increase of the noise reduction multiple means the noise decreases, and the positioning accuracy of the filter is improved accordingly.

5 Conclusion In this paper, the attitude, velocity and position are constructed into a matrix Lie group, and the state errors are defined in the same coordinate frame by group operation. The attitude errors are coupled in the velocity errors and position errors. At the same time, the dynamic equation of error state in Lie algebra space is obtained by using Lie group and Lie algebra theory, and the dynamic model of error state which is independent of system state is constructed by considering the rotation of the Earth. The state update and measurement update equations based on left InEKF satisfying 5G location measurement model are derived. The simulation results show that the SINS/5G integrated navigation based on left InEKF has better positioning accuracy than that based on EKF, and the InEKF-based one has the advantage of fast convergence under large misalignment angle. However, the 5G positioning system used in this paper is a simulation system, which cannot reflect the 5G signal characteristics in the real environment. In the future, the positioning effect under real scenes should be considered including the clock synchronization between users and 5G base stations. Meanwhile, the InEKF algorithm will be applied to the initial alignment and data fusion positioning problems of the integrated navigation system based on inertial sensors, and the error definition of bias in the common frame should be considered. Acknowledgements. The authors of this paper would like to thank Yu Jiang of our research group for providing a 5G positioning simulation platform. This research was supported by a grant from the National Key Research and Development Program of China (2018YFB1305001).

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References 1. Yang, Y.: Concepts of comprehensive PNT and related key technologies. Acta Geodaetica et Cartographica Sinica 45(5), 505-510 (2016). https://doi.org/10.11947/j.AGCS.2016.201 60127 2. Liu, J., Guo, W., Guo, C., et al.: Rethinking ubiquitous mapping in the intelligent age. Acta Geodaetica et Cartographica Sinica 49(4), 403–414 (2020) 3. Liu, J., Gao, K., Guo, W., Cui, J., Guo, C.: Role, path, and vision of “5G + BDS/GNSS.” Satell. Navig. 1(1), 1–8 (2020). https://doi.org/10.1186/s43020-020-00024-w 4. Peng, Y., Tian, Y., Zhang, W., et al.: Positioning accuracy analysis for 5G/GNSS fusion system. J. Xiamen Univ. Nat. Sci. 59(1), 101–107 (2020) 5. Guo, C., et al.: Intelligent and ubiquitous positioning framework in 5G edge computing scenarios. IEEE Access 8, 83276–83289 (2020) 6. Axel, B., Silvere, B.: The invariant extended kalman filter as a stable observer. IEEE Trans. Autom. Control 62(4), 1797–1812 (2017) 7. Ross, H., Maani, G., Ryan, M.E., Jessy, W.G.: Contact-aided invariant extended kalman filtering for robot state estimation. Int. J. Rob. Res. 39(4), 402–430 (2020) 8. Wang, M.: Research on Dynamic Model and Algorithm of Inertial-Based Integrated Navigation. National University of Defense Technology, Beijing (2018) 9. Yan, G., Weng, J.: Lectures on Strapdown Inertial Navigation Algorithm and Integrated Navigation Principles. Northwestern Polytechnical University Press, Xi’an (2019) 10. Arsenault, J.: Practical considerations and extensions of the invariant extended Kalman filtering framework. MA Sc. thesis, McGill Univ., Montreal, PQ, Canada (2019) 11. Whittaker, M.P., Crassidis, J.L.: Relative inertial navigation employing a common frame error definition. In: AIAA Scitech 2020 Forum, p. 1596 (2020) 12. Luo, Y., et al.: SE_2(3) based Extended Kalman Filter for Inertial-Integrated Navigation (2021). arXiv preprint arXiv:2102.12897.

Analysis of Management and Control and Scheduling Mode for Mega Constellation Lei Lei1 , Wei Chen2(B) , Si-zhe Cai1 , Hui-li Gao1 , and Chen Chi1 1 China Xi’an Satellite Control Center, Xi’an 710043, China 2 Hebei Agricultural University, Baoding 071001, China

Abstract. China’s management of mega constellations in the future will face the trend of large deployment scale, large number of satellites, large amount of data exchange between satellites and ground stations, and high requirements for joint and stable operation. At the same time, the conventional satellite control center will also face the trend that the number of satellites is increasing year by year while the available TT&C resources are insufficient. Since the mode of “dedicated system, dedicated network” will be adopted to mega constellation management and control, in this paper, we proposes a sharing management and control mode between conventional satellite control and mega constellation management. Here we introduces two indicators, the maximum mission support capability and the effective load rate, to make a quantitative analysis and comparison, thus to provide an effective theoretical and technical support for the demonstration of the management and control mode of mega constellations. Keywords: Mega constellations · Sharing management and control mode · Dedicated system · Quantitative analysis

1 Introduction China is in urgent need to carry out research on the construction, operation and maintenance management technologies of mega constellation systems, and lay a foundation for efficient management of large-scale constellations and the construction of new-type central systems [1]. In order to meet the mission requirements of the future mega constellations, in this research, we need to form the management and support capabilities as soon as possible in terms of high-efficient scheduling and distribution of massive data, high-precision retention of constellation configuration, high-density monitoring of health status, and efficient operation of application services. At present, it is generally recommended to adopt a “dedicated system, dedicated network” approach for the management and control mode of mega constellation, and establish a special mega constellation management and control center, which is independent of the existing satellite management and control center, and responsible for retention of configuration, platform and load monitoring, and scheduling multi-beam TT&C resources according to the task [2, 3]. Based on mega constellation operating scenario,this paper analyzes the requirements of various resources, conducts an in-depth © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 467–477, 2021. https://doi.org/10.1007/978-981-16-3142-9_44

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analysis and comparison of the management, control and scheduling modes, and proposes a sharing management, control and scheduling method that meet the maximum mission requirements of the existing satellite control center and the mega constellation. Finally, through the simulation experiment, various management, control and scheduling modes are quantitatively compared by indicators of both maximum support capacity and the effective load rate, and the results are concluded.

2 Analysis of Operating Scenarios of Mega Constellation 2.1 Requirements for the Mega Constellation Control Center First, normally, mega constellation control center has the ability to be visible to each satellite in every circle, and uses random access technology [4] to timely master satellite working status and receive the active measurement and control requirements of the satellite. Second, it has the ability to implement multiple circles of routine measurement and control for each constellation satellite under normal circumstances, and implement specified circle of measurement and control for designated satellites under emergency conditions. Third, in order to complete the satellite orbit control and determination, it is also necessary to provide front-control and back-control support of measurement and control for the designated satellite. 2.2 Requirements for Existing Satellite Control Center Due to the pre-planned scheduling mode and coordinated interactive process adopted by the satellite control center, And with the proliferation of the number of satellites and the user demand, there are such problems as a large increase in the computational complexity and a limitation on the response ability of the task with high timeliness. Therefore, the traditional work mode of “pre-planning + center-configuration + controlchain-building" annot fully adapt to management and control of the mega constellation. In addition, intensive routine events, dynamic allocation of equipment, and switching between the random access mode and the traditional mode will become the normal state. Therefore, a new mode which can automatically realize the satellite-to-ground link with visibility will need to be established. 2.3 Analysis of Disadvantages of the Constellation Independent Control Mode One is split use of multi-beam resources. The distribution of satellite task sets and corresponding command parameters of each station are directly completed by the mega constellation control center without passing through the existing satellite control center, and the corresponding beam resources are exclusively used by the mega constellation control centers. If the existing satellite control center needs to use the multi-beam resources of the dedicated network, the “center-to-center” mode is adopted to coordinate with the task center. Then, multi-beam resources are arranged by the task center. In fact, this mode forms the separation and use of resources. Since the existing satellite control center does not know the status of relevant beam resources and the actual performance parameters of beams, there are the technical and management links in coordination and use.

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The other is unable to meet the constellation failure emergency requirements. According to the current independent control mode of the mega constellation, the mega constellation control center does not have the basic beam scheduling working mode, and in case of any failure in the random access of mega constellation satellites, It is impossible to handle the failure by relying on the multi-beam antenna of mega constellation. because the scheduling mode of “manual designation” and “planned driving” is not established for the multi-beam antenna of mega constellation, If we do not rely on the existing satellite control center for task sharing, it may be fail to respond to “emergencies” of a large number of satellites.

3 Analysis of Resource Sharing Management and Control Mode 3.1 Analysis of Resource Sharing Requirements In the management of mega constellation, multi-beam resources are abundant since mega constellation have not completed the full-orbit deployment in the early stage. Thus the mega constellation center can interact with the existing satellite control center, and share some resources to support its requirements. Moreover, in the long run, the resource shortage of the satellite control center will inevitably exist, and there is a demand for the use of the multi-beam equipment of the mega constellation. Meanwhile, considering that some constellation control tasks also need to rely on the existing satellite control center for resource support in case of large-scale failure of the random access equipment in charge of mega constellation control. Therefore, the mega constellation and the existing satellite control center are necessary to share resources to meet the mutual task. 3.2 Design of Resource Sharing Management and Control Mode As shown in Fig. 1, for the shared mode design of satellite control and mega constellation control, the core idea is that the multi-beam antenna needs to meet not only the mega constellation access requirements, but also the public network requirements for measurement and control. The task set formed by mega constellation control center is first sent to the resource management center, which will break it down to the measurement and control equipment and be responsible for releasing the scheduling plan. In order to improve that resource utilization efficiency of the series of multi-beam, The resource management center additionally inserts a small number of public network tasks to be undertaken by the multi-beam stations of the mega constellation according to the condition of the remaining idle beams after the series of task sets are occupied, and then sends them to the multiple beam stations. At the same time, the status of each multi-beam station is also transmitted to the constellation management center through the resource management center, so as to facilitate the resources management center to accurately grasp the status and determine the number of public network tasks that can be additionally inserted. When the control channel of the ground multi-beam antenna points to the satellite, the satellite initiates a resource use request on demand, and the ground multiple-beam station corresponding to this control channel starts to play the role of a resource request proxy

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after receiving the resource usage request. If the multi-beam station has the appropriate idle resources, the multi- beam station will directly agree to the satellite request, and notify the satellite to switch to the service link according to the idle resource parameters. If the multi-beam station does not have the appropriate free resources, it will forward the resource use request to all suitable ground station networks, and confirm the occupation of idle resources to the resources granted the earliest according to the corresponding resource feedback results. The satellite is then notified to switch to service link operation according to the resource parameters. If that multi-beam station does not receive any idle resource usage permission, it transfers to the resource schedule center to apply for a transferable resource search and feeds the resource scheduling center search result back to the satellite. The satellite establishes the service link according to the corresponding license, and if no resource is obtained, the satellite chooses to abandon the request or initiate the request at another time. The scheduling flow is shown in Fig. 2. Tradional satellite cluster

Plan driven 䇗ࡈ傧ࣞ

Giant Constellaon 1

Giant Constellaon 2

Free access

䳅䙽᧛‫ޛ‬ Free access

Tradional satellite cluster 䇗ࡈ傧ࣞ+䳅 Plan-driven䳅+ 䙽᧛ Free access ‫ޛ‬

Giant Constellaon 1

Giant Constellaon 2

Free access + plandriven

Free access + plan䳅䙽᧛‫ޛ‬+䇗ࡈ傧ࣞ driven

Mul-beam equipment for giant constellaons Satellite Control Center Mulbeam Equipment Satellite Control Center Single Beam Equipment Tradional measurement and control link Military communicaon link

Satellite Control Center

Giant Constellaon Control Center 1

Giant Constellaon Control Center 12

Satellite control and giant constellaon independent control mode design diagram

Satellite Control Center

Giant Constellaon Giant Constellaon Control Center 1 Control Center 2 Schemac diagram of the design of shared control mode for satellite control and giant constellaon

Fig. 1. Schematic diagram comparison for mega constellations of independent management and control mode and resource sharing management and control mode

From the comparison of the independent control and resource sharing control modes of the mega constellation, in the resource sharing control mode, public network resources and the multi-beam resources of the mega control center can be used interchangeably. Therefore, the usage rate of multi-beam resources is higher, and the task allocation subject is concentrated in the existing satellite control center, which is more conducive to the sharing of resources. After multiple mega constellations are established, multiple constellation task centers will transparently share the status of multi-beam resources, facilitating collaborative work to maximize resources, as shown in Table 1.

4 Simulation Analysis 4.1 Simulation Condition To compare the independent control and resource sharing control modes, it is necessary to clarify the number of available resources and satellites in the existing satellite control

Analysis of Management and Control and Scheduling Mode for Mega Constellation Giant ConstellaƟon Control Center 1

Giant ConstellaƟon Control Center 2

Satellite Control Center TradiƟonal satellite cluster

Mega ConstellaƟon 1 Satellite

Resource applicaƟon agent

Mega ConstellaƟon 2 Satellite

Demand type Resource use applicaƟon Resource code Beam number

Resource use applicaƟon Demand type Beam number Idle beam applicaƟon

Yes

Resource use applicaƟon Demand type Beam number Idle beam applicaƟon

Resource applicaƟon agent

Resource applicaƟon agent No

No Are there res ources available

No

Yes

Are there res ources available

Yes AutomaƟc allocaƟon of service beam channels

471

Are there res ources available

No Return business type Beam number

AutomaƟcally assign resource codes

Return business type Beam number

Generate beam scheduling task set 1

Generate beam scheduling task set 2

Are there transferab le resources

Yes

Yes Yes

Generate mulƟ-beam antenna 2 status

Generate beam scheduling Maximum task set

Task set sending Complete demand TT&C

AutomaƟc allocaƟon of service beam channels

Task set sending

Generate mulƟ-beam antenna 2 status Complete business measurement and control

Generate all antenna states

Complete Demand TT&C

Fig. 2. Scheduling process of resource sharing management and control mode

Table 1. Analysis of advantages and disadvantages of resource sharing management and control model Compare content

Independent mode

Resource sharing mode

Resources used alternately

No

Yes

Utilization ratio of multi-beam

Low

High

Task allocation subject

Constellation Control center

Existing satellite Control center

Coordination of task centers

No

Yes

Transparency of resource status

No

Yes

center and the mega constellation control center. The parameters and equipment of the available resources of the existing satellite control center and the mega constellation control center, as well as the scale and parameters of measurement and control tasks are shown in Table 2 and Table 3. 4.2 Ground Resources Effectiveness Evaluation Indicators The maximum support capability refers to the maximum number of laps that the resource scheduling system can guarantee measurement and control tasks by the reasonable arrangement of schedulable resources in accordance with the optimal algorithm within the total evaluation time. It intuitively reflects the number of tasks that the measurement and control network can undertake under the current number of equipment, and is one of the main indicators for evaluating the scheduling of measurement and control resources.

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Table 2. Available equipment resources for existing satellite control center and mega constellation control center Source of equipment

Number of comparing down-link beams to uplink beams

Position

Visible pitch angle

Beam width

Growth

Existing satellite control center

More

South

3°

1°

1 set/year

More

North-east

3°

1°

1 set/year

Equal

Northwest

3°

1°

1 set/year

Equal

South

3°

1°

-

Constellation control center

Table 3. Satellite measurement and control requirements for existing satellite control centers and mega constellation control centers Subject Number Track of height satellites

Requirements Duration Maximum of TT&C return visit interval of single star

SAT

200

500km

Up 1.5 down 1.6 pcs/ day

MC

860

1175km 30 pcs / 20 days

Number of Annual simultaneous growth TT & C rate satellites per station

≥ 5min

-

-

50 pcs

≥ 5min

≤ 10h

≤ 48 pcs

170 pcs

The calculation of the maximum support capability is given by formula (1.1).  Nu ∗ Tr ∗ i∈U Ui  pmax = Nu ∗ T0 + i∈U Mi

(1.1)

In the formula, Tr is the total time in an evaluation period, Ui is the i-th satellite, T0 is the minimum time interval of the satellite tracking arc, Mi is the tracking time of the i-th satellite, U is the satellite collection and Nu is the number of elements in satellite collection U. The effective load rate refers to the ratio of the total time that the measurement and control equipment has undertaken tasks to the total time that the measurement and control equipment can actually support the measurement and control in the total evaluation time. This indicator describes the actual measurement and control time of equipment allocated by the scheduling algorithm. The effective load rate calculation is given by formula (1.2).   (Nu ∗ T0 + i∈U Mi ) ∗ ωi ∗ Ri  (1.2) Loadon = Nu ∗ Tr ∗ i∈U Ui

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ωi is the weight value of the i-th satellite, and Ri is the measurement and control requirement of the i-th satellite. 4.3 Simulation Results 4.3.1 Analysisof the Visibility of Satellites Under the Independent Control Mode of the Existing Satellite Control Center and the Mega Constellation Control Center The parameter initialization bases on the visible relationship between the ground station and the satellite, the shielding angle, the duration, the conflict with the arc segment that has undertaken the task, and other constraint conditions. We can generate the visible window forecast through STK calculation, and filter out the cycles that meet the requirements and are added to the available scheduling set.

Fig 3. Relationship between the number of visual satellites and time under the independent control of the existing satellite management and control center in 2025

With a small number of satellites and a large number of multi-beam equipment foundations in the early stage, the mission requirements can be guaranteed by the equipment capability alone. However, by 2025, that number of multi-beam devices and satellite will have grown to the maximum within the evaluation cycle, and especially for the mega constellations, the device capability has fallen far short of the task requirement. At this time, the advantages of the resource sharing management and control mode can be better reflected. From the analysis under the independent control mode in 2025, it can be concluded that the number of satellites that can be seen at the same time in each time period is about 170, as shown in Fig. 3, in which the existing satellite control center is under independent control. At the peak time, the maximum number of satellites can be seen is about 250, which is far less than the measurement and control capability of the equipment of the existing satellite control center in 2025. Under the independent control

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mode, the mega constellation control center is as shown in Fig. 4. The number of visible satellites in each time period is about 130, and the maximum visible number is about 160 at the peak time, which is far larger than the measurement and control capability of the equipment in the independent control mode of the mega constellation in 2025.

Fig. 4. Relationship between the number of visual satellites and time under the independent control of the mega constellationmanagement and control center in 2025

4.3.2 Analysis and Comparison of Maximum Support Capability Under Independent Control and Resource Sharing Control from 2020 to 2025 As shown in Fig. 5, from the simulation results, it can be seen that the existing satellite control center’s maximum support capability under the independent control mode and the resource sharing control mode is increasing year by year. As shown in Fig. 5, from 2020 to 2022, the existing satellite control center’s maximum support capacity under resource sharing control mode is higher than that under independent control mode, and both are at the same level in 2023.Followed by 2024 to 2025, The existing satellite control center’s maximum support capacity under resource sharing control mode is smaller than that under independent control. For the mega constellation control center, as shown in Fig. 6, the maximum support capability in the resource sharing control mode is always larger than that in the independent control mode. 4.3.3 Comparison of Effective Load Rate Under Independent Control and Resource SharingControl from 2020 to 2025 As shown in Fig. 7, the effective load rate of the existing satellite control center in the resource sharing control mode is always lower than that in the independent control mode. As the equipment capability increases year by year, the effective load rate of the existing satellite control center under the mode of independent control and shared

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Fig. 5. The maximum support capability of the existing satellite control center under independent control and shared control

Fig. 6. The maximum support capability of the mega constellation control center under independent control and shared control

control gradually approaches. As shown in Fig. 8, the effective load rate of the mega constellation control center in the resource sharing mode is always lower than that in the independent control mode. With the increase of years, the number of satellites to be controlled by mega constellations has increased dramatically. By 2022, the effective load rate of the mega constellation control center under independent control mode has exceeded 100%. If the equipment capability has not been increased, the resource sharing control mode effectively reduces the effective load rate of mega constellation control.

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Fig. 7. Theeffective load rate of the existing satellite control center under independent control and shared control

Fig. 8. Theeffective load rate of the mega constellation control center under independent control and shared control

5 Conclusion The main idea of this paper is to simulate and analyze the maximum support capacity and effective load rate under the two control modes: First, we analyzed the situation of the existing satellite control center and the mega constellation control center under the independent control mode. Second, we analyzed the situation of the existing satellite control center and the mega constellation control center under the resource sharing control mode. Through analysis, it can be concluded that under the situation of shortage

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of ground equipment resources, it is of great help to increase the support capability of the measurement and control by optimizing the management strategy and adopting the appropriate management and control mode. Similarly, the resource sharing management and control mode provides a new solution to the problem of excessive equipment capacity planning in the early stage, and can support the measurement and control tasks of other systems to the greatest extent possible by reasonably utilizing the excessive resources. In addition, the resource sharing management and control mode can effectively reduce the urgency of planning new equipment in a system with insufficient other resources. It shows that this control mode which interacts with the existing satellite control center to some extent and shares some resources is effective in increasing the maximum support capacity of the both measurement and control systems and reducing the effective load rate of the respective systems. This will be very useful for practical engineering applications.

References 1. Shaodong, F., Xiao, J., Yangzhi, L., Guangxia, L.: Traffic modelling and simulation in low earth orbit constellation system. J. Astronaut. 31(1), 179–184 (2010) 2. Satellites Strategy Based on Navigation System. Fourth International Conference on Space Information Network. Wuzhen, Zhejiang, China (2019) 3. Yury, N.: Fundamentals of the route theory for satellite constellation design for Earth discontinuous coverage. Acta Astronaut. 128, 459–465 (2016) 4. Jinliang, L., Hui, D., Xiaozhou, Y., Zaiming, W.: Random access satellite emergence task response technology. Aerosp. Electron. Warfare. 33(3), 7–10 (2017)

Deployment Location Algorithm of Navigation Base Station Based on GDOP Analysis Jintao Yao1,2(B) , Hongli Li1,2(B) , and Bin Li1,2 1 The 20th Research Institute of China Electronics Technology Corporation, Xi’an, China 2 Shaanxi Key Laboratory of Integrated and Intelligent Navigation, Xi’an, China

Abstract. Regional navigation (RNAV) is an important backup and enhancement means of satellite navigation. When satellite navigation is restricted by terrain and electromagnetic interference for a specific area, it has the ability to provide highprecision navigation service. Because the base stations are close to the user, the layout of the base stations have significant impact on the performance of the regional navigation system. When RNAV provides services for the designated area, in order to obtain high positioning accuracy, the reference source must have good geometric distribution. Therefore, this paper proposes a deployable location algorithm based on iterative division of deployable-area to calculate the deployable location of the reference source. Firstly, the deployable-area and Served-area are defined in mathematical language, and then the Deployable-area is divided iteratively, according to the principle of the number of stations and GDOP minimization, the optimal deployable location is calculated. The simulation results show that the proposed method can quickly get the deployable position of the reference source with good geometric distribution, and provide important support for the RNAV system to have high precision positioning service capability. Keywords: Regional navigation (RNAV) · GDOP · Iterative division of space area · Deployable location of reference source

1 Introduction When satellite navigation system is unavailable, RNAV [1] is a feasible and effective means of navigation. The base station can be carried on the air or ground platform for rapid deployable, and can provide high performance Space-time benchmarking services for the disturbed-area. Because the distance between base station and user is very close in RNAV, the geometric distribution of the base station has a significant impact on the navigation performance [2]. In order to improve the positioning accuracy of regional navigation, this paper studies the deployable location of navigation reference source based on the GDOP [3, 7, 10], more details in [8, 9, 11, 12]. There are many researches on the geometric distribution of radio navigation system at home and abroad, such as the geometric layout of six pseudolites [4]. The geometric layout of four pseudolites is studied [5]. The geometric layout of four, five and nine © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 478–486, 2021. https://doi.org/10.1007/978-981-16-3142-9_45

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pseudolites was designed [6]. However, served area is not clearly defined, and the number of base stations is fixed and the deployable-area is unlimited. In practical applications, it is necessary to define the three-dimensional area being served, the deployable space should be limited, and the number of navigation base stations may change. Therefore, the methods mentioned above are only applicable to a few specific scenarios. In view of the limitation in the practical application of regional navigation, this paper proposes a deployable location algorithm of navigation base station based on iterative segmentation of deployable area based on GDOP analysis. Firstly, the deployable area and served area are defined by mathematical language, and then the deployable area is divided iteratively. According to the number of stations and GDOP constraint rules (results of this paper are based on minimizing GDOP of served area), the optimal deployable location is quickly calculated. Finally, two typical scenarios are designed to verify the effectiveness of the algorithm.

2 Method of Location Deployable 2.1 Application Principle Relationship The precondition of the algorithm is that the constraints “served area”, “deployable area” and “number of deployable base stations” will be sent to the spatiotemporal information service system by other combat information systems through the network according to the requirements of real-time combat application. The calculation model of regional navigation base station in the spatiotemporal information service system calculates the deployable position of regional navigation base station in real time, and sends the deployable position information to the command information system through the network. The command information system deploys the base station to the designated position to provide the reference spatiotemporal information service for the refused area. Its application principle is shown in Fig. 1. Deployable-Area Base Staon

use r

Staons leave for aim posions

use r

use r

staons

Detecon system

Calculaon parameters

Calculaon model of reference staons posion

Deployment locaon infomaon

Space-me service system

Command system Communicaon system

Staons is in inial posion

Other system

Fig. 1. Schematic diagram of algorithm application principle

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Fig. 2. (a) definition of Area, (b) bottom surface (Q) of Area

2.2 Segmentation Method of Area In order to facilitate the calculation, the Area (three-dimensional space) is defined. As Fig. 2(a) show, the parameters include: four vertices (V1 , V2 , V3 , V4 ) of bottom surface, height (H ) and central spot (C). Especially, the order of the four vertices is counter clockwise, H /2 is often used in the following, the Area is a quadrilateral when H = 0, the coordinate format of all points is (longitude, latitude, height), the central spot C is the midpoint of the line segment composed of the gravity centre of the upper and lower bottom surfaces. Then the method of Area segmentation is proposed. Details show in Fig. 3 and Fig. 2.

Fig. 3. Schematic diagram of method for Area segmentation

3 Deployment Location Algorithm of Base Stations Generally, the deployable area and served area are three-dimensional space region. In order to calculate the deployment locations of base station, the Served-Area must be sampled to get a limited number of user point firstly. then use deployment location algorithm to calculate deployment locations. 3.1 Sampling Method of Served-Areas For the area in Fig. 6(a), set the sampling times is 3. Segmentation method of area is used to sample the served area. The result is shown in Fig. 5(a), the number of sampling points is 4685.

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3.2 Deployment Location Algorithm

Fig. 4. Flow chart of deployment location algorithm

Define the deployable area DA and service area SA. Set n is the number of base station, K is the number of iterations, Constrains of GDOP is minimizing the mean value of User-set is produced by sampling the SA. Details of algorithm can be find in Fig. 4. Before the iteration, a segmentation is performed to divide deployable area into 4 subareas by Segmentation method of area. At the beginning of iteration, divided-area are the above 4 subareas. To divide them, the set of areas is obtained. According to the role of minimizing the mean value of GDOP, select n subareas from set to update divided-area. If the times of iteration is less than k, continue iteration. Finally, output the latest set of center pots of divided-area. 3.3 Important Influencing Factors There are three main factors in the algorithm: number of user sampling points, number of base stations, iterations of area segmentation. Number of User Sampling Points. It can be seen from Fig. 5(a) and Fig. 5(b) that the change of sampling points has no effect on the location calculation results. The number of sampling point 77, 589, 4685, corresponding to served area iterating 1, 2 and 3. Number of Base Station. It can be seen from Fig. 5(d) that with the increase of the number of base stations (4, 5, 6), the GDOP will decrease gradually. But the computing time will be greatly increased, which is 17, 1826, 28304 s. When only four base stations are used, the running time of the algorithm is in the order of tens of seconds, which can quickly calculate the results and meet the real-time application. Iterations of Area Segmentation. It can be seen from Fig. 7(c) and Fig. 8(c) that GDOP gradually decreases to a stable value with the increase of iterations, and the calculation results remain basically unchanged after five iterations.

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Fig. 5. (a) Sampling of served area. (b) Changes in deployment location as the number of user samples increases. (c) Changes in GDOP as the number of user samples increases. (d) Impact of changes in the number of base stations.

4 Simulation and Analysis Two common scenarios are designed, and simulation are carried out to verify the proposed algorithm.

(a)

(b)

Fig. 6. (a) deployable area contains the served area, (b) deployable area is on the side of the served area.

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4.1 The Deployable Area Contains the Served Area As shown in Fig. 6(a), the deployable area includes the served area, parameters are shown in Table 1. Table 1. Parameters of area Area

Vertexs

Longitude (°)

Latitude (°)

halfH (m)

Deploy region

Vertex1

118.618077

24.069700

10000

Vertex2

118.641443

23.742159

\

Vertex3

119.080209

23.700000

\

Vertex4

119.025688

24.145538

\

Vertex1

118.766063

23.929769

10000

Vertex2

118.768859

23.820560

\

Vertex3

118.945204

23.822936

\

Vertex4

118.927030

23.929769

\

Service region

The number of base stations is set to 4, the number of user is 77(sampling layers is 1), carry out multiple iterations.

Fig. 7. (a) Front view of user area and deployable location. (b) Top view of user area and deployable location. (c) GDOP with the change of calculations. (d) GDOP of served area

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The result show that the deployable locations are roughly distributed around the served area, with two at high altitude and two at low altitude, as shown in Table 2, Fig. 7(a) and Fig. 7(b). As can be seen from Fig. 7(c), after five iterations, the GDOP value is very small and almost no change. The GDOP of the served area is shown in Fig. 7(d), as shown from Fig. 7(d) that the GDOP of served area centre is the smallest and gradually becomes larger around. Table 2. Stations position and statistics of GDOP Stations Longitude (°)

Latitude (°) Altitude(m) GDOP

Sta1

118.756303

23.972231

625.0

Sta2

118.702765

23.752430

19375.0

Sta3

118.987097

23.766836

625.0

Sta4

118.940999

23.963569

19375.0

Min 1.6 Max 2.7 Average 1.9

4.2 The Deployable Area Is on the Side of the Served Area As shown in Fig. 6(b), the deployable area is on one side of the served area. The specific parameters are shown in Table 3. The number of base stations is set to 4, the number of user is 77(sampling layers is 1), carry out multiple iterations. The result show that the deployable locations are roughly distributed around the served area, with two at high altitude and two at low altitude, as shown in Table 4, Fig. 8(a) and Fig. 8(b). As can be seen from Fig. 8(c), after five iterations, the GDOP value is very small and almost no change. The GDOP of the served area is shown in Fig. 8(d). Table 3. Parameters of area Area

Vertexs

Longitude (°)

Latitude (°)

halfH (m)

Deploy region

V1

117.820000

24.000000

10000

V2

117.840000

23.700000

\

V3

118.641443

23.742159

\

V4

118.618077

24.069700

\

V1

118.766063

23.929769

10000

V2

118.768859

23.820560

\

V3

118.945204

23.822936

\

V4

118.927030

23.929769

\

Service region

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Table 4. Stations position and statistics of GDOP Stations

Longitude (°)

Latitude (°)

Altitude (m)

Sta1

118.211286

23.989784

625.0

Sta2

118.225530

23.803830

19375.0

Sta3

118.628604

23.746601

625.0

Sta4

118.606014

24.063515

19375.0

GDOP Min 4.8 Max 15.8 Ave 8.4

Fig. 8. (a) Front view of user area and deployable location. (b) Top view of user area and deployable location. (c) GDOP with the change of calculations. (d) GDOP of served area

In the two above scenarios, we can get the locations of the base station which make the GDOP of the served area smaller. Especially, we can get very small GDOP when deployable area contains the served area.

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5 Conclusion Aiming at the layout of base station in practical application scenario of RNAV, a deployment location algorithm based on iterative segmentation of deployable area is proposed. Two common scenarios in practical application are designed for simulation, the results show that the algorithm can using in the case of variable number of base stations and limited deployment area. The algorithm proposed in this paper only needs to give the served area and deployment area, and the number of iterations and base stations. The Constrains (in this paper, the Constrains is mean value of GDOP of regional sampling points is minimized) of GDOP and other factors can also be changed to suit various requirements. At the same time, the algorithm proposed in this paper can also be applied to the location calculation of other radio navigation base stations such as cellular positioning system. Acknowledgments. This study is supported by the key industry innovation chain (cluster) industrial field project “Beidou intelligent navigation terminal” (Project No.: 2019zdlgy08–02) of Shaanxi provincial key R & D plan.

References 1. Zhai, J., Hongli, L.V.: Research on high precision regional navigation system technology. Modern Navig. 7(02), 79–85 (2016) 2. Wang, W., Liu, Z.: Augmented Beidou satellite system by airborne pseudolites. (2010) https:// doi.org/10.3724/SP.J.1011.2010.01081 3. Krauter, R.: Geometry in GPS Positioning. Periodica Polytechnica-Civil Eng. 43, 43–53 (1999) 4. Yang, Y., Gao, S., Haifeng, Y.: Geometric layout design of near space pseudolites. Syst. Eng. Electron. Technol. 03, 532–538 (2014) 5. Wei, H., Yang, J.J., Ping, H.: Study on pseudolite configuration scheme based on near space airships (2009) 6. Mao, Y., Sun, F.P.: The analysis of pesudolite-only configration. Surverying Mapp. Sichuan 29(3), 115–118 (2006) 7. Meishan, G., Hongli, L.V., Huifeng, W.: Analysis on layout planning of regional navigation system reference sources. In: Proceedings of the 4th China Annual Conference on Satellite Navigation - s5 Satellite Navigation Enhancement and Integrity Monitoring (2013) 8. Yarlagadda, R., Ali, I., Al-Dhahir, N., et al.: GPS GDOP metric. IEE Proc. Radar Sonar Navig. 147(5), 259–264 (2000) 9. Teng, Y., Wang, J., Huang, Q.: Minimum of geometric dilution of precision (GDOP) for five satellites with dual-GNSS constellations. Adv. Space Res. 56(2), 229–236 (2015) 10. Deng, P., Lijian, Y.: GDOP performance analysis of cellular positioning system. J. Southwest Jiao tong Univ. 02, 184–188 (2005) 11. Han, T., Wu, H., Lu, X., et al.: The Mathematical Expectation of GDOP and its Application (2013) 12. Gang, X.: GPS Principle and Receiver Design. Electronic Industry Press, Beijing (2009)

Research on Loran-C ASF Correction Method Based on GA-BP Neural Network Yuqi Wang1,2(B) , Wei Wang1,2 , and Rui Luo1,2 1 The 20th Research Institute of China Electronics Technology Corporation, Xi’an

710068, China 2 Shaanxi Key Laboratory of Integrated and Intelligent Navigation, Xi’an 710068, China

Abstract. During the propagation of Loran-C signal along the ground, it is easily affected by the earth conductivity, atmospheric refractive index, temperature, humidity etc. Therefore the signal will have a large time delay. The ASF as a part of the whole signal propagation delay which is difficult to predict, has a crucial impact on the positioning accuracy of Loran-C. It is necessary to correct the ASF can get accurate positioning accuracy. If we need to get accurate ASF prediction value, we need a lot of data for training. So this paper proposes to use BP neural network algorithm based on GA. This method uses GA which has the characteristics of better global optimization. It can speed up the convergence speed of BP and solve the problem of falling into local minimum in the training process. Then, the area where Loran-C signal propagates is rasterized, and each grid is marked to establish a database. Through the training of GA-BP, the network coefficients corresponding to each grid are obtained, and a complete ASF correction prediction database is established. Finally, the ASF modified prediction database is used to calculate the predicted value. Comparing with the actual value, the results show that the method is feasible. Keywords: Loran-C · ASF · Rasterization · Neural network

1 Introduction As an important part of the national integrated PNT system, Loran-C navigation system uses low-frequency and high-power signal, which propagate along the surface and has strong anti-interference ability. In the field of military applications, it can be used as an important backup means of satellite navigation, which is of great significance. However, the positioning performance of Loran-C is far lower than that of satellite navigation system. Therefore, in order to effectively improve the positioning accuracy of Loran-C, the time delay in the process of signal propagation must be corrected [1]. At present, the accuracy of Loran-C navigation and positioning is mainly affected by the ASF propagation delay in the process of signal propagation. Through the study of the propagation characteristics of long wave signal broadcast by Loran-C navigation system, the propagation signal will be affected by many factors, such as weather, terrain and so on, resulting in large delay and poor navigation accuracy. The paper [2] used the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 487–495, 2021. https://doi.org/10.1007/978-981-16-3142-9_46

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Millington algorithm to predict the ASF value, but did not consider the earth elevation, atmospheric refractive index and other factors. So the prediction of ASF value is quite different from the actual value. The paper [4] used BP neural network algorithm to predict ASF value, but only the relationship between longitude, latitude and ASF is considered. And did not consider the factors such as temperature, humidity and earth conductivity. So, the prediction accuracy can’t meet the practical requirements. First, the signal propagation path is rasterized according to the earth surface space grid and coding (GJB 8896–2017) standard, and each grid has a unique coding. Then, considering that temperature, humidity, earth conductivity and atmospheric refractive index have great influence on ASF value, an improved BP neural network method based on genetic algorithm (GA) is used to predict ASF value. Finally, the ASF correction database is established.

2 Design of Loran-C ASF Correction Method Based on GA-BP Neural Network The Loran C ASF correction method based on GA-BP neural network is designed in this paper. The premise is that the ASF correction database can obtain the temperature, humidity, earth conductivity, atmospheric refractive index on each grid in real time through the network. ASF correction modeling system consists of integrated user terminal and data server. Among them, the integrated user terminal can obtain the satellite positioning and Loran-C positioning data at the same time, and process the data (based on the satellite positioning data) to obtain the Loran-C signal transmission delay. Then, the information of signal transmission delay and related signal transmitting and sampling location are sent to the data server through the network. Then, the data processing server associates the acquired data of sampling time with the corresponding data of temperature, humidity, earth conductivity and atmospheric refractive index from the Internet to form training samples [8]. Finally, the Loran C ASF correction method based on GA-BP neural network proposed in this paper is used to train long-term accumulated samples and generate Loran C ASF correction database (Fig. 1).

Fig. 1. Loran C ASF correction system connection diagram

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2.1 ASF Revises Database Design Strategy The design of ASF correction database is based on the earth surface space grid and coding method specified in the earth surface space grid and coding standard [5] (GJB 8896–2017). The method can divide the earth surface longitude latitude coordinate space into 32-Level grid at most. Each grid can cover the earth surface space seamlessly and without overlapping, and each grid can be coded with a global unique integer grid. Therefore, the standard can be used to establish the raster ASF correction database [6] of Loran C navigation system. In this paper, the grid is divided into 9 levels, and the grid size is 1°. Grid naming is composed of global identifier g (the layer 0 identifier) and grid coding, which is expressed as “G + coding”. Grid coding is determined by coding order and longitude, latitude of grid positioning corner. Coding sequence: for each level of grid coding below level 1 grid, z-order coding shall be adopted on the basis of the upper level grid coding. The direction of z-order coding is related to the level 1 grid of the grid, as shown in Fig. 2.

Fig. 2. Grid Z sequence coding direction

This method mainly focuses on grid processing of Loran-C service coverage. Therefore, according to the coding rules of the Northeast hemisphere, the location corner corresponding to each grid code is the southwest corner, and the two boundaries containing the location corner belong to the grid. Firstly, the longitude and latitude of the location corner of the grid are converted into binary. If the converted binary is less than 9 bits, 0 is added before the first binary, and then the latitude and longitude represented by the binary are combined with each other. Finally, every two bits of the 18 bit binary from left to right are converted into a decimal number to obtain the trellis code. Using this coding method, the database is established, and the corresponding relationship between longitude, latitude and coding is established. The format of rasterization is G(long, lat, d). Among them, long and lat respectively represent the longitude and latitude of the positioning corner of the grid, and d is the grid code [4]. As shown in Table 1. 2.2 BP Neural Network Training Method Based on GA Because genetic algorithm optimizes the initial weight and threshold of BP algorithm, it can better avoid BP algorithm falling into local minimum and accelerate algorithm convergence, so this paper uses this method to predict ASF value of Loran C.

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Latitude

71

50

Binary

01000111

00110010

Binary(9 bits)

001000111 000110010

Decimal

G000001101000011101 → G001220131

Firstly, the original data are normalized to get the input data of BP neural network; Then the initial weights and thresholds of the optimized BP neural network are obtained by GA; Finally, the optimized initial weights and thresholds are used to train the neural network, and the final weights and thresholds of the neural network are obtained. The rasterized ASF correction database is composed of the optimized initial weights and thresholds and the rasterized ASF code obtained in 2.1. The specific process is shown in Fig. 3 [10].

Measured sampling data of mobile platform Meteorological data

Database

GIS MAP Information base

The standard training sample data is generated and stored No

Normalized input data Neural network model training for non-real time ASF delay correction data Generating the weight parameter file of neural network model

Yes

Is enough model training sample data collected

The initial weight and threshold of BP neural network after optimization is formed by genetic algorithm

Generating raster ASF data correction Database End

Fig. 3. A modified algorithm of Loran C ASF based on GA-BP neural network

3 Loran-C ASF Correction Method Based on GA-BP Neural Network 3.1 The Initial Weights and Thresholds of BP Neural Network Are Obtained by Genetic Algorithm 1. Initial weights and thresholds of randomly generated BP neural networks. The generated weights and thresholds are connected in the order of input layer- hidden layeroutput layer to generate N chromosomes.

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In this paper, BP neural network is a 4 × 5 × 1 structural network, so the length of a single chromosome is 31. 2. The fitness function F(x) = c − E is used to calculate the fitness value of each chromosome in the population generated in step 1), where c is the constant with larger value; 3. According to the fitness value of each individual in the population, they are arranged in descending order. The selection probability of each individual in the population is the ratio of the fitness value of the individual to that of the whole population. 4. Arithmetic crossover is used in crossover operation. There are two individuals x1   and x2 , new individuals x1 and x2 are generated by crossover operation. 



x1 = αx1 + (1 − α)x2  x2 = αx2 + (1 − α)x1

(1)

5. Uniform variation method was used. x1 = Umin + r(Umax − Umin )

(2)

[Umin , Umax ] is the range of chromosome values. r is a random number uniformly distributed in the range of [0,1]. 6. If the exit condition is satisfied, the initial weights and thresholds of BP neural network are obtained; otherwise [10], go to step 2) (Fig. 4);

Generating initial weights and thresholds of BP neural network

Produce initial population Calculate fitness Selection Crossover Variation No

Preserve the best individuals

Whether the optimal criteria or the maximum number of cycles are met

Choose the best individual The optimized BP neural network weights and thresholds are formed

Yes

Fig. 4. Flowchart of optimizing initial weights and thresholds of BP neural network by GA

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3.2 2BP Neural Network Algorithm 1. According to the positioning data of the satellite receiver, the grid G of the user is determined. And determine the grid coding. The propagation distance of Loran signal in the grid is calculated, and the unit transmission delay of the grid is obtained. 2. The temperature, humidity, earth conductivity and atmospheric refractive index [9] of grid G at k time are taken as the input of BP neural network. The network input is Xk = [xk1 , xk2 , xk3 , xk4 ](k = 1, 2, · · · N ). ASF value of grid G at k time is taken as the output of BP neural network. The network output is Yk = (yk1 )(k = 1, 2, · · · N ).yk1 is the unit transmission delay of a grid in the propagation path of Loran signal. 3. The weights and thresholds obtained by GA are used as the initial weights and thresholds of BP neural network to train the samples. i is the neuron in the input layer, j is the neuron in the hidden layer, and q is the neuron in the output layer. Then the weight between the input layer and the hidden layer is ωij , and the weight between the hidden layer and the output layer is γjq .  The input of the jth neuron in the hidden layer is kj = 4i=1 ωij xki +σj , where σj is the threshold of the jth neuron. The neuron output is: akj = f (kj ).  The input received by output layer neurons is kq = N j=1 γjq akj , The last output is bkq = f (kq + θq ),θq is the threshold of the output layer. f () is a hyperbolic function. 4. So the cost function of time k is N Ek =

q=1 (bkq

− ok )

(3)

N

5. The gradient descent strategy is used to dynamically adjust the weights and thresholds of the hidden layer and the output layer to minimize the cost function E at time k, and the optimal weights and thresholds of the grid at time k are obtained (Fig. 5).

Earth Conductivity

Atmospheric Refractive Index ASF Temperature

Humidity

Input Layer

Hidden Layer

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Fig. 5. The structure of BP neural network for predicting ASF value

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3.3 Propagation Delay Correction of Non-real Time ASF After the user platform obtains the coarse positioning results, it calculates the grid GJ , J = 1, · · · m on the signal propagation path. According to the environmental information of signal propagation path, generate the input data of grid GJ . According to the rasterized ASF correction database, the delay correction DJ of each grid GJ is obtained. Finally, the correction of ASF propagation delay is obtained. As show in Fig. 6. Start GIS map information base According to the initial location of the user platform, determine the grid GJ where the platform is located

Calculate and determine the grid GJ through which the user platform receives the signal propagation path

Real-time meteorologica l data

The model input data of the grid GJ is generated according to the transmission path environment information

Calculating ASF delay correction data DJ of grid GJ with ASF correction database Generate grid GJ correction on propagation path, (J=1, ,m); Sent to the user platform

User platform calculates full path ASF propagation delay correction ΔASFJ And modified propagation delay End

Fig. 6. Non-real-time ASF propagation delay correction flowchart

4 Simulation Example The long wave signal transmitted by PuCheng station is used for training and testing. The temperature, humidity, earth conductivity, atmospheric refractive index in about half a year are recorded, and the recorded data is used as the input of neural network. The theoretical value is calculated according to the satellite data, and the difference is made with the value obtained by Loran receiver, and the difference is taken as the output of neural network. Using the grid code of GIS map and the weight of GA-BP algorithm, the raster ASF correction database is established. According to the meteorological data of each grid on the propagation path, combined with the established database, the signal propagation delay of the whole path is calculated. 200 sets of data were used for verification, and the predicted values were compared with the measured values. In Fig. 7, the red line represents the measured value and the green line represents the predicted value. Figure 8 shows the error between the measured and predicted values of 200 groups in Fig. 7. As can be seen from Fig. 8, the overall error is less than 100 ns.

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Fig. 7. Measured and predicted values of Loran-C signal propagation

Fig. 8. Error between prediction value and true value of Loran-C signal propagation

5 Summary The time delay of Loran-C signal on land includes PF, SF and ASF. Among them, PF and SF can be obtained more accurately by calculation, but the factors affecting ASF are complex and cannot be obtained more accurately by calculation. Therefore, the neural network weights of each grid on the propagation path are obtained by GA improved BP neural network algorithm. Secondly, the path of signal propagation is gridded and coded according to the standard of earth surface space grid and coding (GJB 8896–2017). Finally, the ASF correction database is established by one-to-one correspondence between the grid coding and the weight. Finally, according to the established database, the ASF value is predicted. The simulation results show that the proposed method is reasonable and effective, and can better meet the requirements.

References 1. Wunong, X., Bian, S., Chen, Y.: Studyon ASF correction of loran C ground wave propagation. Ship Electron. Eng. 31(10), 49–51 (2011) 2. Zhan, J., Chen, Y., Li, W., Han, B., Zhu, R.: Millington’s method and forecasting of loran C signal’s propagation. Ship Power Technol. 29(6), 6–9 (2009) 3. Huang, X., Yang, D., Lin, H.: Methonds of ASF correction in Loran-C system. Comput. Eng. Appl. 11(45), 144–146 (2009) 4. Xu, B., Shi, W., Huo, L.: ASF correction of loran-C based on BP neural network. Ship Electron. Eng. 26(2), 71–72 (2006) 5. GJB 8896–2017, Earth’s surface spatial grid and code (2017) 6. Pyo-Woong, S., Joon, H., et al.: Universal kriging for loran ASF map generation. IEEE Trans. Aerospace Electron. Syst. 55(4), 1828–1842 (2019) 7. Tong, H., Xu, H., Kong, J.: The emulational analysis for Loran C/Beidou integrated navigation method. Ship Sci. Technol. 32(1), 99–103 (2011) 8. Li, R., Su, J., Wang, N.: Analysis the error of the ASF in long-wave time service. J. Astronaut. Metrol. Meas. 32(3), 17–20 (2012) 9. Zhang, Y., Li, S., Li, H.: Research on high precision atmospheric refractive index interpolation method. Electron. Opt. Control 26(7), 65–69 (2019) 10. Ahua, M., Zhou, S., Liu, Q., Jin, X.: Using genetic algorithm to improve BP training algorithm. Comput. Simul. 22(2), 150–151 (2005)

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11. Yan, H., Cheng, W., Pan, Y., He, G.: A quick self-adaptive algorithm of BP network based on genetic algorithm. Comput. Simul. 22(1), 103–106 (2005) 12. Fang, Y., Jiang, Z., Gui, W.: ASFC-based DNN modeling for prediction of silicon content in blast furnace ironmaking. In: The 13th World Congress on Intelligent Control and Automation, pp. 527–533 (2018)

On Precise Inertial Force Modeling for Autonomous Orbit Propagation in Earth-Centered Fixed System for Earth Satellites Haihong Wang1(B) , Jingshi Tang2(B) , Jinjun Zheng1 , Qiuli Chen1 , Chengbin Kang1 , Weisong Jia1 , and Shaojun Bi1 1 Institute of Telecommunication and Navigation Satellites, CAST, Beijing, China 2 School of Astronomy and Space Science, Nanjing University, Nanjing, China

[email protected]

Abstract. It has been a common practice to propagate satellite orbits in Earthcentred inertial system, such as the dynamic J2000 mean-equator-mean-equinox system or the International Celestial Reference System. Nonetheless, we can occasionally find in papers that orbits are propagated in Earth-centred fixed (ECF) system in various applications. For navigation purposes, it is always wondered by our fellow colleagues whether using the ECF system for orbit propagation, which is consistent to GNSS product, can spare the trouble of constant reference frame conversions and lessen the dependency on the Earth Orientation Parameters (EOP). Here in this paper, we quantitatively investigate the precise modelling of inertial forces for orbit propagation in ECF systems (OPECF). We focus on the navigation purpose and test various OPECF models on the Earth medium and geosynchronous orbit satellites. We show that, as long as the propagation errors need to be contained, orbit propagation in ECF system still requires complicated and careful EOP modelling to handle the inertial forces on the rotating system. Keywords: Orbit propagation · Earth-centered fixed system · Inertial force modeling

1 Introduction Orbit propagation (OP) onboard the Earth medium and geosynchronous orbit satellite is essential for implementation of future autonomous operation of GNSS constellations. Normally, the application would involve orbit propagation, without filtering, for a typical length of 2 to 4 h, with high accuracy and high efficiency. The normal practice of orbit propagation is in the Earth-centred inertial (ECI) system, while the GNSS product is about Cartesian coordinates in the Earth-centred fixed (ECF) system. Therefore, it seems redundant and costly that the reference frames are converted back and forth to calculate the geopotential acceleration. Besides, the dependency on the accurate Earth Orientation Parameter (EOP) is also a problem for onboard autonomous © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 496–504, 2021. https://doi.org/10.1007/978-981-16-3142-9_47

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operation. Therefore, whether sticking to the ECF system for OP lessens the requirement becomes a natural question. Propagating the orbit in body-fixed rotating system requires a fictitious inertial force, which is related to precise modelling the angular momentum and its variation. Although OP in body-fixed system is not new in papers (see e.g., Huang et al. (2016), Montenbruck and Ramos-Bosch (2008), Scheeres et al. (1996)), but modelling details are rarely discussed. This may not be a problem for qualitative analysis in asteroid exploration (Scheeres et al., 1996) where the angular velocity can be considered fixed in terms of both magnitude and orientation, or to be used in filtering onboard user satellite with an expected orbit accuracy of a few meters (Montenbruck and Ramos-Bosch, 2008) where small insignificant modelling errors can be corrected in time by process noises. However, mismodeling the inertial force could be a problem if the model errors are left unchecked during onboard OP. Precise OPECF modelling requires delicate handling of Earth precession and nutation, as well as other seemingly insignificant contributions from EOP (DUT1 and polar motions). No matter what frames are adopted for ECI and ECF systems, the conversions consist of all these fundamental contributions. Without loss of generality, we choose in this paper the mean J2000 system, WGS84 and the rotations using IAU1976/IAU1980 models based on the dynamic J2000 mean equinox (see e.g., McCarthy and Petit (2003), Montenbruck and Gill (2000)). The problem is investigated in the background of autonomous operation, where the orbit is propagated for 4 h. For high accuracy, OPECF error is expected to be contained within 1 cm and exhibits no significant growing trend. The paper is organized as follows. the equations of motion for the OPECF problem in Sect. 2, together with the relevant models. In Sect. 3, various OPECF models are tested, including a complicated reference model and three approximated models for comparison. Discussions and conclusions are presented in Sect. 4.

2 The Equation of Motion and the Inertial Force It is unconventional that the Earth satellite orbit is propagated in the ECF system, so details in previous literatures are insufficient to show the cost of OPECF and thus the advantage or disadvantage cannot be fully estimated. Overall Earth rotation consists of various complicated motions. The point of modelling the details is that the Earth rotation is nonuniform, in terms that both the angular rate and the rotation axis vary over time nonuniformly. Failing to precisely model these details may lead to inaccurate inertial force, which could contribute to error accumulation over time. In this section we first present the equation of motion to be integrated in ECF and then analyse the motions and model the inertial force. 2.1 The Equation of Motion in the Rotating Frame By denoting the parameters in inertial and non-inertial frames with small and capitalized letters, it is obvious that we need to find the following relation   ¨ = R ¨ R,  R, ˙ r¨ R (1)

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˙  ¨   Where R , R , R are position, velocity and acceleration vectors in ECF, while r¨ is the acceleration vector which has the same form as we normally calculate in ECI. The equation of motion in a rotating frame is available in textbooks on analytical mechanics (see e.g., Liang (2016)), which reads as follows      ¨ = r¨ − 2ω ˙ − ω  − dω  R  ×R × ω  ×R  dt × R (2) 

where ω is the rotation velocity of the non-inertial frame with respect to the pole of ECI, which is perpendicular to J2000 mean equator for the mean J2000 system. In (2), the first acceleration is the one we normally calculate in ECI, retaining the same form but with ECF Cartesian coordinates. It has the following form,         μ   + F lunisolar R  + F SRP R  + F drag R,  R ˙ r¨ = − 3 R + Fgeopotential R (3) R which includes the two-body gravitation and various perturbing accelerations like geopotential, lunisolar gravitation, solar radiation pressure (SRP), atmospheric drag and so on (Liu 2000). The second acceleration is the Coriolis force exerted on a moving object in a rotating frame, while the third acceleration is the centrifugal force. Both accelerations involve  ω , which can be obtained by rotating (0,0,0) (suggesting no rotation in ECI) to ECF. During each rotation, one has to consider the variation of the rotation angle. By taking rotating angle α about x axis as an example, the equation reads  T ω  out = Rx (α)ω (4)  in + α˙ 1 0 0 



in

out

where ω and ω are input and output rotating vectors corresponding to the original and new frames. Rx (α) is the rotation matrix about the x axis, with a rotation angle of α and an angular rate of α˙ . The rate α˙ has to be calculated carefully to include all necessary factors. The fourth acceleration, often referred to as the Euler acceleration, is even more   complicated, since we have to further model the variation of the rotation axis d ω dt, which requires the acceleration of the rotation angle. The inertial forces come from the rotations between ECF and ECI. As it is implemented based on the IAU1976/IAU1980 model, the rotation matrix can be written as:  = (PM )(ER)(NU )(PR)r R

(5)

where the precession (PR), nutation (NU), Earth rotation (ER) and polar motion (PM) rotation matrices are (PR) = Rz (−zA )Ry (θA )Rz (−ξA ) (NU ) = Rx (−ε −ε)R  z (−ψ)R   x (ε) (PM ) = Ry −xp Rx −yp (ER) = Rz (SG )

(6)

The rotation angles represent the precession arguments (zA , θ A , ξ A ), the nutation arguments (ε, ψ), the Greenwich apparent sidereal time (S G ) and the polar motion

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arguments (x p , yp ). Their definitions and notations follow the common conventions (McCarthy and Petit, 2003). It is their analytical formulas, as well as the variation of EOP, that matter to modeling the inertial forces, which will be discussed in the following subsections. 2.2 The Coriolis Force and the Centrifugal Force Both the Coriolis force and the centrifugal force require the rotation velocity of the non-inertial frame. As is previously shown, Eq. (4) has to be repeated for each rotation and a complete rotation sequence (6) requires first order time derivatives of all relevant rotation angles. For precession arguments, only the linear rates are used while higher order terms are ignored:   (7) ξ˙A = z˙A = 2306 .2181 c , θ˙A = 2004 .3109 c where the angular rates are in arcsecond per century (also applied to the following rates). For nutation arguments, the linear rates of the amplitudes are small (A1j , B1j in (8)), however, the contributions from the change rates of the lunisolar fundamental arguments are not trivial and must be considered, which have the following form ⎧  5 

106 5 ⎪   ⎪ ⎪ ⎪ ψ˙ = kji α˙ i (t) cos kji αi (t) A0j + A1j t ⎪ ⎪ ⎨ j=1 i=1 i=1 (8)  5 

106 5 ⎪ ⎪   ⎪ ⎪ ˙ε = kji α˙ i (t) sin kji αi (t) B0j + B1j t ⎪ ⎪ ⎩ j=1

i=1

i=1

where the change rates of the fundamental arguments are (9) Only the linear rates of the fundamental arguments are considered while higher order terms are ignored. It is obvious that due to the relatively large change rates, their contribution to the nutation arguments is not negligible. For the mean obliquity and the Greenwich mean sidereal time, the change rates are accounted for with their respective linear terms, which are   ◦ ε˙ = −46 .8150 c , S˙ G = 87900h .0513367 c (10) based on which the change rate of the equation of equinoxes (EE) can be derived   d (μ) dt = d (ψ) dt · cos ε (11) The discussion is not yet completed, since the EOP variations have not been accounted for. The DUT1 and x p , yp arguments have no analytical forms but are released

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0.02 0.01 0 -0.01 0 10

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Fig. 1. Day-to-day change of Earth rotation parameters

in tabulated format and are usually interpolated when being used. Figure 1 shows the EOP day-to-day change from January 1972 to April 2019. The polar motion has linear rates within 0 .01/d ~ 365 .25/c, while that of DUT1 is within 4 × 10–3 s/d, which amounts to about 0 .06/d ~ 2191 .5/c. These rates are taken into account by using (4). For DUT1, it is added to the overall rate of Greenwich apparent sidereal time as follows   S˙ G = S˙ G + d (μ) dt + d (DUT1) dt

(12)

The rates of EOP appear small but cannot just be ignored for granted. Later we will test them by examining the OP errors when DUT1 rate is respectively included and excluded. 2.3 The Euler Force 

The Euler force involves the time derivative of ω . This term is always ignored in qualitative analysis, for example in asteroid exploration (Scheeres et al., 1996) or in conceptual demonstration (Huang et al., 2016), where rotation models are not yet clearly defined or are not significantly relevant. While in our case, centimeter-level accuracy is required, and the Euler force has to be quantitatively accurate.   Taking the rotation about x axis as an example, the rotating vector d ω dt in the original and new frames are related as follows     T    dω  dt out = Rx (α) d ω ˙ x (α)ω  dt in + αR  in + α¨ 1 0 0

(13)

where the notations are consistent with (4) and Rx  (α) is the partial derivative matrix of Rx (α) with respect to rotation angle α. For the first rotation, the equation is     T dω  dt out = α¨ 1 0 0

(14)

The first-order time derivative of α has been sufficiently discussed in the previous subsection. For the second-order time derivative α, ¨ most arguments have negligible higher order terms with time, which can be safely ignored. Exceptions are the nutation

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arguments, which vary periodically and the relatively rapid change of lunisolar fundamental arguments contribute to nonnegligible variations in the nutation arguments, as well as the EE term which affects the Greenwich apparent sidereal time. Mathematically speaking, the following second-order time derivatives (accelerations) have to be considered ⎧  5 2  5 ⎫ 106 ⎨ ⎬ 2   d + A t k α ˙ (t) sin k α (t) = − A (ψ) 0j 1j ji i ji i ⎭ ⎩ dt 2 j=1 i=1 i=1 ⎫ ⎧  5 2  5  106 ⎨ ⎬   (15) d2 kji α˙ i (t) cos kji αi (t) − B0j + B1j t (ε) = 2 ⎭ ⎩ dt j=1

i=1

i=1

d2 d2 d2 SG = 2 (μ) = 2 (ψ) · ε 2 dt dt dt

3 Numerical Tests Our tests are twofold. First, we need to verify that the proposed models of inertial forces for OPECF are sufficiently accurate compared to the solutions obtained in the ECI system. To that end, it is noteworthy that the fictitious inertial forces act on the system as a whole, regardless of the actual dynamical model (3). So, we choose to compare the OP results in a two-body problem (TBP). One reason that the TBP is used is that TBP in ECI has strict, analytical, closed form solutions. Any deviation from the TBP solution can be attributed to the error of the ECF solutions. The other reason is that since the inertial force reflects the rotating frame itself, regardless of the perturbing forces, OPECF mismodeling errors affect the actual perturbed two-body problem generally as much as the TBP. The second purpose of the tests is to demonstrate the necessity of the proposed model, which answers the question whether integrating the equation of motion in ECF has lesser requirement on rotation model complexity and EOP. For this, we select three alternative models which are slightly simplified. The selected models for the tests are listed in Table 1. The models slightly differ regarding how the Greenwich apparent sidereal time is handled. Except for the excluded terms, Models B, C and D handles the inertial forces the same way as Model A. The tests are performed to an arbitrary geosynchronous orbit satellite, with the following initial elements ◦

a = 42171.3822 km e = 0.0025463 i = 56 .4263 ◦ ◦ ◦

= 86 .2642 ω = 176 .9579 M = 181 .2697

(16)

We also arbitrarily select two initial epochs, as follows (t0 )1 = 2009y 06m 09d 16h 48m 46s .998 (t0 )2 = 2013y 12m 09d 16h 48m 46s .998

(17)

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Models Note A

Complete model, including all contributions discussed in Sect. 2. EOP linear rates are included

B

Excluding DUT1 rate, EE rate and EE acceleration

C

Excluding EE rate and EE acceleration

D

Excluding EE acceleration

For each test, the orbit is propagated for 4 h. The unperturbed ellipse in ECI is converted to Cartesian coordinates, which are then rotated to ECF system. These solutions are considered as true reference values. On the other hand, orbits are also propagated in ECF, with models in Table 1 to handle the inertial forces. The OPECF solutions are compared with the true reference values, in both the Keplerian elements in ECI and the Cartesian coordinates in ECF. For the Keplerian elements, we show the differences between in-plane elements (semi-major axis a, eccentricity e, and argument from ascending node λ = M + ω) and the differences between the orientation elements (inclination i and right ascension of ascending node ). The comparison results of both tests are plotted below. 3.1 Results of Test no. 1 Test NO.1 has an initial epoch of (t 0 )1 . The comparison results of the four models are plotted in Fig. 2 to Fig. 3.

Fig. 2. OPECF error of test NO.1 using Model A (left) and Model B (right). The errors of inplane elements (a, e, λ), orientation elements (i, ) and ECF Cartesian (x, y, z) are plotted in the top, center and bottom panels respectively. For element errors, they are all converted to distance by multiplying the Earth equatorial radius of the reference ellipsoid (~6378.137 km) so different elements can be plotted in the same panel. OPECF results in the following figures are organized in the same way

3.2 Results of Test no. 2 Test NO.2 has an initial epoch of (t 0 )2 The comparison results of the four models are plotted in Fig. 4 to Fig. 5.

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Fig. 3. OPECF error of test NO.1 using Model C (left) and Model D (right)

Fig. 4. OPECF error of test NO.2 using Model A (left) and Model B (right)

Fig. 5. OPECF error of test NO.2 using Model C (left) and Model D (right)

4 Discussion and Conclusion We present in this paper a precise modeling of inertial forces for orbit propagation in the Earth-centered fixed system. The tests show that the proposed model can guarantee millimeter-level accuracy. The overall position errors are within 2 mm in 4 h, exhibiting no growing trend. However, the tests also suggest that for centimeter-level accuracy, modeling the    inertial forces is not simple. The rotation vector ω and its time derivative d ω dt have to be modeled with sufficient details. Even neglecting the EE acceleration results in up to 3 cm to 4 cm OP error within 4 h, with obvious growing trend. Based on the analysis and the numerical tests, we do not think integrating the equation of motion in ECF is more favorable than in ECI, especially for practical precision

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applications such as GNSS onboard calculation. The requirement on the rotation model is not lessened and it still needs complicated models to keep centimeter-level accuracy. Acknowledgement. This work is supported by the National Natural Science Foundation of China (Grant No. 11873031), the Foundation Program of Basic Enhancing Plan (2019-JCJG-JJ-441) and the Fundamental Research Funds for the Central Universities (020114380037).

References Huang, L., Shuai, P., Zhang, X., Lin, Q.: A method of pulsar-based dynamic or-bit determination in the earth-fixed reference frame for near-earth spacecraft. J. Astronaut. 37(8), P895–900 (2016) (China) Montenbruck, O., Ramos-Bosch, P.: Precision real-time navigation of LEO satel-lites using global positioning system measurements. GPS Solut. 12, P187–198 (2008) Scheeres, D.J., Ostro, S.J., Hudson, R.S., Werner, R.A.: Orbits close to asteroid 4769 castalia. Icarus 121, P67–87 (1996) McCarthy, D.D., Petit, G.: IERS Convention 2003. International Earth Rotation and Reference Systems Service Central Bureau, P33–56 (2004) Liang, K., Ju, G., Shi, Y.: Mechanics (ed. 4), Higher Education Press, Beijing (2016) (China) Liu, L.: Orbit Theory of Spacecraft, National Defense Industry Press, Beijing (2000) (China).

A Beidou Laser Link Allocation Scheme Based on Network Throughput Optimization Zheng Huang(B) , Wenbin Gong, and FengWei Shao 99 Haike Road, Pudong New Area, Shanghai, China

Abstract. The Beidou-3 navigation system has carried out the experimental scheme design of laser intersatellite link [1], and according to the characteristics of laser intersatellite link, the conception of spatial backbone network is put forward. Taking this backbone network as the breakthrough point, this paper analyzes the network throughput of Beidou-3 inter-satellite link, and points out that the main bottleneck restricting the network performance lies in the transmission capacity of the inter-satellite link. To solve the problem of topology optimization of high-speed inter-satellite link network, aiming at matching the network throughput between the satellite-ground link and the inter-satellite transmission link, a Beidou laser link allocation scheme based on network throughput optimization is proposed, and the link allocation is realized by searching through a Dijkastra algorithm based on the longest visibility. Simulation results show that the link allocation scheme based on this algorithm can match the data throughput between satellite-ground link and inter-satellite link, solve the bottleneck problem of satellite-ground transmission and improve the network throughput. Keywords: laser network · Throughput · Minimum hops · Inter-satellite routing

1 Introduction At present, Beidou-3 satellite navigation system has been successfully networked, providing global users with "all-weather, all-day, high-precision" positioning [2]. At the same time, Beidou navigation system’s unique short message system [3] has also become Beidou’s characteristic. However, there are more and more on-board business data generated by constellations, which makes it difficult to land the data, which is mainly manifested in the mismatch between the amount of business data accessed between satellites and the amount of data transmitted between satellites and ground. Different from GPS global base stations, China can only set up ground base stations in China. In order to communicate with overseas satellites, inter-satellite links have been established. However, the shortcomings such as low communication rate and small capacity between satellites are gradually revealed.The next generation BDS needs to solve these problems. At present, there has been a great deal of research on the design of inter-satellite link allocation scheme, but there are few articles about coordinating the amount of data transmitted between satellites and the ground. Dong Mingxi [5] aims at the parameters such as link utilization, end-to-end transmission delay and link space geometry, and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 505–514, 2021. https://doi.org/10.1007/978-981-16-3142-9_48

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uses simulated annealing algorithm to solve the global optimal topology. Wang Junying et al. [6] proposed a spatial information network link allocation scheme based on access traffic distribution, aiming at the problem that the uneven distribution of ground access traffic leads to link congestion in some areas. Liu Canyou studied the design of the highspeed inter-satellite link of navigation constellation, and completed the pre-allocation of the connection of each node in the inter-satellite link by using the optimized Dijkastra algorithm in the way of finite state machine. In this paper, according to the existing spatial network configuration, the intersatellite backbone network is constructed. Aiming at the problem of inter-satellite satellite-ground link throughput mismatch, a Beidou laser link allocation scheme based on network throughput optimization is proposed. The characteristics of China’s satellite ground stations and Beidou laser inter-satellite link are fully considered, and the high-speed communication and high-precision measurement requirements of navigation satellite inter-satellite links are taken into account. Combined with the characteristics of low and high orbit constellations, the network throughput, link utilization, end-to-end transmission delay, traffic load balance and other parameters are taken as optimization objectives In the aspect of chain building, different from the mode of finite state machine [7], the principle of "longest visibility" is adopted to select satellites for chain building, so as to make full use of resources and ensure the maximum use of one-time chain building.

2 Conception of Spatial Network of Next Generation BDS Considering the large communication capacity of laser equipment, the data between MEO satellites can’t make full use of its bandwidth. Introducing LEO constellation as the data access of MEO constellation can not only solve the problem of difficult landing of LEO constellation data, but also make full use of MEO constellation resources. In this paper, the configuration constellation of 24MEO + 3IGSO + 24LEO is taken as an example.It is assumed that each MEO’s load platform is equipped with three laser terminal devices, and the effective pointing range of the link is 0–90. Each IGSO can establish a laser link with MEO, and the beam range has a half cone angle of 80 to the ground axis. IGSO and ground base station carry out high-speed Ka link construction. 2.1 High-Speed Laser Link Between Satellites Different from traditional microwave link communication, space laser communication provides important support for the development of the next generation Beidou navigation system because of its small size, low power consumption and high speed. Due to the limitation of satellite platform resources [9], the laser terminal equipment carried by each satellite is also limited. The MEO satellite of Beidou-3 satellite only carries two laser terminals to carry out the experiment. In the future network design, it is proposed that each satellite be equipped with three or more laser terminal devices to establish laser network links and complete corresponding simulation experiments to achieve the desired results..

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2.2 Inter-satellite Backbone Network The establishment of laser link needs to go through the processes of capturing, scanning, tracking, link building and so on, which is time consuming. Considering the characteristics of MEO constellation, the inter-satellite backbone network carries out permanent laser chain building for satellites that are continuously visible in the same orbit. This backbone network not only reduces the overhead of link construction, but also plays a great role in load balancing of inter-satellite links. Due to the small amount of data generated by overseas satellites, the backbone network takes overseas satellites as transit, which reduces the capacity load of domestic visible satellites and provides a path for overseas satellites to transmit data.. 2.3 Design and Analysis of Laser Backbone Network 2.3.1 Laser Backbone Network Design According to the requirements, the initial laser backbone network is established. For the convenience of analysis and explanation, the satellites are divided according to different orbits, which are explained by the plan. As shown in Fig. 1, all inter-satellite links are linked by laser, and this network is called backbone network. The satellite linked with IGSO is called the target star, and the final routing address of all data in backbone network is the target star. By forwarding the data to IGSO, the on-board data can be landed. According to the principle of the minimum number of hops, the satellite opposite to the target star is selected to link with other orbital planes, and the original target star reached by 4 hops is changed into the target star reached by 2 hops. The landing of overseas stars can also be solved through backbone network. The remaining laser equipment terminals on MEO constellation are used to establish links with LEO constellation, and are responsible for returning on-board data.

Fig. 1. Initial laser backbone network design

2.3.2 Performance Analysis of Laser Backbone Network According to the existing model, the backbone network is simulated, and the parameters are set as the transmission speed of the laser port is 1 Gbps, and the transmission speed of IGSO is 1 Gbps. The following conclusions are drawn:

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1) In the case of ensuring that the network does not appear to be congested, the data is continuously transmitted, and the maximum transmission rate of each satellite is 125 Mbps. 2) When MEO satellite data are evenly distributed, as shown in Fig. 2, the throughput of inter-satellite link is as follows: the maximum transmission rate of each satellite is 142 Mbps, and IGSO output is 1 Gbps.

Fig. 2. Maximum transmission rate when evenly distributed

Through the above analysis, it can be found that when the backbone inter-satellite link rate reaches a relatively high 1 Gbps, each MEO access satellite can only provide an average access capacity of 142 Mbps. Since the normal working method is to return overseas data to the domestic ground station, the throughput capacity of the satellite-toearth link has become the main bottleneck restricting network performance. Based on the above simulation, in order to further improve network performance, it is recommended to increase the rate of IGSO and MEO. At the same time, the export rate of MEO and IGSO is unreasonable. It is recommended to connect some MEOs to ground stations through laser links to achieve high MEO utilization.

3 Optimal Design of Next Generation Beidou Space Laser Backbone Network 3.1 Low, Medium and High Mixed Constellation Design Considering that China’s satellites can only set up stations on the ground, and LEO satellites are fast and have short visibility to ground base stations, it is difficult for LEO constellation to communicate with the ground, so it is proposed to consider that the next generation Beidou system will undertake the access of some communication data of LEO constellation. Backbone inter-satellite links can be established between space MEO satellites and between MEO and IGSO satellites. Because IGSO has good visibility to the ground, IGSO satellites are given priority in the scheme design to communicate with the ground through high-speed Ka data transmission links with more stable communication links, so as to realize data interaction between space network and ground network. With the above-mentioned initial scheme, the throughput of the satellite-ground link restricts the throughput of the whole network between satellites. In order to make up for the problem of insufficient IGSO data, this paper plans to select some MEOs for laser communication with the ground to optimize the overall performance of the network, as shown in the Fig. 3.

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Fig. 3. Low, medium and high mixed constellation design

3.2 Improved Laser Backbone Network Design 3.2.1 The Basic Idea For three IGSO, they can link the same ground station at the same time, and analyze its visibility to Beijing, Sanya, Kashgar and Weinan (the lowest elevation angle is calculated at 10). One IGSO is invisible to the ground station for one hour every day, while three IGSO are invisible to the ground station at different times. In view of the above situation, it is considered to set up two Ka communication devices for each one. since one IGSO is invisible to the ground station, the MEO can switch to the other IGSO for ground communication, so as to ensure that the MEO keeps permanent link building for the ground station through the IGSO. Or GEO is introduced, and GEO is continuously visible to the ground station. when IGSO is invisible to the ground, MEO will link GEO with laser, and GEO will transmit to the ground station through Ka link. For the convenience of analysis, this paper holds that IGSO is "permanently visible" to the ground. For LEO constellation, taking MEO2 as an example, it is concluded that if it is linked with LEO with visible time exceeding 1 h, the built-in chain rate in one cycle can reach 83.33%, and if the visible persistence is not considered, it can be permanently linked with LEO constellation. As the LEO constellation is internally linked, if a MEO satellite is linked with the LEO constellation, the data of the LEO constellation can be transmitted to the satellite all the time. The LEO constellation will not be described in detail later, but will be reflected only by the probability of the accessed data. For MEO constellation, different orbital planes are used to distinguish the visibility of ground stations, as shown in Fig. 4. With the granularity of 15 min, in a regression period, the three orbital planes are always invisible to the ground intersection for a period of time, and the invisibility rate of the orbital planes is 11.46%. During this period, the satellites on this orbital plane are all overseas satellites, and the data can only be transmitted back to the ground station through IGSO. Considering the limited amount of data sent by IGSO, the link between the track plane and the other two ground-visible track planes is established by laser, and the data is transmitted back to the ground. In addition, the visibility rate of more than one MEO to the ground in each orbital plane is 84.8%, so it is considered to select MEO satellites in the same orbital plane for laser link building of ground stations. According to the above characteristics, MEO’s visibility to the ground can be divided into two situations according to different track surfaces, as shown in the figure. In the first

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Fig. 4. Visibility of different tracks facing the ground

case, all three track surfaces are visible to the ground, and in the second case, one track surface is invisible to the ground station. For the first case, consider selecting a MEO for laser link building with the ground, and no link building communication between different tracks; In case 2, two MEOs are selected from the track surface visible to the ground station for laser link building, and another MEO is selected for link building with the track surface invisible to the ground (Figs. 5 and 6).

Fig. 5. Case 1 The track surface and the ground station are both visible

Fig. 6. Case 2 Invisible between track surface and the ground station

3.2.2 A Minimum Hop Count Dijkastra Algorithm Based on Longest Visibility Hop number refers to how many routes data need to pass from a satellite node to the output terminal, while the minimum hop number refers to different configurations of

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the whole network, and compares the hop numbers to select the network configuration with the minimum hop number. According to the requirements of the backbone network, considering the constraints of the system, several laser nodes are selected from several satellite nodes to achieve the minimum hop count of the whole backbone network. min Z =

M 

ti pi + λf

(3.1)

i=1

In the formula, t represents the time length of each stage, p represents the average hop count of this stage, f represents the switching times between laser links, λ is the weight, and the two numbers before and after the plus sign are balanced in the same order of magnitude. The conditions are   (3.2) Ek = eij , i = 1, 2, 3, . . . . . . , N , j = 1, 2, 3, . . . . . . , N   Vk = vij , i = 1, 2, 3, . . . . . . , M , j = 1, 2, 3, . . . . . . , M

(3.3)

Dk = [di ], i = 1, 2, 3, . . . . . . , N

(3.4)

In the formula, e indicates the visibility among 24 MEOs, v indicates the visibility of IGSO to MEO, and d indicates the visibility of MEO to ground station. Eij represents the duration of continuous visibility from the current time, which is obtained according to the visibility matrix per minute. For example, at time t, P minutes can be seen between I and J, and the value of eij is t + p, which can maximize the visibility between satellites. All k represents a matrix mark in minutes. The specific algorithm steps are as follows: 1) Using the visibility matrix, select IGSO and track surface to build chain. 2) According to the visibility of MEO to the ground, judge the situation. Case 1: Intra-orbit communication does not support off-orbit communication. Calculate the time T and the number of hops in this case. Case 2: Off-orbit communication, calculate the communication duration in this case, select MEO which can be seen to the ground in the other two orbital planes to build links, recalculate the intra-orbit communication duration in the previous stage, calculate the communication duration in this case, and calculate the hop count respectively. 3) The total hop count calculated by comparison is ignored if it is greater than the original hop count; if it is less than the original hop count, it is overwritten and the link routing table is recorded. 4) Continue to steps 1–3. 5) Output the routing table with the least number of hops. According to the above algorithm, the link establishment status between the satellites can be obtained at the minimum number of hops in a regression period.

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4 Performance Analysis In this paper, the STK simulation software is used to build a simulation scene, which lasts for 7 days and a regression cycle. The visibility of each minute is exported to a matrix, and the corresponding processing is carried out. The algorithm search is carried out by using Matlab, and the network link-building state in a cycle is obtained. According to different situations, the throughput of the network is analyzed. Among them, MEO satellites linked with LEO constellation generate data on MEO with a probability of 80%. 4.1 Throughput When the Heterogeneous Network is not Communicating In this case, a link is built in the same orbit, and an MEO is selected to communicate with the ground, and IGSO communicates with the ground through a high-speed Ka link. Each satellite leaves a capacity of 50Mbps for navigation service data. The simulation shows that when the amount of data connected to LEO reaches 363 Mbps, the network outputs 1821 Mbps, which can be transmitted without blocking, and the average number of hops in this situation is 2.375. The probability of occurrence is maintained at 80% (Fig. 7).

Fig. 7. The relationship between transmission data and congestion

4.2 Throughput of Inter-orbit Network Communication In this case, an MEO whose orbital surface is not visible to the ground station, establishes a link with the other two orbital surfaces to transmit the accessed LEO service data back to the ground. In this case, the business model is the same as when the off-track network does not communicate. The simulation shows that when the amount of data connected to the LEO reaches 390 Mbps, the network outputs 1742 Mbps, which can be transmitted without blocking, and the average number of hops in this situation is 2.4 hops. The occurrence rate of this situation remains at 20% (Fig. 8).

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Fig. 8. The relationship between transmission data and congestion

5 Concluding Remarks This paper analyzes the network throughput of the existing Beidou-3 inter-satellite link. Simulation analysis shows that the main bottleneck restricting network performance lies in the transmission capacity of the satellite-to-ground link. In order to further improve the network performance, a Beidou laser link allocation scheme based on network throughput optimization is proposed, which improves the speed of IGSO and MEO, and at the same time, connects some MEOs to ground stations through laser links, thus realizing high utilization rate of MEO. Experimental results show that, according to the improved laser network design, the amount of LEO data accessed is 2.5 times that of IGOS, which is significantly improved. The bottleneck affecting network throughput lies in the maximum transmission rate between IGSO and MEO, and the maximum transmission rate between MEO and ground station. All the MEO-equipped laser port devices adopted in this paper have the same performance. In the future design, different performance indicators will be considered for the laser port according to different access targets, such as improving the performance of the laser devices connected to IGSO and ground stations and improving the throughput of the whole network. Since direct sunlight will affect laser chain building, the influence of direct sunlight will be considered in the follow-up to improve chain building.

References 1. Liu, C., Zhang, F., Wang, X., Cao, Y., Zhang, B.: Design and analysis of high-speed intersatellite links in navigation constellations. Academic Exchange Center of China Satellite Navigation System Management Office. The 11th China Satellite Navigation Annual Conference Proceedings-S13 Autonomous Navigation. Academic Exchange Center of China Satellite Navigation System Management Office: Zhongke Beidouhui (Beijing) Technology Co., Ltd., 2020: 6 2. Xin, Z., Junpo, N., Yunqing, L., Shoufeng, T., Shifeng, W.: Integrated laser communication/ranging technology and link characteristics analysis in navigation satellites. Progress Laser Optoelectron. 52(06), 87–93 (2015) 3. Baojun, L., Yingchun, L.: Special topics on beidou global satellite navigation system·editor’s notes . Sci. China Phys. Mech. Astronomy 51(01), 5 (2021)

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4. Longping, Z., Yamin, D., Yingyan, C., Xue Shuqiang, G., Shouzhou, H.D.: Analysis and optimization of Beidou GEO/IGSO/MEO satellite orbit determination ground station configuration . J. Surv. Mapp. 45(S2), 82–92 (2016) 5. Mingji, D., Baojun, L., Yingchun, L., Lisha, Z.: Dynamic optimization of navigation satellite laser inter-satellite link topology based on multi-objective simulated annealing algorithm. China Laser 45(07), 217–228 (2018) 6. Junying, W., Zhibo, Y., Wenfeng, L., Kangxun, Z., Xiangyu, L.: Research on laser link allocation method of spatial information network based on access traffic distribution. J. Nanjing Univ. (Natural Sci) 56(06), 877–884 (2020) 7. Hong, Seong, Chang, et al.: FSA-based link assignment and routing in low-earth orbit satellite networks. IEEE Trans. Veh. Technol. (1998) 8. Tianshu, W., Peng, L., Fang, D., Xian, L., Ma Wanzhuo, F., Qiang. : Development status and prospects of space laser communication technology. Chinese Eng. Sci. 22(03), 92–99 (2020) 9. Gao Shijie, W., Jiabin, L.Y., Shuang, M., Yanjun, N., Huisheng, Y.: The development status and trend of microsatellite laser communication system. Chinese Optics 13(06), 1171–1181 (2020)

Mechanism Analysis and Mitigation of Visual Navigation System Vulnerability Yawei Zhai, Yuanwen Fu, Shizhuang Wang, and Xingqun Zhan(B) Shanghai Jiao Tong University, 800 Dongchuan Rd, Shanghai, China [email protected]

Abstract. Autonomous systems have attracted significant interest from academia and industry in recent years. To achieve accurate and reliable positioning, and to improve navigation robustness in complex operational scenarios, visual navigation has become indispensable. However, visual systems are vulnerable to many influencing factors. Therefore, this paper introduces the “vulnerability” concept for visual navigation, which originates from satellite navigation. We analyze the underlying causes of visual vulnerability and propose mitigation methods accordingly. Following the pipeline of visual navigation systems, several internal and external vulnerability factors are revealed: image blur, object motion, incorrect feature matching, biased depth recovery, repeated texture, etc. The causing and influencing mechanisms are analyzed, based on which we propose some mitigation methods. Using the well-known open-source datasets (e.g., TartanAir, EuRoc), it is proved that visual navigation is highly and frequently vulnerable due to the factors above. Some typical examples are offered to illustrate the vulnerability factors. Besides, experiments are carried out to validate the proposed vulnerability mitigation approaches, and the results show their effectiveness. Keywords: Vulnerability · Visual navigation · Autonomous systems · reliability

1 Introduction Future autonomous systems are expected to bring significant convenience for people’s daily life. To ensure operation safety, their corresponding navigation systems must continuously provide position solutions with high reliability, while meeting the accuracy requirement. In addition, because those systems will be applied over various scenarios, the navigation systems should also provide high robustness against operational environment changes [1]. Therefore, providing high reliability and robustness for autonomous systems is one of the key research challenges in navigation field today. The particular interest of this paper is on Visual Navigation (VN), which has been identified as one of the main navigation sensors for autonomous applications [2]. It aims at estimating the ego-motion of an agent by extracting information from raw images, and the key is to find the projections of spatial points (correspondences of pixels) in the consecutive frames. Typical VN approaches include feature-based approach [3, 4], direct approach [5], and a hybrid of feature-based and direct approaches [6]. For its prevalence, © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 515–524, 2021. https://doi.org/10.1007/978-981-16-3142-9_49

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this work takes feature-based stereo visual navigation as an example. But the proposed methods are also applicable to other VN systems with appropriate modification. The baseline workflow of feature-based stereo VN is presented in Fig. 1 [7–9], where the main steps include pre-processing, feature extraction, feature matching, outlier rejection, and the final state estimation.

Fig. 1. Baseline workflow of feature-based stereo visual navigation

Comparing to radio navigation and inertial navigation, VN is more vulnerable to landmark uncertainty and disturbances. To quantitatively analyse its impact, this work introduces the VN “vulnerability” concept, which is inspired by the same concept from Global Navigation Satellite Systems (GNSS) field [10–12]. Regardless of the fact that there has been enormous work on improving VN accuracy and stability [13–15], it is desired to improve the reliability of VN systems under various scenarios. Although there is usually an outlier rejection step in a typical VN system (step 4 of Fig. 1), it cannot meet the reliability requirements to support autonomous applications, e.g., driverless cars and unmanned aerial vehicles. Analysing the vulnerability factors and developing mitigation techniques for VN are critical to improve navigation accuracy and reliability, and it is also necessary for assessing VN quality in real-time. The rest of this paper is organized as follows. Section 2 provides the definition of VN vulnerability and analyses its root causes. Then, Sect. 3 presents mitigation approaches against VN vulnerability. Dataset-based experiments are carried out in Sect. 4 to illustrate VN vulnerability and validate the effectiveness of the proposed methods. Finally, Sect. 5 concludes this paper.

2 Definition and Root Cause Analysis of VN Vulnerability VN systems are frequently subject to various threats and challenges due to its working principle. In this work, this natural fact is named “VN vulnerability”, as inspired by GNSS vulnerability. For GNSS, its vulnerability is mainly because GNSS signals are

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very weak during long-distance transmission. Meanwhile, there are a lot of unintentional and intentional signal interferences. Similar vulnerability analysis methods apply to VN system. In this section, we will analyze the root causes of VN vulnerability based on a baseline workflow of feature-based stereo visual navigation systems. As mentioned above, the general principles are also applicable to other VN systems with slight modifications. Comparing to Fig. 1, Fig. 2 provides a more detailed work process of VN, which lays the foundation for the following analyses.

Light & Weather Scene (source segment)

Scene-camera optical environment (propagation segment)

Distortion& Noise

Left

Raw images

Camera

Right

Camera (user segment)

Processing

Depth map (current frame)

Feature Extraction Feature Matching

Depth map (last frame)

Feature Extraction

3-D Feature Correspondences State estimation

VN software (algorithm segment)

Fig. 2. All-in-loop workflow of feature-based stereo visual navigation

As shown in Fig. 2, there are four connected segments in a standard VN workflow: scene (source segment), scene-camera optical environment (propagation segment), camera (user segment), and VN software (algorithm segment). This division is an analogy to GNSS, which is divided into constellation (space segment), atmosphere (propagation segment), receiver (user segment), and user algorithm (including signal processing and state estimation). Figure 1 only addresses the algorithm segment, while the errors and outliers of visual measurements are mostly introduced in the first three segments. To capture all the sources of VN vulnerability, we provide a qualitative analysis on the first three segments (also named as “measurement segment”) as follows. 2.1 Scene (Source Segment) Just like a GNSS constellation, scene determines the richness and quality of the information in the raw images. Figures 3a and 3b show two different scenarios for an exemplary illustration. Obviously, Fig. 3a has richer information, because its textures are clear

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with almost no repetition. In contrast, Fig. 3b only conveys little information, which is attached with less and repetitive texture. Therefore, extracting high-quality feature points is easier for Fig. 3a. Besides, as shown in Fig. 3c, when there are moving objects in the image, VN systems may output large error. This is because the assumption that the landmarks are static is the basis for visual navigation. To sum up, from the perspective of VN vulnerability, the scene itself is the most important factor. Scenes lacking texture, with repeated texture, or with non-static objects, are one of the main sources of vulnerability.

Fig. 3. Three typical visual scenes

2.2 Scene-Camera Optical Environment (Propagation Segment) Similar to the atmospheric propagation errors and multipath effects in GNSS, for VN, the optical environment from the scene to the camera will also introduce disturbances to the visual measurement. Common optical environmental characteristics include light, air humidity, and weather, etc. For example, over a day period, the varying light conditions will cause different gray levels of the images. Besides, for the same scene, the images taken on rainy days and sunny days will show significant difference, given that the light from the scene to the camera may be refracted in rainy days. The ideal assumptions for VN are (a) there is sufficient and stable illumination, and (b) the light travels in a straight line from the scene to the camera. However, the actual optical environment does not necessarily meet such assumptions, which is another cause of VN vulnerability. 2.3 Camera (User Segment) Camera is a sensor used in VN to generate raw images. Generally, the pinhole camera model is regarded as an ideal camera model. The pinhole camera model describes the  T relationship between a real-world spatial point Pc = x y z (expressed in the camera  T  coordinate system) and its image P = u v in a 2-D phase plane, as shown in the following equation. ⎡ ⎤ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ x x u fx 0 cx 1 1 ⎣ v ⎦ = ⎣ 0 fy cy ⎦ · ⎣ y ⎦  K · ⎣ y ⎦ (1) z z 0 0 1 z z 1 where fx and fy are the focal lengths in pixels; cx and cy are the coordinates of the camera’s optical center in the pixel plane in pixels. fx , fy , cx and cy are the intrinsics, and K is

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called the camera’s internal reference matrix, which is a deterministic and time-invariant parameter. Then, let us consider the pose of the camera (called the external parameters of the camera), i.e., the rotation matrix R and translation vector t of the camera. Therefore, for a stationary point Pw in the world coordinate system, we have: Pc = R · Pw + t Substituting (1) into (2), we get: ⎡ ⎤ u ⎣ v ⎦ = 1 K(R · Pw + t) z 1

(2)

(3)

Equation (3) describes the transformation relationship between a point in the scene and the coordinates of its phase plane, which is the basis for VN. However, the imaging process is easily affected by distortions and noise, which introduces errors in Eq. (3). Generally, distortions are deterministic that can be corrected. But noise is random, and its presence can make (a) the projection relation inaccurate or (b) the grayscale of a pixel no longer accurate. The grayscale disturbance of pixels will directly affect the feature matching process. In addition, there may be motion blur, lens fogging, and lens obscuration during camera imaging, which significantly reduces the image quality. To sum up, noise, blur, and occlusion are the common sources of VN vulnerability in user segment. 2.4 VN Software (Algorithm Segment) The goal of the VN algorithm is to determine the pose of the camera based on the original image (i.e., R and t). As shown in Figs. 1 and 2, typical process of an VN algorithm includes binocular depth recovery, feature extraction, feature matching, and state estimation. The algorithm will not introduce additional errors, but only propagate the error from measurement to state estimation. In other words, the VN algorithm maps the vulnerability factors in the first 3 segments to navigation performance. 2.5 Summary of VN Vulnerability Factors and Their Impact This subsection summarizes the sources of VN vulnerability and their effects, as shown in Table 1. The vulnerability factors in the measurement segment mainly affect (a) the projection relationships (i.e., u and v) in Eq. (3) and (b) the gray value of each pixel. From Eq. (3), (a) directly affects the estimation of the agent’s navigation state. In contrast, (b) may lead to large navigation errors by causing incorrect feature matching and inaccurate depth recovery.

3 VN Vulnerability Detection and Mitigation Techniques To prevent the users from being threatened by large visual navigation errors, it is imperative to design a real-time VN vulnerability detection mechanism and incorporate vulnerability mitigation techniques into VN algorithms.

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Segment

Vulnerability factor

Negative impact

Scene

Lacking textures

Lacking features

Repetitive textures

Incorrect feature matching & incorrect depth recovery

Non-static objects

Incorrect state estimation

Illumination change

Incorrect feature matching & incorrect depth recovery

Rainy day

Incorrect state estimation

Foggy day

Lacking features

Distortion

Little effect after de-distortion

Noise

Inaccurate state estimation

Blur

Incorrect state estimation

Scene-camera

Camera

3.1 Real-Time Vulnerability Detection Three vulnerability detectors are developed to alert the users when (a) the number of tracked features is not adequate, (b) there are a significant number of repetitive textures, or (c) the image quality is poor. These three factors can directly influence the availability of VN. Similar to the “Dilution of Precision (DOP)” concept in GNSS, the number of tracked features and their spatial distribution will impact VN accuracy. In our prior work [16], we established the analytic relationship between the VN error covariance and the distribution of the feature correspondences. Accordingly, the first vulnerability detector is to alert the users when the navigation accuracy cannot meet the requirement. This detector can be expressed as follows:  0, if F(FP) > accuracy requirement availability = (4) 1, if F(FP) ≤ accuracy requirement where F(FP) denotes the estimated navigation accuracy with the matched feature point set FP. The second detector to avoid the occurrence of severe incorrect feature matching events. At some scenes (e.g., bushes, floors), there might be a large number of repetitive textures. This will potentially lead to the event that incorrectly-matched features account for a large proportion of all the pairs. To avoid this, we define the effective feature subset as: 

 (5) SF = pi | d (pi ) − d pj > T , ∀j = i 

where d (pi ) − d pj represents the Hamming distance between two feature points pi , pj ; and T is the threshold for feature matching. Then, the number of effective features and their distribution will determine the availability of the VN system through Eq. (4). The final detector is designed to filter out bad-quality images. In some cases, the image may be blurred or unclear, which means the image cannot be directly used for

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visual navigation. There are existing algorithms to assess the quality of an image [17, 18], and we can set a threshold for the image quality. If an image cannot pass the three detectors above after image augmentation (e.g., deblur [19]), the VN system should send an unavailable flag. 3.2 VN Vulnerability Mitigation In this subsection, two vulnerability mitigation techniques are introduced to mitigate the effects of non-static objects and incorrect depth recovery. It is worth mentioning that although RANdom SAmple Consensus (RANSAC) is often used for outlier rejection, there are a considerable number of outliers remaining in the “inlier set” after RANSAC. Therefore, we design the following two approaches as a supplement to remove the outliers. Employing the real-time object detection techniques, e.g., YOLO [20], is the first technique for vulnerability mitigation. For the objects that are very likely non-static, e.g., cars, pedestrian, birds, the associated features should be considered unreliable, and thus their weights are set to zero in the process of pose estimation. This technique is useful in removing the outliers caused by non-static objects. The principle of another approach is residual-based consistency check. The residual vector of a feature correspondence is defined by: 



ri = R · Pc1 + t − Pc2

(6)

where Pc1 and Pc2 are the coordinates of the same physical point in two camera coordinate systems (at two epochs); R and t are the estimated rotational and translational parameters of the camera between the two epochs. If the residual vector of a feature point is larger than a preset threshold in any direction, then this feature should be removed from the pose estimation process. This technique can be used to exclude the outliers caused by non-static objects and incorrect depth recovery. 



4 Experimental Results and Discussion 4.1 Examples of VN Vulnerability Using open-source dataset, this subsection shows typical VN vulnerability examples: incorrect feature matching, non-static objects, and inaccurate depth recovery.

Fig. 4. An example of incorrect feature matching

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Figure 4 shows an example of incorrect feature matching, where the feature extraction is based on ORB. Figure 4a is the original matching result using conventional algorithms, whereas Fig. 4b is the truth obtained by manual check. As shown in this figure, there are many incorrect feature matching events, which is caused due to close descriptors. Figure 5 demonstrates a scenario where there are non-static objects in the image. Many extracted features (labeled by circles) locate in the passing car, which could potentially lead to large navigation errors. For vehicular navigation, this scenario is very common, and thus it is one of the major causes of VN vulnerability.

Fig. 5. An example of non-static object

Figure 6 shows a typical example for inaccurate depth recovery, where the depth estimation is realized based on Semi-Global Matching (SGBM). Figure 6a presents the raw images, and Fig. 6b shows the estimated and the true depth map. Besides, Fig. 6b labels the features with large depth errors (over 1 m) in red in the estimated depth map. For some features, the errors are significantly large, which is mainly caused by the disturbance on the pixel grayscale.

Fig. 6. An example for inaccurate depth recovery

4.2 Validation of Detection and Mitigation Techniques Dataset-based experiments are carried out in this subsection to further illustrate and validate the proposed VN vulnerability detection and mitigation techniques. First, Fig. 7 illustrates the detector that is used to limit severe incorrect feature matching events. After removing the features with similar descriptors using Eq. (5), most features remain in Fig. 7a, while there are only a few features left in Fig. 7b. Therefore, the scenario shown in Fig. 7b is more vulnerable. Figure 8 demonstrates the effect of object detection on removing features extracted from non-static objects. This figure shows the object detection result output by YOLOv4, and it shows that this technique can effectively identify the objects that are likely

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Fig. 7. Effective analysis result of the detector design for two scenarios

Fig. 8. Object detection result output by YOLO-v4

to be non-static. Taking this scenario as an example, the VN algorithm should set the weights of the features extracted from the cars to zero in the state estimation process.

Fig. 9. Residuals of each feature correspondence in three directions

Finally, Fig. 9 shows the residuals of each feature correspondence for the scenario of Fig. 5. As shown in this figure, the residuals of some features are larger than the preset threshold, which indicates they are likely to be faulted. And by manual check, it is proved that most of these features suffer from incorrect feature matching, non-static object, or inaccurate depth recovery. Therefore, the experiment result suggests the effectiveness of the residual-based vulnerability mitigation technique.

5 Conclusion This paper proposes vulnerability concept for Visual Navigation (VN) system, and develops corresponding mitigation techniques. Based on the baseline workflow of VN, this work points out the internal and external vulnerability factors in image generation, depth restoration, feature matching, scenario itself, etc. Besides, we analyze the generating and influencing mechanism of typical vulnerability events, such as movement, illumination changes, mismatches, and depth estimation errors. Experiments are carried out to analyze the impact of vulnerability on VN performance, and to validate the proposed vulnerability detection and mitigation methods. It is shown that incorrect feature matching,

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non-static objects, and inaccurate depth recovery are three main causes of VN vulnerability. And employing object detection and residual based detection can effectively mitigate their impact.

References 1. Luo, Y., Yu, Y., Jin Z., Zhao, H.: Environment-centric safety requirements for autonomous unmanned systems. In: 2019 IEEE 27th International Requirements Engineering Conference (RE), pp. 410–415 (2019) 2. Pomerleau, F., Colas, F., Siegwart, R.: A review of point cloud registration algorithms for mobile robotics. Found. Trends Robot. 4(1), 1–104 (2015) 3. Gonzalez, R., Rodriguez, F., Guzman, J., et al.: Combined visual odometry and visual compass for off-road mobile robots localization. Robotica 30(6), 865–878 (2012) 4. Cumani, A.: Feature localization refinement for improved visual odometry accuracy. Int. J. Circuits Syst. Signal Process. 5(2), 151–158 (2011) 5. Naroditsky, O., Zhou, X., Gallier, J., et al.: Two efcient solutions for visual odometry using directional correspondence. IEEE Trans. Pattern Anal. Mach. Intell. 34(4), 818–824 (2012) 6. Scaramuzza, D., Siegwart, R.: Appearance-guided monocular omnidirectional visual odometry for outdoor ground vehicles. IEEE Trans. Robot. 24(5), 1015–1026 (2008) 7. Jiang, Y., Xu, Y., Liu, Y.: Performance evaluation of feature detection and matching in stereo visual odometry. Neurocomputing. 120, 380–390 (2013) 8. Parra, I., Sotelo, M., Llorca, D., et al.: Robust visual odometry for vehicle localization in urban environments. Robotica 28(3), 441–452 (2010) 9. Arun, K., Huang, T., Blostein, S.: Least-squares fitting of two 3-d point sets. IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9(5), 689-700 (1987) 10. Jing, S., Zhan, X., Liu, X., Feng. S.: GNSS vulnerability assessment method based on application suitability. In: Proceedings of the 27th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2014), pp. 2291–2298 (2014) 11. Hsu, L.-T.: Analysis and modeling GPS NLOS effect in highly urbanized area. GPS Solutions 22(1), 1–12 (2017). https://doi.org/10.1007/s10291-017-0667-9 12. Zhao, X., Zhan, X., Yan, K.: GNSS vulnerabilities: simulation, verification, and mitigation platform design. Geo-spatial Inf. Sci. 16(3), 149–154 (2013) 13. Nister, D., Naroditsky, O., Bergen, J.: Visual odometry. In: Proceedings of International Conference Computer Vision and Pattern Recognition, pp. 652–659 (2004) 14. Frahm, J.-M., Georgel, P., Gallup, D., et al.: Building rome on a cloudless day. In: Proceedings of European Conference on Computer Vision, pp. 368–381 (2010) 15. Scaramuzza, D., Fraundorfer, F.: Tutorial: visual odometry. IEEE Robot Autom. Mag. 18(4), 80–92 (2011) 16. Wang, S., Zhan, X., Fu, Y., Zhai, Y.: Feature-based visual navigation integrity monitoring for urban autonomous platforms. Aerosp. Syst. 3(3), 167–179 (2020). https://doi.org/10.1007/ s42401-020-00057-8 17. Weken, D.V., Nachtegael, M., Kerre, E.E.: Using similarity measures and homogeneity for the comparison of images. Image Vis. Comput. 22, 695–702 (2004) 18. Wang, Z., Simoncelli, E.P., Bovik, A.C.: Multiscale structural similarity for image quality assessment. The Thirty-Seventh Asilomar Conference on Signals, Systems & Computers 2, 1398–1402 (2003) 19. Chen, T., Ma, K., Chen, L.: Tri-state median filter for image denoising. IEEE Trans. Image Process. 9(12), 1834–1838 (1999) 20. Bochkovskiy, A., Wang, C., Liao, H., “YOLOv4: Optimal Speed and Accuracy of Object Detection”. 2020, arXiv:2004.10934.

Pedestrian Collaborative Inertial-Only SLAM Yiming Ding, Zhi Xiong(B) , Zhengchun Wang, Zhiguo Cao, and Wanling Li College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Jiangsu 210016, China [email protected]

Abstract. The unbounded accumulative error of the inertial navigation system is the most important factor hindering the practical application of the inertial pedestrian navigation system. In this paper, an occupancy grid-based simultaneous localization and mapping framework using only inertial information is proposed. Inertial information is utilized as an virtual environment perceptrons to construct the occupancy grid-based environment map. Simultaneously, the inertial system eliminates its cumulative errors by using the constructed maps. On this basis, the constructed map is used to establish the relative observation of pedestrians in formation to realize accurate and stable positioning in the formation of pedestrians. Experimental results show that the proposed algorithm has high real-time performance and stable positioning accuracy. The average positioning error of the formation is less than 6 m in a single-story multi-room environment of 2500 m2 for 20 min. Keywords: Inertial pedestrian navigation · SLAM · Indoor navigation

1 Introduction With the development of micro-electromechanical system technology, the inertial pedestrian navigation system has become a hotspot of indoor positioning research. The system has a wide range of applications in hotspots such as firefighting, indoor security, tunnel patrols, and other fields. However, due to the influence of Inertial Measurement Unit (IMU) noise, the inertial pedestrian positioning system will produce significant drift over time. The cumulative error of inertial pedestrians positioning system suppression method has quite a few related research and achieved great progress. Zero velocity [1], zero angular velocity [2], straight-line detection [3] algorithms are used to suppress the accumulated errors of the system. To improve the modal adaptability of the system, multiple IMU systems were adopted [4, 5]. The lower limb structure was modeled to establish constraints between multiple sensors, which enhanced the robustness of the system and expound the applicable motion modes. Map matching algorithms [6] could eliminate the accumulated errors of the inertial pedestrian system. This method matches the pedestrian trajectory with the prior map so that the system can achieve long-term stable navigation in the known environment. However, the prior environment maps are difficult to obtain, so the use of this method is severely limited.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 525–534, 2021. https://doi.org/10.1007/978-981-16-3142-9_50

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In this paper, an inertial based collaborative SLAM method for indoor pedestrians is proposed. This method only uses inertial information to construct and estimate indoor environment maps without any type of visual or other sensors. By introducing the gridbased FastSLAM method, the cumulative errors of the inertial positioning system can be effectively eliminated. Also, the single-person inertial SLAM method is extended to the multi-person formation collaborative SLAM method to meet the requirements of formation positioning. This method accelerates the map construction process by integrating a multi-person map, realizes the rapid construction of the environment, and improves the overall positioning performance of the formation. A three-person real-time verification platform was built to conduct experimental analysis, and the effectiveness of the method was verified.

2 Single-Pedestrian Inertial-Only SLAM The essence of single-pedestrian indoor SLAM with pure inertial composition is based on the output of the odometer u with inertial information on spatial observations z for pedestrian poses x and map Θ The problem of a posteriori estimation, i.e. estimating the joint distribution of map and poses. p(x1:t , |z1:t , u1:t )

(1)

where z1:t is the all observations of the environment from 1 to t moment. x1:t is the poses from start to the t moment, u1:t is the step-heading change vector from the pedestrian inertial odometer output. The above joint distribution can be decomposed into the single- pedestrian position estimation problem and the inertial probability map estimation problem for known positions according to the Rao-Blackwellized criterion [7]. p(x1:t ,  | z1:t , u1:t ) = p(x1:t | u1:t , z1:t )

N 

p(θi | x1:t , z1:t , u1:t )

(2)

i=1

The decomposition shows that the estimation of the joint probability distribution of map and poses can be decomposed as the product of the posterior distribution of individual poses and the inertial probability map distribution of known poses. Since the distribution of the single pedestrian’s pose and the map is more complex and difficult to describe accurately using parametric distributions, the FastSLAM method is introduced to achieve the estimation of the joint map and pose distribution. The state of each particle consists of the single pedestrian’s poses and the map, and the particles are independent of each other, then the state of the m-th particle can be defined as   (3) Xt[m] = xt[m] [m] where m = 1, 2, · · · M denotes the m-th particle, and M is the total number of particles in the particle filter, and xt[m] denotes the estimated pose of the m-th particle at time t, and [m] denotes the map estimation of m-th particle. The estimation process mainly

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Fig. 1. Illustration of the inertial pedestrian occupancy grid-based FastSLAM procedure

consists of four steps: particle state propagation, map update, particle weight calculation, and particle importance resampling, and the process is shown in Fig. 1. The pedestrian’s pose is first sampled, as shown by the yellow dots in the diagram. Since it is less likely that the pedestrian will be able to access the places with obstacles, the grid where the yellow particles are located in the diagram has a greater probability of being accessible, as shown by the white grid in the diagram. As the pedestrian moves one step, the particle state is propagated through the motion model and a one-step prediction of the pedestrian’s position is obtained. As the pedestrian moves onto the already constructed map, particles that fall on a larger accessibility probability are given a larger weight, and particles that fall on an obstacle zone are given a smaller weight. At the same time, the map probability is updated by a static binary Bayesian filter based on the particle’s positional distribution at this point, and the probability that the newly explored area of the pedestrian is accessible is further increased, corresponding to an increase in the number of white grids in the map. The particles are then resampled. To avoid the loss of particle diversity due to multiple resampling, particle diversity is first discriminated based on the variance of the particle weights at this point, and the importance of the particles is resampled when the variance of the particle weights is too large, and in the resampling process, the map carried by the discarded particles is discarded as well. The errors in the pedestrian posture and the map are corrected for in the weight calculation and importance resampling process. 2.1 Map Representation and Estimation The system uses an occupancy grid map to create a uniform description of the pedestrian movement environment. The environment is partitioned into several equal-scale quadrilateral grids, each of which carries a probability of representing the accessible area covered by that grid, and since the system does not have a priori map information, the initial probability of the grid is 0.5. The purpose of inertial probabilistic map estimation is to estimate the probability that a grid in a map is an accessible area using the trajectory of a pedestrian. The estimation process is based on the basic fact that the grid at the location where the pedestrian passes through has a high probability of being accessible. Therefore, the more times a grid is passed, the higher the probability that it is an accessible area when moving through the pedestrian environment. Given that the probability distribution of each grid in the map is independent of each other, the whole estimation process of the map can be decomposed into the estimation of the posterior

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probability estimates for several independent grids. p(|z1:t , x1:t ) =

M 

p(θi |z1:t , x1:t )

(4)

i=1

where θi denotes the first i grid, and M is the total number of grids in the map. A static binary Bayesian filter is used to estimate the probability of a single grid. p(θi |zt ,xt ) p(θi ) − log 1−p(θ lt,i = lt−1,i + log 1−p(θ i |zt ,xt ) i)

(5)

p(θi |z1:t ,x1:t ) lt,i = log 1−p(θ i |z1:t ,x1:t )

(6)

of which

are the posterior probability ratios of the grid, the p(θi ) is the prior probability of the map grid, and p(θi |zt , xt ) ∈ (0.5, 1] is the inverse observation model of inertial information on the environment, describing a single observation of the map grid by inertial information. The larger this value is the faster the posterior probability converges, but taking a disproportionately large value can lead to erroneous observations being given too much weight, causing the results to converge to the wrong outcome.here taken as p(θi |zt , xt ) = 0.9. The single observation probability of a pedestrian being in a passageway is 0.9. Equation (5) can then be reduced to p(θi |zt ,xt ) lt,i = k × log 1−p(θ i |zt ,xt )

(7)

where k is the number of times the grid has been experienced. 2.2 Pedestrian Inertial Odometer and Motion Model Step size estimated by the pedestrian inertial odometer dt together with the amount of heading change ψt together form the control vector of the pedestrian motion model ut , then the pedestrian positional state transfer equation has xt = xt−1 + ut

(8)

⎤ ⎡ ⎤ ⎡ ⎤ px,t−1 dt cos(ψt−1 ) px,t ⎣ py,t ⎦ = ⎣ py,t−1 ⎦ + ⎣ dt sin(ψt−1 ) ⎦ ψt ψt ψt−1

(9)

⎡

where px.t and py.t are the pedestrian t the position at the moment, and ψt is the single pedestrian t the momentary heading. After propagation through the motion model, the particles obey a distribution p(xt |xt−1 , ut ) and let 1 ∼ t − 1 The particle position distribution at the moment obeys p(x1:t−1 |z1:t−1 , u1:t−1 ), then the particles from moment 1 to moment t obey a distribution p(x1:t |z1:t−1 , u1:t ), called the proposed distribution.

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2.3 Particle Weight Calculation and Importance Sampling As mentioned above, the particles at the moment t − 1 propagated through the motion model obey the distribution p(x1:t |z1:t−1 , u1:t ), and the degree of difference between it and the target distribution p(x1:t |z1:t , u1:t ) The degree of difference is characterized by the weight of the particles, which in this system is the ratio between the target distribution and the proposed distribution. wt[m]

=



[m] p x1:t |z1:t ,u1:t

[m] p x1:t |z1:t−1 ,u1:t

(10)



where p zt |xt[m] , [m] t−1 is the probability distribution of the pedestrian observation model. The weight calculation process integrates the particle state propagation process with the pedestrian observation of the map to achieve an estimate of the joint posterior probability distribution of the pedestrian poses and the map. The new set of particles obtained by resampling the weighted particles based on the weights after the particle weights have been calculated Xt that obeys the joint a posteriori probability distribution of the desired single-particle poses and maps. In importance resampling, the frequent resampling process leads to loss of particle diversity, making it difficult to form a loop back to the particles and thus to construct valid observations, therefore, to avoid loss of particle diversity, the degree of dispersion of the particles is evaluated before resampling. D=

N

1

[m] m=1 wt

(11)

when D resampling is performed when it is too large, otherwise [m] wt[m] = η · wt−1 · p(θi |z1:t , x1:t )

(12)

where η is the normalization factor.

3 Collaborative Inertial-Only SLAM The proposed collaborative Inertial-Only SLAM method fuses the inertial information of each pedestrian in a formation, estimate a common map, and establish the relative observation information between pedestrians through the common map to correct the positioning error of each pedestrian in a formation. The objective of pure inertial composition pedestrian indoor cooperative SLAM is to estimate the posterior distribution of the formation’s positional and shared maps.

1 n , |z 1 , u1 1 n n n (13) , . . . , x1:t p x1:t 1:t 0:t−1 , x0 , . . . , z1:t , u0:t−1 , x0 n denotes the first n pedestrian 1 ∼ t position at the moment of the formation, where x1:t n denotes the first n pedestrian and  denotes the map shared by the formation, and u0:t−1 0 ∼ t − 1 The step size and heading control vector at the moment. According to the RaoBlackwellized criterion, since pedestrian observations in the formation are independent

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of each other, and assuming that pedestrian movements are independent of each other, Eq. (13) has the following decomposition.

1:N 1:N 1:Np 1:N 1::N p x1:t p ,  | z1:t p , u0:t−1 , x0 p , x0 p Np



n 1:N 1:N n n = p  | x1:t p , z1:t p p x1:t | z1:t , u0:t−1 , x0n

(14)

n=1

where Np is the total number of individual pedestrians in the formation. The posterior probability of Eq. (14) is solved using a similar approach to that of single-player inertial SLAM. The formation inertial SLAM particle state contains the poses of the individual pedestrians in the formation with a shared map.   N 1[m] 2[m] (15) , x1:t , · · · , x1:tp[m] , [m] Xt[m] = x1:t The estimation process also consists of four steps: particle state propagation, map update, particle weight calculation, and particle importance resampling.



N Np[m] 1[m] 1 2 xt1[m] = A ut−1 , ..., xt p[m] = A ut−1 , xt−1 , xt−1 m[m] = t

Np 

M ztn , xtn[m] + m[m] t−1

n=1 Np

wt[m] =

 [m] S ztn , xtn[m] , m[m] t−1 wt−1

(16)

n=1

where A is the motion model described, the M is the map update model, and S is the weight update model. Since only state propagation, static binary Bayesian estimation of a single grid and weight update operations are required for each particle in the filtering process, these operations do not vary with the number of particles, time and movement distance, etc. Let the number of particles be n, then the time complexity of the algorithm is O(n).

4 Experiments and Analysis In order to verify the algorithm real-time and effectiveness, and evaluate the algorithm positioning accuracy, the experimental design of real-time verification platform. A fivenode inertial odometer was experimentally designed to obtain the pedestrian’s stride length-heading control vector. Each node inertial sensor has a gyroscope zero bias stability of 10°/h and an accelerometer zero bias stability of 15 μg. As shown in Fig. 2, the inertial odometer contains five nodes for the feet, legs, and waist, with the feet using a zero velocity correction method to estimate the pedestrian stride length and the legs and waist sensors used to estimate the pedestrian heading. The data was collected and processed using a Raspberry Pi 4B processor and the results of the inertial odometry estimation were sent to a handheld terminal via Bluetooth.

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(a) Foot mounting

(b) Waist mount

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(c) Leg mounting

Fig. 2. Distribution of five-node pedestrian inertial odometer nodes

As shown in Fig. 3, a Xiaomi 10 mobile phone and Huawei MatePad were used for inertial composition and error correction for the handheld terminals. The number of people in the experimental formation was 3. The step heading information for each pedestrian in the formation was transmitted to the cloud and shared via the mobile network.

Fig. 3. The pedestrian collaborative inertial-only SLAM handhold terminal

The experimental environment is the 5th floor of the teaching building in Fig. 4, which has an area of approximately 2500 m2 and contains corridors, rooms, corners, and other structures. The red points in the diagram are the accuracy assessment points and the locations of these points were pre-measured using a high precision wheeled odometer with the start and endpoint as the origin and the right direction in the diagram as the positive x-axis and the upward direction as the positive y-axis, then the coordinates of the four assessment points are (0,0), (56,0), (56,47.2) and (0,47.2) respectively. three testers started at the start point, moved around the floor, and randomly entered any rooms and accuracy assessment points, the estimated position of the navigation system was recorded as the testers passed the error assessment points, and the positioning error of the navigation system was obtained by comparison with pre-measured values, for a total experiment duration of 20 min. Figure 5 shows the results of the composition in the experiment, where each color block is the corresponding grid in the composition method and the color of the block indicates the probability that the grid is a accessible area, where white is 50% and dark blue is 100%. The side length of the grid in this algorithm is 2 m, which corresponds to the width of the corridor in the plan. As can be seen in the figure, the method is effective in constructing the availability area in the space experienced by the traveler. Again the grid coordinates of the accuracy assessment points are selected to compare with the grid

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(a) Top view

(b) Floor plan

Fig. 4. The pedestrian collaborative inertial-only SLAM experiment environment

coordinates estimated by the system and the maximum error in the construction of the map by this method does not exceed two grids (4 m).

Fig. 5. Pedestrian collaborative inertial-only SLAM mapping result

Fig. 6. The trajectory of the inertial pedestrian odometer

The positioning trajectories corresponding to this experiment are shown in Fig. 6 and 7a, 7b, 7c. The three curves in Fig. 6 are the positioning trajectories of the three testers from the inertial odometer output of the step- heading control vector after heading projection only, and the error of the pure inertial heading projection results gradually increases as the pedestrian movement time increases. Figure 7a, 7b, 7c shows the positioning results of the proposed algorithm in the test, which shows that the cumulative positioning error of each tester in the formation, especially the heading cumulative error, was corrected, and the system suppressed the dispersion of the cumulative error in a long time pure inertial positioning so that the positioning error was stable within a certain range. As there is a certain randomness in the Monte Carlo sampling method, to evaluate the performance of this algorithm, the same set of experimental data was processed 100 times using the method proposed in this paper, and the cumulative distribution of positioning errors is shown in Fig. 8, in which the blue, red and yellow curves are the cumulative distribution of positioning errors for the three test persons within the formation, and it can be seen that the maximum error for each person within the formation does not exceed 6 m, and the 50% of the three persons CEP of 1.50 m, 1.26 m and 2.32 m respectively.

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Fig. 7a The tester #1 trajectory of the proposed method

Fig. 7b The tester #2 trajectory of the proposed method

Fig. 7c The tester #3 trajectory of the proposed method

Fig. 8. The position error cumulative distribution function of pedestrian collaborative inertial-only SLAM

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5 Conclusion This paper proposed a pedestrian collaborative inertial-only SLAM framework, which enables the collaborative construction of a map of the environment using only inertial information, while using the constructed map to correct for inertial system errors, enabling a long, accurate, and stable pedestrian inertial collaborative positioning system. The maximum positioning error of the formation did not exceed 6 m during 20 min of movement in a 2500 m2 single-story multi-room environment. At present, the method only locates the pedestrian formation in two-dimensional space, and it can be extended to three-dimensional space in the future to expand its applicability.

References 1. Cho, S.Y., Park, C.G.: Threshold-less zero-velocity detection algorithm for pedestrian dead reckoning. In: European Navigation Conference (ENC), pp. 09–12 (2019) 2. Yu, P., Song, C., Chen, J.: Research on heading angle constraint algorithm of pedestrian navigation system. Navig. Positioning Timing 005(006), 68–72 (2018)

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3. Zhang, X., Zhang, R., Guo, M., Mi, L., Song, M., Zhang, Y.: Yaw error selfbservation algorithm for pedestrian navigation via footounted inertial navigation system. J. Chin. Inertial Technol. 23(04), 457–466 (2015) 4. Niu, X., Li, Y., Kuang, J., et al.: Data fusion of dual foot-mounted IMU for pedestrian navigation. IEEE Sens. J. 19, 4577–4584 (2019) 5. Qian, W., Zeng, Q., Wan, J., Xiong, Z.: Pedestrian navigation method based on kinematic mechanism of human lower limb. J. Chin. Inertial Technol. 23(01), 24–28 (2015) 6. Jiang, C., et al.: A practical method utilizing multi-spectral LiDAR to aid points cloud matching in SLAM. Satell. Navig. 1(1), 1–11 (2020). https://doi.org/10.1186/s43020-020-00029-5 7. Carlone, L., Ng, M.K., Du, J., Bona, B., Indri, M.: Rao-Blackwellized particle filters multi robot SLAM with unknown initial correspondences and limited communication. In: 2010 IEEE International Conference on Robotics and Automation, Anchorage, AK, pp. 243–249 (2010)

An Efficient and Robust Indoor Magnetic Field Matching Positioning Solution Based on Consumer-Grade IMUs for Smartphones Jian Kuang, Taiyu Li, and Xiaoji Niu(B) GNSS Research Center, Wuhan University, Wuhan, China [email protected]

Abstract. This paper proposes an indoor magnetic field matching positioning (MFMP) scheme based on consumer-grade inertial measurement units (IMUs). The proposed MFMP can efficiently generate a magnetic field map and achieve robust matching positioning without calibrating the magnetometer bias. In the magnetic field map generation stage, a pedestrian positioning and orientation system (P-POS) is employed to provide the precise position and attitude of the smartphone during the data collection, and rasterization and bilinear interpolation methods are utilized to generate a three-dimensional grid magnetic map. In the real-time positioning stage, the position and attitude generated by pedestrian dead reckoning (PDR) are used to improve the position distinguishability of the magnetic field features and obtain the transformation relationship (from the navigation frame to the sensor frame). And the differential magnetic field features in the sensor frame are used to achieve matching positioning independent of the magnetometer bias. The slight differences in the magnetic field maps based on different smartphones show that the proposed scheme can efficiently generate a high precision magnetic map. Additionally, the positioning results of multiple tests using multiple smartphones show that the proposed scheme is less affected by the magnetometer bias. Furthermore, it has similar positioning performance in different smartphones, achieving continuous and robust meter-level positioning accuracy. Keywords: Magnetic matching · Inertial Measurement Unit (IMU) · Pedestrian Dead Reckoning (PDR) · Indoor positioning · Pedestrian navigation

1 Introduction Due to the interference of steel materials, indoor geomagnetic field has ubiquitous distortion features in the building, which can be used for indoor positioning. Compared with the radio positioning signals (including WiFi [1], Bluetooth, 5G [2], UWB [3], etc.), magnetic field signals have the advantages of ubiquity, stability, and immunity to human body influence. Therefore, magnetic field matching positioning (MFMP) has become one of the mainstream indoor positioning methods for mass consumer application [4].

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 535–545, 2021. https://doi.org/10.1007/978-981-16-3142-9_51

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MFMP includes two stages: magnetic field map generation and real-time positioning. In the magnetic field map generation stage, the correlation between the magnetic field features and the geographic coordinates with certain measurement methods is established. The walking survey (WS) is the most used method to generate a magnetic field map. For the reason that WS achieves a balance between measurement accuracy and cost comparing with the methods of the point by point and crowdsourcing [5]. Nevertheless, the measurement efficiency and accuracy of WS are still limited, which cannot meet the requirements for generating magnetic field maps in a wide range of indoor scenes. In the real-time positioning stage, the similarity calculation between the observed and the reference magnetic field features coming from the magnetic field map is used for determining the current user’s location. Dynamic time wrap (DTW) [6] and particle filter (PF) [7] are the two most frequently used methods in the published literature. However, the frequently changing magnetometer bias seriously deteriorates the performance of the above methods. Many researchers try to use the differential magnetic field features in the navigation coordinates (n-frame) to eliminate the effect of magnetometer bias [8]. Unfortunately, the projection of the magnetometer bias in the n-frame is not a fixed value, so the differential magnetic field features in the n-frame cannot achieve the purpose of eliminating the magnetometer bias. To solve the above-mentioned typical problems of the magnetic field signals-based positioning method, this paper designs an indoor MFMP solution based on consumergrade inertial measurement units (IMUs), which can efficiently generate a magnetic field map and achieve robust matching positioning without calibrating the magnetometer bias.

2 Overview of Magnetic Field Positioning Solution Figure 1 shows the flow of the MFMP scheme, which can be divided into two parts: 1) Magnetic field map generation stage. A pedestrian positioning and orientation system (P-POS) is used for providing accuracy coordinates of the data collection trajectories and attitude of the smartphone, and a bilinear interpolation method is utilized to generate a

Fig. 1. The flow of the MFMP scheme based on consumer IMUs

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three-dimensional grid magnetic map. 2) Online positioning stage. The relative position and attitude coming from the pedestrian dead reckoning (PDR) algorithm are used for correlating the observed magnetic field features to form the magnetic field profile to improve the position distinguishability. Additionally, the differential magnetic field profile in the sensor frame (b-frame) is used to eliminate the influence of the magnetometer bias and provide stable positioning results.

3 Magnetic Field Map Generation Stage The magnetic field map is the basis of the matching positioning scheme. The construction and maintenance efficiency of the magnetic field map determines the cost of the entire positioning solution and the accuracy of the magnetic field map defines the upper limit of the accuracy of the MFMP method during the online positioning stage. The test results of [9] show that P-POS can provide decimeter-level positioning and degree-level attitude when adjacent control points are separated by 50m. Inspired by this method, this paper uses the P-POS based walking survey method to collect the magnetic field map data, as shown in Fig. 2. The P-POS consists of a foot mounted IMU (Foot-IMU) and a handheld smartphone. Then, the sensor bias must be deducted from the magnetometer observation for obtaining the accurate environmental magnetic field features after data collection. The simple ellipsoid fitting method is used for estimating the magnetometer bias [10]. And the estimated attitude of the smartphone coming from P-POS are used for projecting the compensated magnetic field feature from the b-frame to the n-frame   ˜ b − bm (1) Mn = Cnb M  T is the 3D magnetic field feature in the n-frame, including where Mn = mn me md ˜ b is the output of the three-axis magnetometer; north, east and vertical components; M n bm is the magnetometer bias; and Cb is directional cosine matrix from the b-frame to n-frame. Due to the high sampling rate of the magnetometer (e.g., 100 Hz) and the uneven distribution of the reference trajectories, there are some areas that will be collected multiple times while some areas are not covered. Therefore, rasterization and interpolation are employed to generate a uniformly distributed magnetic field map. Rasterization: 1) Generate a minimum rectangle according to the estimated coordinates of the reference trajectories, and divide the rectangle into grids of the same size. 2) The observed magnetic field features are allocated to the grid according to the estimated coordinates of the smartphone, and the magnetic field features in the same grid are averaged. Linear interpolation: 1) Determine the position coordinates of the grid to be interpolated (e.g., grid No. 0 in Fig. 3), and set the search radius (e.g., 1m) of the effective grid. 2) Traverse the eight directions (i.e., east, south, west, north, northwest, northeast, southeast, and southwest) of grid No. 0. If the grid with a valid magnetic field feature is detected, it will return true, such as the grids numbered 1–7 in the Fig. 2. 3) Based on the objective fact that the magnetic field features can only be interpolated, the grid No.

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3 will be eliminated; 4) The other valid grids are used for obtaining the magnetic field features of grid No. 0 by linear interpolation. The linear interpolation formula can be expressed as M0n =

n + M n + Mn M1,5 2,6 4,7

3

(2)

dj−0 Mn +di−0 Mn

i j n = ; Min is the magnetic field feature of the i-th grid; di−0 = where Mi,j di−0 +dj−0 √ (xi − x0 ) + (yi − y0 ) is the distance between the i-th grid and the 0-th grid.

Fig. 3. Obtain a magnetic field feature by linear interpolation

Fig. 2. The structure of the P-POS

4 Real-Time Positioning Stage Because of the low dimensionality of the magnetic field feature in one position, the time series of the magnetic field features and the corresponding relative positions are correlated to form a combined feature, called the magnetic field profile (MFP). As shown in Fig. 4, the magnetic field features at the four positions (i.e., A, B, C, and D) are regard as an MFP. Because the relative spatial relationship (such as direction and distance) changes between two adjacent magnetic field features are preserved, a MFP will has a higher degree of position discrimination. Based on the relative positions and attitude angles estimated by the PDR [11, 12], an observed MFP can be expressed as ⎧ n n

⎫ ˜ b⎬ ⎨ r1 Cb 1 M 1 oMFP = (3) ··· ⎩ n n ˜ b ⎭ M r C k

b k

k

where rn is the plane position in the n-frame, including the north and east directions; Cnb is the cosine matrix of the direction from the b-frame to the n-frame, provided by the ˜ b is the output of the magnetometer; and k is the length of a observed MFP. PDR; M Then, the problem of MFMP can be simplified as finding the conversion relationship (i.e., translation and rotation parameters) between the relative trajectory and the absolute trajectory. However, the conversion relationship and the coordinates of the absolute

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Fig. 4. Magnetic profile

trajectory are both unknown, so we cannot estimate the translation and rotation parameters by using mathematical analysis methods. An alternative approach is to generate all possible reference trajectories based on the relative trajectory by traversing possible translation and rotation parameters. Then the conversion relationship is determined according to the similarity between the observed and the reference magnetic field features corresponding to the candidate reference trajectories. Figure 5 shows the detail process of generating candidate reference trajectories. 1) Obtain the relative trajectory S based on the relative position sequence calculated by PDR, and rotate S by θ around the first point to obtain the trajectory S  . 2) Translate S by n in the north-south direction to obtain the trajectory S  . 3) Translate S by e along the east-west direction to obtain the trajectory S  .

Fig. 5. The generation workflow of a candidate trajectory

Fig. 6. Reference magnetic feature at (n, e) from the bilinear interpolation method

The candidate trajectory S  can be expressed as:    rjn = C(θ ) rjn − r1n + r1n + rn

 cos(θ ) − sin(θ ) n ,rj is the coordinates of sin(θ) cos(θ) the j-th point of the candidate reference trajectory. The corresponding direction cosine matrix Cnb also needs to be adjusted accordingly  

 Cbn = Cnn Cbn j (5)  T where rn = n e ,C(θ ) =



(4)

j

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⎡

⎤ cos(θ ) − sin(θ ) 0     where Cnn = ⎣ sin(θ) cos(θ) 0 ⎦, Cbn is the directional cosine matrix from j 0 0 1 b-frame to n-frame corresponding to the j-th point of the candidate reference trajectory. Since the magnetic field map is composed of uniformly distributed reference points, the sampling points of the candidate reference trajectory cannot be exactly coincident with the reference points. Therefore, the bilinear interpolation method is used to obtain the reference magnetic field features with higher resolution, as shown

in Fig. 6. The corresponding reference magnetic field feature of a given point n e is n n n n + α2 M0,0 + α3 M1,1 + α4 M1,0 M n ≈ α1 M0,1 −n)(e−e0 ) −n)(e1 −e) 0 )(e−e0 ) ,α2 = (n(n1 1−n ,α3 = (n(n−n ,α4 = where α1 = (n(n1 1−n 0 )(e1 −e0 ) 0 )(e1 −e0 ) 1 −n0 )(e1 −e0 ) A reference MFP can be expressed as ⎧    ⎫ n Cn b⎪ ⎪ r M ⎪ ⎪ 1 1 b ⎨ ⎬

rMFP =

(6) (n−n0 )(e1 −e) (n1 −n0 )(e1 −e0 ) .

1

 · · · ⎪ ⎪ ⎪ ⎩ r n C n M b ⎪ ⎭ k b k

(7)

k

  T where M1b = Cbn M1n is the reference MFP in the b-frame. 1 Based on the characteristic that the magnetometer bias is a fixed value in the bframe, the differential MFP in the b-frame is used for eliminating the influence of the magnetometer bias. In order to avoid large errors of the selected reference magnetic field feature, this solution performs de-averaging processing on the observed MFP and the reference MFP respectively. Then, the DTW algorithm is used to calculate the similarity between the observed MFP and the reference MFP. The DTW compresses or stretches the reference axis of the two sequences to be matched so that two sequences with different lengths have better matching results. This will help solve the problem that the PDR algorithm cannot accurately estimate the pedestrian step length.

5 Test Results and Analysis The test is conducted in a typical office building scene with a size of about 94 m × 22 m. Figure 6 shows the indoor structure where the red box is the test area (Fig. 7).

Fig. 7. Indoor structure of the test scene

In the magnetic field map generation stage, testers use a P-POS (Fig. 2) to provide high precision position and attitude of the smartphone. And the system time of the

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smartphone and Foot-IMU is aligned via Bluetooth communication. In addition, in order to evaluate the performance of real-time magnetic field matching positioning algorithm, the positioning accuracy evaluation in this paper is performed in offline mode. Three smartphones (Google pixel2, pixel3 and Mi8) are employed to generate the magnetic field map of the test area, which takes 800 s, 825 s, and 770 s respectively. The effective area is about 500 m2 , so the average data collection efficiency of the magnetic field map is about 37 m2 /min. If the tester follows the “#” path at a speed of 1.2 m/s in an indoor open area of 100 m2 , the data collection efficiency will reach 55 m2 /min. Figure 8 shows the Google pixel2-based magnetic field map. The horizontal and vertical axes are east and north positions respectively, and the colors represent the values of the magnetic field feature. Subgraphs (a)– (c) are the north, east and vertical, respectively. The magnetic field features of the adjacent geographic locations has a gentle transition, which is consistent with objective physical phenomena. Figure 9 shows the difference between the magnetic field map Mi8 and Google pixel2. The differences in most areas are distributed around 0. We learn that the P-POS provides position and attitude angle with good repeatability which can meet the requirements of generating a magnetic field map. In addition, the difference in magnetic field features in some areas reached about 100 milligauss (mGauss). The reason is that the accuracy of P-POS is limited (which is at about decimeter level). the magnetic field feature decay with the 3rd power of the spatial distance, small position and attitude errors will cause obvious magnetic field feature deviation near the magnetic field interference source.

Fig. 8. Magnetic field map based on Google pixel2. (a) north, (b) east, (c) vertical

Fig. 9. The difference of magnetic field maps based on Mi 8 and Google pixel2. (a) north, (b) east, (c) vertical.

Figure 10 shows the probability density function of the difference of the magnetic field map different smartphones. Table 1 summarizes the root mean square (RMS), 68% and 95% of the difference of the magnetic field maps based on different smartphones. The difference in the three directions of the magnetic field maps based on any two smartphones is less than 20 mGauss (RMS), and 95% of the difference is less than 40 mGauss. Compared with the noise level of magnetometers built in most smartphones is about 10–20 mGauss, and the errors caused by P-POS and map generation algorithms are very small. Therefore, the magnetic field map generation method designed in this paper is highly efficient and precise.

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Fig. 10. The cumulative density function of the difference of two magnetic field maps

Table 1. Root mean square, 68% and 95% of the difference in magnetic field maps of different smartphones (unit: milligauss) Mi8- Pixel3

Mi8-Pixel2

Pixel2-Pixel3

RMS

68%/95%

RMS

68%/95%

RMS

68%/95%

北

16.0

12.1/32.3

13.0

10.1/25.2

18.4

16.2/35.6

东

19.4

16.7/39.1

14.7

13.1/28.7

19.1

18.3/36.3

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13.6

11.6/27.7

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18.4

17.6/36.2

Based on the magnetic field map of Pixel2, we conducted 8 tests using 4 different smartphones (Honor V10, Google Pixel2, Pixel3, and Mi8). As the proposed algorithm does not need to calibrate the magnetometer bias, the real-time positioning algorithm evaluation stage will no longer perform bias compensation on the magnetometer observations. Because the magnetic field feature matching method does not have the global positioning ability and cannot quickly complete the autonomous initialization of the system state, MFMP usually used as an auxiliary positioning method. Here, the initial position is manually given, and WiFi/Bluetooth can be used to give a rough position (such as the position error is less than 10 m) for the real-time positioning program. Figure 11 shows the trajectories of 8 tests of the 4 smartphones. The red line is the reference trajectory given by P-POS; the blue line is the trajectory of PDR, and the green line is the trajectory of MFMP. The sub-pictures (a) and (b) correspond to Honor V10; (c) and (d) correspond to Google Pixel3; (e) and (f) correspond to Mi 8, (g) and (h) correspond to Google Pixel2. The trajectories generated by the PDR in different tests have different scale and deformation error, and the trajectories of MFMP have a good coincidence with the reference trajectories. Figure 12 shows the cumulative density function of position error of the 8 tests. “V10-1” is the first test of Honor V10. The positioning errors are relatively concentrated and most of which are within 1.5 m. Figure 13 shows the magnetometer bias estimated by each of the 8 tests, where “T1-x” is the bias of the x-axis of the magnetometer in the first test. It can be observed that the magnetometer bias has arrived hundreds or even thousands of mGauss, with a fluctuation of tens of mGauss. Table 2 lists the RMS, 68%

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Fig. 11. The trajectories of 8 tests using 4 smartphones. (a) and (b) correspond to Honor V10, (c) and (d) correspond to Google Pixel3, (e) and (f) correspond to Mi 8, (g) and (h) correspond to Google Pixel2

Fig. 12. Cumulative density function of position error of 8 tests

Fig. 13. The estimated magnetometer bias.

and 95% of the positioning error of the 8 tests. The RMS of the positioning errors of the 8 tests were distributed between 0.67 and 1.01 m, and the floating range was 0.34 m. Comparing with the length of a pedestrian step (about 0.6 m), the fluctuation range of the positioning error is small. Table 2. RMS: 68% and 95% of positioning error of 8 tests (unit: m) Test

V10-1

V10-2

Pix3-1

Pix3-2

Mi8-1

Mi8-2

Pix2-1

Pix2-1

Mean

RMS

0.67

0.79

1.01

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0.78

0.87

0.74

0.84

0.83

68%

0.66

0.74

1.00

0.88

0.78

0.86

0.70

0.72

0.79

95%

1.27

1.53

2.10

1.89

1.48

1.43

1.32

1.77

1.60

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In summary, although the magnetometer bias reaches thousands of mGauss and the fluctuation range reaches tens of mGauss, it has no obvious influence on the matching algorithm in this study. It can be learned that the proposed MFMP algorithm is not sensitive to the magnetometer bias, and the positioning performance difference between multiple smartphones is also small. In addition, the average positioning error of the 8 tests is 0.83 m (RMS), showing that the proposed method can reach the meter-level/submeter-level positioning in office buildings.

6 Conclusion and Outlook This study has greatly improved the relative positioning and attitude estimation ability of the consumer-grade IMUs by using the constraint information formed by the pedestrian movement characteristics. The magnetic field map construction efficiency and real-time positioning stability have consequently been enhanced. In the magnetic field map generation stage, a P-POS is used to provide decimeterlevel positioning and degree-level attitude (including roll, pitch and heading) of the smartphone. The test results of using three types of smartphones to generate magnetic field maps show that the data collection efficiency of the proposed method has reached 37 m2 /min, and the difference of the magnetic field maps based on different smartphones is less than 20 mGauss (RMS). In the real-time positioning stage, the position and attitude provided by PDR are used to improve the position distinguishability of the magnetic field feature and obtain the transformation relationship from the navigation frame to the sensor frame, so the differential MFP in the b-frame can be used for eliminating the impact of the magnetometer bias. The results of the 8 field tests of 4 smartphones show that the positioning error is distributed between 0.67 and 1.01 m, reaching an average positioning performance of 0.83 m (RMS). The experimental results have completely verified that the MFMP method designed in this study is less affected by the magnetometer bias, and there is no significant difference in positioning performance between different smart phone terminals. Because the smartphone indoor MFMP scheme proposed in this study is highly dependent on the stability of the PDR., we will focus on automatically monitoring the integrity of the PDR and adapting it to a variety of typical smartphone usage modes in the future, such as texting, calling, and swinging. More, we will explore the method of generating magnetic field maps based on crowdsourced data to further reduce the cost of system.

References 1. Zhuang, Y., El-Sheimy, N.: Tightly-coupled integration of WiFi and MEMS sensors on handheld devices for indoor pedestrian navigation. IEEE Sens. J. 16(1), 224–234 (2015) 2. Liu, J., Gao, K., Guo, W., Cui, J., Guo, C.: Role, path, and vision of “5G + BDS/GNSS.” Satell. Navig. 1(1), 23 (2020) 3. Van Herbruggen, B., et al.: Wi-PoS: a low-cost, open source ultra-wideband (UWB) hardware platform with long range sub-GHz backbone. Sens. Basel 19(7), 1548 (2019)

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4. Kuang, J., Niu, X., Zhang, P., Chen, X.: Indoor positioning based on pedestrian dead reckoning and magnetic field matching for smartphones. Sens. Basel 18(12), 4142 (2018) 5. Li, Y.: Integration of MEMS Sensors, WiFi, and Magnetic Features for Indoor Pedestrian Navigation with Consumer Portable Devices. University of Calgary (2016) 6. Subbu, K.P., Gozick, B., Dantu, R.: Locate me-magnetic fields based indoor localization using smartphones. ACM Trans. Intell. Syst. Technol. 4(4), 1–27 (2013) 7. Haverinen, J., Kemppainen, A.: Global indoor self-localization based on the ambient magnetic field. Robot. Auton. Syst. 57, 1028–1035 (2009) 8. Kim, B., Kong, S.: Indoor positioning based on Bayesian filter using magnetometer measurement difference. In: IEEE Vehicular Technology Conference Proceedings (2015) 9. Niu, X., Liu, T., Kuang, J., Li, Y.: A novel position and orientation system for pedestrian indoor mobile mapping system. IEEE Sens. J. 21(2), 2104–2114 (2020) 10. Tabatabaei, S.A.H., Gluhak, A., Tafazolli, R.: A Fast calibration method for Triaxial magnetometers. IEEE Trans. Inst. Meas. 62(11), 2929–2937 (2013) 11. Kuang, J., Niu, X., Chen, X.: Robust pedestrian dead reckoning based on MEMS-IMU for smartphones. Sens. Basel 18(5), 1391 (2018) 12. Liu, T., Niu, X., Kuang, J., Cao, S., Zhang, L., Chen, X.: Doppler shift mitigation in acoustic positioning based on pedestrian dead reckoning for smartphone. IEEE Trans. Instrum. Meas. 70, 1–11 (2020)

Research on Signal Acquisition Technique of Inter-satellite Links of Navigation System Jian Wang1(B) , Xuan Wang2 , Yuqian Pan1 , Xiaofang Zhao1 , Xinuo Chang1 , and Zhendong Li1 1 China Academy of Space Technology, Beijing 100094, China 2 32021 Troop, Beijing 100094, China

Abstract. Through the establishment of inter-satellite links, we can improve satellite autonomous operation, measure the distance between the satellites and get information from other satellites. By studying the traditional acquisition methods, a method based on fractional Fourier transform (FRFT) is proposed to solve the problems of receivers that have larger Doppler frequency and Doppler changing rate under high dynamic environment. With this method the signal energy can be gathered on the fractional Fourier domain, and by using constant false alarm rate detection the algorithm can improve the acquisition probability effectively. At last, the simulation proved that the algorithm can perform very well to the acquisition under high dynamic environment. It is proved that the algorithm proposed in this paper can provide reference to the acquisition of inter-satellite links. Keywords: Inter-satellite links · Acquisition · High dynamic · Constant false alarm rate

1 The Introduction Global satellite navigation system for the outcome is increasing, the influence of the war against the growing global navigation satellite system, the ground operation control and measurement and control system become the weak link of the whole big system, easy to suffer the loss of function, improve the operation ability of the satellite, has become the key to improve the ability to fight. At the same time, the link between navigation satellite star by the distance between the satellite measurement and information transmission, can make up for the inadequacy of the ground can’t follow-up measurement, for our country in the span is limited, the overseas present situation of the site is restricted under construction with global competitiveness of satellite navigation system has the decisive significance, and also for our country the performance of satellite navigation system are of great potential. However, for the satellite-borne navigation receiver, the relative velocity and acceleration between satellites are large, and the orbit of the navigation satellite is diverse, which will bring a large Doppler frequency and rate of change to the signal. In addition, the signal noise of the inter-satellite link is low when it reaches the on-satellite receiver, so the traditional method [1].. It is difficult to capture the signal of inter-satellite link. In this paper, based on the analysis of traditional signal acquisition © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 546–553, 2021. https://doi.org/10.1007/978-981-16-3142-9_52

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methods, a acquisition method based on fractional Fourier transform is proposed. The theoretical analysis and simulation results show that this method can realize the fast acquisition of inter-satellite link signals.

2 Performance Analysis of Traditional Capture Algorithms 2.1 Serial Search Technology Based on Time-Domain Autocorrelation Serial search technique based on time domain autocorrelation [2], the use of timefrequency two-dimensional search, docking received signals, for pseudo code phase, Doppler information and other two-dimensional search, is more common. However, this method cannot meet the requirement of fast phase capture and is difficult to meet the requirement of high dynamic. The search structure is shown in Fig. 1:

Fig. 1. Autocorrelation serial search acquisition process Based on the time domain

2.2 Cycle Correlation Capture Technology Based on FFT Based on FFT cycle correlation capture technology, search carrier, use local code correlation, complete phase search. Due to the large amount of computation, this method is difficult to meet the conditions of limited resources on the satellite. The capture implementation process is shown in Fig. 2.

Fig. 2. The circular correlation acquisition system employing an FFT technique

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2.3 Fast Acquisition Technology of Segmented Matched Filtering Based on FFT Fast Acquisition Technology Based on FFT Segment Matched Filter [3], the twodimensional search is reduced to the one-dimensional search, and the whole Doppler frequency range is searched while searching the phase of a pseudo code, which can accelerate the acquisition speed and shorten the acquisition time. The acquisition process is shown in Fig. 3.

Fig. 3. An acquisition technique based on segmented matched filter.

The complex signal obtained after sampling is expressed as follows: s(n) = C(n) exp(j2π(2Fi + fd )nTs ) + exp(−j2π fd nTs ))

(1)

Where C(n) is the pseudo-random code modulated in the signal, Fi is the intermediate frequency, fd is the Doppler frequency, and Ts is the sampling interval. The signal is filtered by piecewise matched filter. Because the filter’s coefficient is consistent with the spread spectrum code modulated in the input signal, the maximum SNR criterion is satisfied. Assuming that the length of the input signal is M and the number of points of piecewise summation is X, then the number of piecewise matched filters required is p = M/X, and the output of the p-th matched filter is: pmf (p) =

pX 

exp(−j2π fd nTs )

n=(p−1)X +1

=

exp(−j2π fd (pX − X + 1)Ts )(1 − exp(−j2π fd (X − 1)Ts )) 1 − exp(−j2π fd Ts ) sin(π fd (X − 1)Ts ) = exp(−j2π fd Ts (2p − 1)X sin(π fd Ts )

(2)

It can be seen from the equation that the output result of the matched filter is a function of fd , and the estimated value of Doppler frequency can be obtained by taking the FFT of N points (N ≥ P) for the output of p matched filters. (2.18) At present, most of the capture methods based on FFT in the literature adopt this technique.

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2.4 Influence of Inter-satellite Links on Traditional Signal Acquisition Methods For the satellite-borne navigation receiver, the orbit of the navigation satellite is diverse, and the relative velocity and acceleration between satellites are large, and the signal of the satellite has been adjusted at the moment t [4]. The mathematical model of signals is essentially linear frequency modulated (Chirp) signals. FFT for Chirp signals will expand the signal spectrum and decrease the peak value within the minimum resolution bandwidth, resulting in a reduction of the peak signal-to-noise ratio and the capture probability. Figure 4 is the spectrum diagram of Chirp signal after FFT. For a signal of the same length, the greater the acceleration of the star, the wider the spectrum, the greater the drop in the peak. Figure 5 shows the influence of acceleration on signal peak value when a certain type of navigation receiver carries out FFT processing on the signal. It can be seen from Fig. 5 that acceleration has an obvious effect on the decline of signal peak. 4

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Fig. 5. The impact of the correlation peak by acceleration

Fig. 4. The spectrum of chirp signal

3 Fast Acquisition Technique Based on Fractional Fourier Transform According to the analysis in the previous section, in view of the problem that the modulated carrier signal presents the characteristics of approximate linear frequency modulation (CHIRP) signal in the inter-satellite link, this paper proposes a high dynamic signal acquisition method based on FRFT, which can effectively compensate the Doppler frequency and its rate of change simultaneously. The fractional Fourier transform [5–7] is defined as: ∞ Xp (u) =

Kp (u, t)x(t)dt

(3)

−∞

For digital signals, the corresponding discrete algorithm of fractional Fourier transform is as follows.

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Sampling x(t) and Xp (u) in Eq. (3) with sampling intervals of t and u, the definition of the discrete fractional Fourier transform (DFRFT) can be obtained as follows: j

Yp (m) = Ce− 2 tan αm

2 u2

N N  

ej

2π sgn(cos α)rm 2M +1

e

2 tan αr 2 (2N +1)2 t 2

− j2π

2π nr

e−j 2N +1 y(n)

(4)

r=−N n=−N



α|+jsgn(cos α) sin α C = |cos(2M , u = (2N + 1)|cos α| 2Mt+1 . This discrete algorithm +1)(2N +1) only needs two Chirp products and one FFT operation, and its total operation amount is 2P + P2 log2 P (where P = 2M + 1). With small operation amount and fast operation speed, it can quickly realize the fractional Fourier transform of the optimal order of the signal. The principle of the fast acquisition method based on fractional Fourier transform is shown in Fig. 6.

Fig. 6. Capture process based on FRFT

The acquisition algorithm is similar to the fast acquisition method of piecewisematched filtering based on FFT. The input signal is sliding multiplied with the local code, the pseudo code is stripped, and then piecewise-accumulated, and the low-pass filtering is carried out while the sampling rate is reduced. Assuming there are P piecewise matched filters, the output data is the sequence of P point through low-pass filtering and in the form of Chirp signal. The data sequence of P point is processed by the discrete fractional Fourier transform to estimate the Doppler frequency and its change rate. The relation curve between acceleration and transformation order is shown in Fig. 7. As can be seen from Fig. 7, if the search is carried out according to the order of fractional Fourier transform, the interval should be set small due to the small change range of its transformation order, and corresponding to the change range of acceleration, the order is basically unchanged, so it is not easy to search. Since the range of acceleration is relatively large, we can obtain more accurate results with a larger search interval. Therefore, the estimation range of acceleration is searched in the process of capture. The search strategy based on the acquisition method of fractional Fourier transform can be determined: firstly, one-dimensional search is carried out for the received pseudo code signals, and half of the code slice is taken as the search interval. When the code phase is fixed, piecewise matched filtering is carried out for the input signals, and the sampling rate is reduced at the same time. Secondly, the fractional order Fourier domain

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Fig. 7. The relationship of acceleration and transform order

optimal matching order is selected for the output  results of piecewise-matched filtering. When the changing order p = −2acr cot fc a c π (fc is the carrier radio frequency, a is the acceleration, and c is the speed of light), the optimal matching order is obtained. Due to the acceleration value is unknown, we can search for signal according to the scope of the acceleration estimation, namely every a to a search of the signal, at the same time to fractional Fourier transform of signal, if appear higher peak signal, the corresponding order for optimal matching order, according to the position of the correlation peak can be concluded that the doppler frequency estimation, according to the transform order p can be concluded that the doppler frequency rate estimation for (fc /c) · (cot(pπ/2)/((2fc g)/c)), which can be concluded that estimates of the vehicle acceleration for a=(cot(pπ/2)/((2fc g)/c)). In the case of low SNR and no significant correlation peak appears in a single capture, multiple incoherent accumulation can be carried out to detect the signal on the order corresponding to each a. In the above search process of acceleration, the resolution of fractional Fourier domain modulation frequency should be considered in the selection of a. The relation between the modulation frequency K and the resolution is KT > 1/T , that is K > 1/T 2 , where T is the time length of the selected signal, according to which the value range  of a can be deduced to be a > c T 2 · fc . Based on this range, we can reasonably choose the value of a. Capture method based on fractional Fourier transform can at the same time is effective in compensating doppler frequency and its rate of change, and to solve the traditional method in high dynamic environment to the problem of long time coherent accumulation, especially in high speed, low SNR circumstance, the advantage of fractional Fourier transform is superior to the traditional FFT capturing method. Figure 8 and Fig. 9 show the simulation diagram of signal acquisition based on FFT and FRFT when SNR = –40 dB and acceleration A = 50 g. As can be seen from the simulation figure, when the carrier has high acceleration motion, the peak value obtained by the traditional FFT method is not very obvious, while the FRFT method can get a more obvious peak value, which is easy to achieve signal capture. In fact, the above situation is because after FFT for high dynamic signals, the signal spectrum is widened and the signal detection peak value drops, resulting in the loss of signal at low SNR. Now the reason of its peak decline is analyzed. Assume that the carrier signal (complex signal) in a high dynamic environment has the following form:  (5) s(t) = exp j2π fd t + jπ Kt 2

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Where, fd is carrier Doppler frequency and K is modulation frequency, which is caused by carrier acceleration. The above analog signal is sampled. Assuming that the sampling frequency is Fs and the sampling interval is Ts = 1/Fs , the sampled signal can be expressed as:  (6) s(n) = exp j2π fd nTs + jπ K(nTs )2 If we do FFT of N points, then we can get: (2.27) S(k) =

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Where B = KnTs is the bandwidth of chirp signal. By using the mathematical formula |a + b| ≤ |a| + |b|, it is easy to know that, |S(k)| 0 ⎪ ⎪ ⎪ −1 ⎪ ⎨ −tan (PE /PN ) − π, PE ≥ 0, PN < 0 (8) ψ = −tan−1 (PE /PN ) + π, PE < 0, PN < 0 ⎪ ⎪ ⎪ −π/2, PE > 0, PN = 0 ⎪ ⎪ ⎩ +π/2, PE < 0, PN = 0 The transformation matrix from sh -frame to the b-frame is obtained as ⎡ ⎤ cψ sψ 0 Csb = ⎣ −sψ cψ 0 ⎦ h

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According to Eq. (7) and Eq. (9), the transformation matrix from the s-frame to the b-frame can be obtained as ⎡ ⎤ cψcγ + sψsγ sθ sψcθ cψsγ − sψcγ sθ Csb = Csbh Cssh = ⎣ cψsγ sθ − sψcγ cψcθ −sψsγ − cψcγ sθ ⎦ (10) −sγ cθ sθ cγ cθ The installation angle calculated above still has a certain error, which is generally a small angle error. According to Eq. (10), the original IMU output is converted to the b-frame for navigation solution. Then NHC or odometer can be used for the integrated navigation system. At the same time, the linear error model can be used to estimate the remaining installation angle errors [8, 9].

3 Error Analysis Firstly, the error of horizontal installation angle is estimated in ZUPT mode. As the ground is assumed to be horizontal, the error caused by uneven ground is not considered. In ZUPT mode, the estimate accuracy of the horizontal installation angle is mainly affected by the bias of the horizontal accelerometer. Generally, the bias of low-cost MEMS accelerometers is about 10 ~ 70 mg, and the estimate error of the horizontal installation angle is about 4°according to the maximum 70 mg. This error satisfies the assumption of small angle error. The estimate accuracy of the heading installation angle is mainly affected by the displacement error. As stated in the reference [11], it is known that the initial alignment error, gyro output error, and accelerometer output error will affect the position accuracy of SINS. Since the estimate process is relatively short, it can generally be completed within 10 s, so only the gyro constant drift and the accelerometer constant bias can be considered. In the ZUPT mode, if the time is sufficient, the constant drift of the three-axis gyro and the constant bias of the vertical accelerometer can generally be estimated well.

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Therefore, for the short time estimate process, only the initial horizontal attitude error and the constant bias of the horizontal accelerometer should be considered. As stated in the reference [16], the position error is generated by the accumulation of velocity error over time, so the velocity error can be directly analyzed. In addition, considering the low precision of low-cost MEMS-IMU, the short duration of the estimate process, and the small velocity as generally less than 2 m/s, the errors related to the earth rotation rate and the traveling velocity in the velocity error model of SINS can be ignored, so the simplified velocity error model is expressed as δ V˙ E = −φN fU + ∇E and δ V˙ N = φE fU + ∇N . According to the reference [11], the error of horizontal attitude angle in ZUPT mode is expressed as φE = −∇N /f U and φN = ∇E /fU . Substituting into the velocity error model, the velocity error model is obtained as δ V˙ E = 0 and δ V˙ N = 0. It can be seen that the influence of the horizontal attitude error and the constant bias of the horizontal accelerometer can be ignored in the short straight-line driving. Based on the above error analysis, it can be seen that the influence of horizontal attitude error, the gyro constant drift and the accelerometer constant bias on the estimate accuracy of heading installation angle can be ignored.

4 Field Tests To evaluate the estimate accuracy of the proposed method, the field test is carried out by using the Qianxun magic cube of Beidou integrated navigation system. The main technical specifications of MEMS-IMU in the test equipment are shown in Table 1. Table 1. Main specifications of MEMS-IMU Angular rate zero-rate level (◦/s)

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The number of the tested Qianxun magic cube is 4 in the field test. The test route is shown in Fig. 5 and the test equipment is shown in Fig. 6. The initial installation angle is estimated by the method proposed in this paper. After the estimate of the initial installation angle is completed, the navigation mode is changed to normal mode. The method in the reference [9] is applied to estimate the residual installation angle. As it is difficult to directly measure the real installation angle of the test setup, the estimated value of the residual installation angle can be used as the estimate error of the initial installation angle. In addition, it can be seen from the references [8] and [9] that the residual roll installation angle cannot be estimated, so only the estimate errors of the pitch installation angle and heading installation angle are listed in the test results, as shown in Table 2.

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2.54

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From the above test results, it can be seen that the pitch installation angle error estimated by the proposed method is within 2° and the heading installation angle error is within 0.5° which can ensure that the estimated installation angle error is small. In addition, the whole estimate process takes a short time, the static duration is 42 s, the maneuvering duration is only 2 s, and the requirement of the vehicle maneuvering velocity is not very high. In order to verify the influence of IMU bias error on the estimate accuracy of the installation angle, different gyro constant drifts and accelerometer constant biases are added to IMU data of the No. 3 test setup. The test results are shown in Table 3. The test results in Table 3 fully show that the gyro constant drift has little influence on the pitch installation angle and heading installation angle, while the accelerometer constant bias has great influence on the pitch installation angle but has little influence on the heading installation angle. The above results basically verify the conclusion of error analysis in Sect. 3. In summary, the experimental results verify that the proposed method has the characteristics of stable estimate accuracy and short time-consuming. It does not need to have higher requirement for vehicle maneuvering velocity. It only needs to be static for a period of time and then drive in a straight line to complete the estimate of the

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initial installation angle. As the practical operation is convenient, it is very easy to be popularized. Table 3. Test results of increasing IMU bias error Increased gyro constant drift (°/s)

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5 Conclusion Since MEMS-INS/GNSS integrated navigation system may be installed arbitrarily in vehicle environment, a convenient and fast estimate method of the initial installation angle is proposed. The estimated installation angle is used to convert the IMU frame, so that the converted IMU frame approximately coincides with the vehicle frame, which can facilitate the use of odometer or NHC. This method uses the navigation information calculated in virtual navigation coordinate system to estimate the installation angle. It only needs a short static and short-term straight-line driving to complete the initial installation angle estimate. It has the characteristics of simple operation, short time consumption, stable estimate accuracy and so on. As the displacement information of navigation solution is used to estimate the heading installation angle, this method does not have high requirements for dynamic maneuvering and vibration environment. Therefore, this method is applicable to civil passenger cars, small-unmanned vehicles or agricultural vehicles, which has obvious engineering significance. Finally, the effectiveness of the proposed method is verified by the field test.

References 1. El-Sheimy, N., Youssef, A.: Inertial sensors technologies for navigation applications: state of the art and future trends. Satell. Navig. 1(1), 1–21 (2020)

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2. Niu, X., Nassar, S., El-Sheimy, N.: An accurate land-vehicle MEMS IMU/GPS navigation system using 3D auxiliary velocity updates. Navig. 54(3), 177–188 (2007) 3. Hong, S., Lee, M.H., Kwon, S.H., Chun, H.H.: A car test for the estimation of GPS/INS alignment errors. IEEE Trans. Intell. Transp. Syst. 5(3), 208–218 (2004) 4. Noureldin, A., Karamat, T.B., Eberts, M.D., El-Shafie, A.: Performance enhancement of MEMS-based INS/GPS integration for low-cost navigation applications. IEEE Trans. Veh. Technol. 58(3), 1077–1096 (2008) 5. Zhang, Q., Li, S., Xu, Z., Niu, X.: Velocity-based optimization-based alignment (VBOBA) of low-end MEMS IMU/GNSS for low dynamic applications. IEEE Sens. J. 20(10), 5527–5539 (2020) 6. Abdel-Hafez, M.F., Saadeddin, K., Jarrah, M.A.: Constrained low-cost GPS/INS filter with encoder bias estimation for ground vehicles’ applications. Mech. Syst. Signal Process. 58, 285–297 (2015) 7. Dissanayake, G., Sukkarieh, S., Nebot, E., Durrant-Whyte, H.: The aiding of a low-cost strapdown inertial measurement unit using vehicle model constraints for land vehicle applications. IEEE Trans. Robot. Autom. 17(5), 731–747 (2001) 8. Chen, Q., Zhang, Q., Niu, X.: Estimate the pitch and heading mounting angles of the IMU for land vehicular GNSS/INS integrated system. IEEE Trans. Intell. Transp. Syst. (2020). https:// doi.org/10.1109/TITS.2020.2993052 9. Zhao, H., Miao, L., Shen, J.: High accuracy algorithm for SINS/odometer integrated navigation system. Acta Armamentarii 35(4), 433–440 (2014) 10. Yan, G.: Research on vehicle position and azimuth determining system. Doctoral Dissertation, Northwestern Polytechnic University, Xi’an, China (2006) 11. Fu, Q.: Key technologies for vehicular positioning and orientation system. Doctoral Dissertation, Northwestern Polytechnical University, Xi’an, China (2015) 12. Vinande, E., Axelrad, P., Akos, D.: Mounting-angle estimation for personal navigation devices. IEEE Trans. Veh. Technol. 59(3), 1129–1138 (2009) 13. Huttner, F., Kalkkuhl, J., Reger, J.: Offset and misalignment estimation for the online calibration of an MEMS-IMU using FIR-filter modulating functions. In: 2018 IEEE Conference on Control Technology and Applications (CCTA), pp. 1427–1433 (2018) 14. Liu, C.Y.:The performance evaluation of a real-time low-cost MEMS INS/GPS integrated navigator with aiding from ZUPT/ZIHR and non-holonomic constraint for land applications. In: Proceedings of the 25th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2012), pp. 1500–1520 (2012) 15. Qin, Y., Zhang, H., Wang, S.: Kalman filtering and integrated navigation principle, pp. 312– 314. Northwestern Polytechnical University Press, Xi’an (2004) 16. Qin, Y.: Inertial Navigation (2nd ed.), pp. 334–336. Science Press, Beijing (2014)

An Improved Wireless Positioning Algorithm Based on the LSTM Network Xiansheng Yang, Dong Chen, Jianzhu Huai, Xiaoxiang Cao, and Yuan Zhuang(B) The State Key Laboratory of Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan, China [email protected]

Abstract. Given that the BDS-3 (Beidou System-3) has been accomplished and works well, there are increasing demands for localization and navigation in daily life. However, BDS-3’s signals cannot cover some challenging areas such as urban canyons and indoor environments. To extend the availability of the navigation system, other positioning technologies are required to aid the BDS-3. Wireless fingerprint localization technologies (e.g., Wi-Fi, Bluetooth, 5G, etc.) have attracted lots of attention worldwide due to their ubiquitous and cost-effective characteristics, but there are various challenges such as fingerprints spatial ambiguities, RSS (Received Signal Strength) fluctuations over time and RSS variation caused by devices heterogeneity, which impairs positioning accuracy and precision. By analyzing the relationships hidden in adjacent fingerprints, we utilize the EncoderDecoder Framework and the sequence-based Long Short-Term Memory (LSTM) network to convert vulnerable RSS to stable RSS spatial gradient, which can eliminate RSS fluctuation over time and hardware diversity. The sequence-based LSTM also eliminates fingerprint spatial ambiguities using the sequence match. The preliminary experiments show the superiority of the proposed framework over the-state-of-art methods in terms of robustness and precision. Specifically, the proposed framework reduces average positioning errors by 24.68% and decreases the average errors by 36.38% and 6.8% in terms of the resistance to device diversity and RSS fluctuation over time respectively. Keywords: Deep learning · LSTM · Fingerprint · Wireless positioning

1 Introduction With the advancement of urbanization, there are increasing numbers of large buildings such as urban complexes and shopping malls, which not only block the signal of the Global Navigation Satellite System (GNSS) but also expands people’s demands for indoor positioning. There are various existing signals available for indoor positioning, including Wi-Fi [1], cellular networks [2], Radio Frequency Identification devices (RFID), Ultra-Width Ban (UWB), visible light [12] and so on. Among all above technologies, Wi-Fi-based wireless technologies are relatively popular due to their ubiquitous and cost-effective characteristics, but they are also faced with many challenges, such as RSS fluctuation © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 616–627, 2021. https://doi.org/10.1007/978-981-16-3142-9_59

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over time and RSS variation caused by device diversity. The former is that the RSS will be very different on the same point after a long-time interval, which cost people a lot of money and resources to frequently update fingerprint in the database to keep high positioning precision, and the latter is that RSS collected simultaneously by two different brands of devices are also very different, which is another serious problem. Most methods [13, 14] only achieve high precision in some specified scenarios, but fingerprint spatial ambiguity, fingerprint fluctuation over time, and fingerprint variety caused by device diversity still exist, which impaired their precision seriously. So most of them may not work well on real problems. In this work, we have achieved a robust positioning algorithm utilizing the EncoderDecoder framework to fuse fingerprints spatial gradient [10] and fingerprints. Hidden sequential features and hidden sequential gradient features are extracted from adjacent fingerprints in the Decoder Module and adjacent fingerprint spatial gradients in the Encoder Module respectively, and then are matched with the fingerprints in the database by LSTM. This will alleviate fingerprints instability caused by devices heterogeneity and fingerprints fluctuation over time. The main contributions of this paper are as follows: • The proposed algorithm fuses fingerprints and fingerprint spatial gradient using the Encoder-Decoder framework, which can effectively alleviate fingerprint fluctuation over time and fingerprint instability caused by device diversity. • We extract the sequence information hidden from adjacent fingerprints and adjacent fingerprint spatial gradient respectively, and then match fingerprints in the database, which can eliminate the spatial ambiguity of fingerprint and improve positioning precision. The rest of this paper is organized as follows. After reviewing related work in Sect. 2, we present an overview of the proposed model and extensive details of every part of the algorithm in Sect. 3. results based on experimental trials are discussed in Sect. 4. Section 5 concludes the paper.

2 Related Work Traditional fingerprint technologies, such as Nearest Neighbour and K-Nearest Neighbour algorithm [15], calculates the similarity between fingerprints from the database and current position, and then assigns different weights to K nearest positions, so the final position is a weighted average of the K nearest positions. Its time complexity is O(2), which is slow to navigate on a large database in a real-time manner. Mirowski et al. [4] calculated the similarity between fingerprints with time-effectively Kullback–Leibler divergence, but they were also faced with many problems, such as fingerprint fluctuation and spatial ambiguity. Recently, with the increase of the capacity of the GPU (Graphics Processing Unit), some methods from the Artificial Intelligence have become popular. You et al. [5] applied DRL (Deep Reinforcement Learning) to indoor positioning, which provided a new viewpoint. Qun et al. proposed a new model, named Deep Navi [6], which projected various information including geomagnetism, Wi-Fi, and visual image into a common space and then put these features into MDN (Mixed Dense Network) to

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infer current position. Instead of using traditional single-point matching, Hoang et al. [7] used trajectory data for matching, which eliminated questions caused by the RSSI short collecting time per location during positioning and the authors also compared the performances of different Recurrent Neural Networks (RNN). All of the above methods could only achieve high precision in some specified scenarios, but fingerprint spatial ambiguity, fingerprint fluctuation over time, and fingerprint variety caused by device diversity still exist.

3 Positioning Algorithm Using Encoder-Decoder Framework 3.1 Data Processing The data processing program consists of two parts, the offline stage and the online stage, as shown in Fig. 1. In the offline stage, as shown in black arrow in Fig. 1, we transform RSS collected by devices into fingerprints stored in database and optimize the model’s parameters. The entire path is divided into s RP (Reference Points) and the distance between adjacent reference points is d. In this work, the data are collected continuously; that is, a person with the device passes  the trajectory at a constant speed  j j 1 m and then receive RSSi = rssi , . . . , rssi , . . . , rssi rssi means that the RSS is received from jth AP at time ti and position posi = {xi , yi } at time ti {i = 1, 2, . . .}. Then, we can obtain a fingerprint database F = {f1 , f2 , . . . , fn }, where fi = {ti , posi , RSSi } shown in Fig. 1. After the fingerprint database is generated, we train our model and optimize the parameters. Firstly, the data passes through the Window Split Module, forming a fingerprint sequence. Then the fingerprint sequence is put into the Decoder Module and the Gradient Module, respectively.

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The latter processes fingerprint sequence into fingerprint spatial gradients. The fingerprint spatial gradients are put into the Encoder Module where the sequential information is extracted and form the hidden state. Then the output of the Windows Split

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Module and hidden states of the Encoder are put into the Decoder Module together, so the Prediction Module will output the current position. We calculate errors between the real location label and the output of the Prediction Module with the cross-entropy loss function, which will be used to update the parameters of the network through the Back-propagation Through Time (BPTT) algorithm. In the online stage as shown in the red arrow in Fig. 1, the data processing program is similar to the offline stage where the differences are that the output of the Prediction Module is send to users on the online stage directly rather than updating parameters of model on the offline stage. 3.2 Extract Features In the data processing program, the fingerprint database has been established as shown in the table in Fig. 1. The extracting features program is made up of the Window Split Module, the Gradient Module and the Public Module. 3.2.1 The Window Split Module This module mainly allocates the data into different windows. Assuming that the windows size is k in a trajectory, we have gotten fingerprint fp at tp , as shown in Fig. 2, and then extract k–1 fingerprints from the previous fingerprints in a time order, all of which will form wp = fp−k+1 , . . . , fp . We can get W = {wk , wk−1 , …, wn } in a trajectory and note the subscript of w begins with k because the size of window is k.

Fig. 2. Windows split module

3.2.2 The Gradient Module Although the RSS at the same location changes over time, the RSS differences between adjacent locations will be relatively stable and will not change rapidly over time [8].

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Fig. 3. Gradient module

In addition, subtraction between RSS of adjacent location can eliminate the bad effect of devices diversity [3]. If the same trajectory is passed twice at a long-time inter1 is the RSS from jth AP at ith RP for the first time. After a period of val and T(i,j) 2 1 –T 2 ) is very time, we collect T(i,j) at the same position for the second time. (T(i,j) (i,j) large, indicating that RSS changes rapidly over time and fingerprints match with RSS 1 –T 1 2 2 is vulnerable. However, the difference between (T(i,j) (i−1,j) ) and (T(i,j) –T(i−1,j) ) is little, implying fingerprint spatial gradient is stable. Moreover, two devices collect 1 is the RSS that first device received from jth AP at ith RSS simultaneously and S(i,j) 2 RP as well S(i,j) is the RSS that second device received from jth AP at ith RP. The 1 –S 2 ) is totally different, which would dramatically impair the precision of posi(S(i,j) (i,j) 1 –S 1 2 2 tioning. However, the difference between (S(i,j) (i−1,j) ) and (S(i,j) –S(i−1,j) ) is little, which means the fingerprint gradient will eliminate diversity of different brands of devices. From the above analysis, we define fingerprint spatial gradient dwp at tp , which can be calculated from wp directly as shown Fig. 3. From wp to dwp , tp−k+i (i = 1, but RSSp−k+i will be transformed 2…, k) and posp−k+i (i = 1, 2…, k) are invariant  

1 2 m drssp−k+i , drssp−k+i , . . . , drssp−k+i to DRSSp−k+i . We define DRSSp−k+i =   j j j where drssp−k+i = rssp−k+i − rssp and i = 1,2…, k−1; In other words, the subtraction between the RSS at current position and the RSS at end of Window from  the same AP. So we can get dfp−k+i= tp−k+i , posp−k+i , DRSSp−k+i , but note that dwp = dfp−k+1 , dfp−k+2 , . . . , fp , where the dfp = fp at a window. Finally, we can get all fingerprint spatial gradient DW = {dwk , dwk+1 , …, dwn }.

3.2.3 The Public Module Three types of the Public Modules: A, B, and C are presented in Fig. 4. They consist of different MLP (Multi-Layer Proceptions) and these Modules in the same type share

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their parameters with each other, which means there are only three set of parameter values. Since RSS, DRSS and yˆ have different measurement scales, it is unreasonable to concatenate or send them to other Modules (such as the Encoder Module or the Decoder Module) together so we use the Public Module to solve this problem.

Fig. 4. Framework of the proposed algorithm

3.3 Algorithm Framework The Encoder-Decoder Framework [9] is one of the most prevalent frameworks in the deep learning field and perform well in solving many problems. It consists of two parts: The Encoder Module and the Decoder Module. In the Encoder Module, we should design an appropriate neural network to extract features from the input data, acquiring hidden semantic; While in the Decoder Module, we also design a neural network to absorb hidden semantic produced by the Encoder Module and other factors, which is used to predict current position. LSTM [10] is a kind of RNN and is equipped with excellent “memory” because of its three logic gates (the forgetting gate, input gate and out gate). The good “memory” allows it to remember previous information from a long time ago and avoid gradient disappearance problem [11] that stop parameters of neural network updating. This paper fuses fingerprint spatial gradients and fingerprints by EncoderDecoder framework as shown in Fig. 4, which can alleviate the effect of device diversity and RSS fluctuation over time effectively in the positioning system. Considering hidden sequential information in adjacent fingerprints and adjacent fingerprint spatial gradients, we hire LSTM Cell in the Decoder Module and the Encoder Module to abstract hidden sequential information, which relieve the space ambiguity of fingerprint effectively and improve localization precision to some extent. Specifically, fingerprints database F pass through the Window Split Module and the Gradient Module, generating sequential fingerprints database W and sequential fingerprint spatial gradients DW (Sect. 3.2)

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respectively. We take out wi from W as well dwi from DW and then put them into the Decoder Module comprised of multiple LSTM Cells as well the Encoder Module comprised of multiple LSTM Cells respectively. Each LSTM Cell will output cell state and hidden state, both of which have the same dimension and are passed to the next LSTM Cell. For convenience, all cell state and hidden state in the Encoder Module and in the Decoder Module are represented by (cie , hi ), where i = 0, 1, 2.., k and (cid , si ),where i = 0,1,…, k, respectively, and we also set h0 , c0e = the matrix consisted of zero and (c0d , s0 ) = (cke , hk ). So, we can define the Encoder Module as follows:  H, C e = Encoder (DRSSp−k+1 , . . . , DRSSp−k+i , . . . , DRSSp ) (1) where H = {h1 , …, hk } is the hidden state containing sequential information extracted by LSTM Cell from DRSS and C e = {c1e , …, cke } is cell states; the Encoder is a neural network constituted of k LSTM Cells that pass massages to each other by hidden states hi and cell state cie ; DRSSi is fingerprint spatial gradients from dwi .While we define the Decoder Module as follows:   cid , si = Decoder (ˆyi−1 , si−1 , RSSi ) (2) where si is hidden state containing sequential information extracted by LSTM Cell from RSS; yˆ i−1 is output of the Prediction Module at previous time, namely previous position, which also affect the prediction of position at current time. si−1 is the previous hidden state in the Decoder Module and RSSi is fingerprint at current time. Then, we can predict current position as follows: yˆ i = g(ˆyi−1 , si , RSSi )

(3)

yˆ i is the output and the g is the Prediction Module consisted of full-connected layers as well the SoftMax layer. Here we need to discuss the input data of the Encoder Module and the Decoder Module. The input of proposed model consists of two parts, RSS and DRSS. The reason why we input RSS into the Decoder Module is that the relationship between fingerprint and position is more direct, and we can extract the hidden features by LSTM Cells in the Decoder Module. However, the relationship between the fingerprint spatial gradients and the position is more difficult to discover but have pivotal effect on the positioning system especially in the case of complex scenes. We conduct a series of experiments to prove this idea.

4 Experiment Evaluation 4.1 Data Description In order to evaluate the performance of the proposed algorithm, we conduced various experiments on a test site with an area of 4859 m2 (113 m * 43 m). The map is shown in Fig. 5. At the same time, in order to validate the capacity of the model relieving device diversity, we use a total of 4 devices to collect data, including Samsung S5, Xiaomi Mi4_1, Xiaomi Mi4_2 and Xiaomi Mi4 black, and they are divided into two

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groups: group1 consists of Samsung Galaxy S5 and Xiaomi Mi4_2 where 20 trajectories are collected; group2 are made up of Mi4_1 and Mi4_black where 24 trajectories are collected. Two volunteers use a continuous collection method to collect data, which means volunteers go through all trajectories at a constant speed, and the RSS, current time ti as well location coordinates posi are recorded when they arrive at each RP.

Fig. 5. The trial site in our experiment

4.2 Software and Hardware Equipment All the baseline and the proposed model are implemented on a server. We use two NVIDIA GeForce RTX2080Ti image processing units with 10 GB memory. For hyperparameters, we set the learning rate LR = 10e–4 and use the SGD optimizer. The batch size is 100 and the model training phase cost 1,681.81 s; while the prediction phase cost 0.01s for a single sample. We set dropout = 0.5 to avoid overfitting. 4.3 Model Comparison In order to verify the performance of the proposed model, we compared the proposed method with K-Nearest Neighbors algorithm, Support Vector Regression (SVR), Random Forest (RF) and xgboost. Cumulative Distribution Function (CDF), Root Mean Square (RMS) and running time are used as metrics. If not specified, the time sequence length of the proposed method is 4 (window size or TIME STEP = 4) and the grid size is 3 m. 4.3.1 Comparison Schemes on Same Devices We have conducted extensive experiments on four data sets. In this part, test data and training data are collected by the same device, and then the RMS are calculated. The RMS of the proposed framework decrease about 1 m (3.57 m), compared the traditional method (4.74 m). Although the training phase of this method takes the majority of the time (1681.81 s), It only costs about 0.01 s to predict a single position in the online stage,

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which is acceptable in most scenarios. We also separately compared the performance of different methods on the four data sets. The CDF curves of different methods on the four data sets can be found in Fig. 6 and the proposed method is better than other methods, especially in test data of S5 (4.06 m) and Mi4_2 (4.31 m), whose environment is more complex.

Fig. 6. CDF of location error on four datasets

4.3.2 Comparison Scheme on Different Devices In order to test the anti-hardware interference ability of the proposed model, our training data and test data are collected by different devices. The four mentioned devices are divided into two groups. In the first experiment, training data and test data were collected by Mi4_1 and Mi4 black respectively. It can be seen that the RMS of the model in this work (3.73 m) is the lowest, and RMS increased 1.58 m (it was the smallest among all methods) compared with experiments on the data collected by the same devices, indicating the strongest robustness for hardware interference. And Fig. 7 is the cumulative distribution function (CDF) of this experiment. In the second experiment, as shown in Fig. 8, the training data was collected by Mi4_2 and the test data was collected by S5. It can also be found that the proposed algorithm in this framework has the smallest RMS (5.60 m) and the rise in RMS is also the smallest (1.54 m). 4.3.3 Hyper-Parameters Analysis This section extends detailed extensive experiments of choosing optimal the length of the TIME STEP on the data set collected by Mi4_2. As shown in Fig. 9, the left y-axis is training time while the right y-axis is RMS, and the abscissa is the TIME STEP. Because the time of prediction in the actual scene does not change much with the TIME STEP, it is not necessary to describe the test time in detail. It can be seen from Fig. 9 that when the

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Fig. 7. CDF of location error to evaluate robustness in terms of hard ware. Training data and test data collected by Mi4_1 and Mi4 black, respectively

Fig. 8. CDF of location error to evaluate robustness in terms of hard ware, Training data and test data collected by Mi4_2 and S5 respectively

TIME STEP is 4, the performance on this data set is the best (4.31 m), and the training time gradually increases with the length of the TIME STEP.

Fig. 9. The performance of proposed method with respective to value of TIME STEP

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4.3.4 Comparison Scheme on Time In this section, the train data and test data were collected in 2015 and 2017 respectively. Because data (in Fig. 10) was collected not only at different time but also by different devices, we just make the preliminary decision that the proposed method can relieve the RSS’s fluctuation over time through the rough experiment and the literature [3]. From the Fig. 10, it is obvious that the proposed data also reach the lowest RMS, implying that proposed method can alleviate the RSS fluctuation over time.

Fig. 10. The performance of methods on Time fluctuation

5 Conclusion This work proposed an indoor positioning algorithm for sequence matching by fusing fingerprints and fingerprint spatial gradients with the encoder-decoder framework, which is a deep learning technique. The algorithm has effectively alleviated hardware heterogeneity and spatial ambiguities and improved the indoor positioning accuracy by 1.17 m, which is superior to the state-of-the-art algorithms proposed in the literature. As the data were collected on the same day, it is impossible to verify the fingerprint gradient fusion and the mitigation effect of time instability, which remains to be explored. In the future, we will combine our model with the Inertial Navigation technique to improve the robustness of the system when the wireless signal is weak or unreliable. We will also add the barometer to our deep learning framework to further determine the floor level while the user is using an elevator or a lift to achieve ubiquitous indoor positioning.

References 1. Wei, S., Wang, J., Zhao, Z.: LocTag: passive WiFi tag for robust indoor localization via smartphones. In: IEEE INFOCOM 2020-IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS). IEEE (2020) 2. Shi, L., et al.: 5G Internet of radio light positioning system for indoor broadcasting service. IEEE Trans. Broadcast. 66(2), 534–544 (2020)

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3. Wu, C., et al.: Gain without pain: accurate WiFi-based localization using fingerprint spatial gradient. In: Proceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies, vol. 1, no. 2, pp. 1–19 (2017) 4. Mirowski, P., et al.: Probability kernel regression for WiFi localisation. J. Location Based Serv. 6(2), 81–100 (2012) 5. Li, Y., et al.: Deep reinforcement learning (DRL): Another perspective for unsupervised wireless localization. IEEE Internet Things J. 7(7), 6279–6287 (2019) 6. Niu, Q., et al.: DeepNavi: a deep signal-fusion framework for accurate and applicable indoor navigation. In: Proceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies, vol. 3, no. 3, pp. 1–24 (2019) 7. Hoang, M.T., et al.: Recurrent neural networks for accurate RSSI indoor localization. IEEE Internet Things J. 6(6), 10639–10651 (2019) 8. Zheng, Y., Jiing‘ao, X., Lina, Y.: Indoor localization: challenges and opportunities. J. Northwest Univ. (Nature Science Edition). 48(2), 172–182 2018 9. Tokushige, H., Fossorier, M.P.C., Kasami, T.: A test pattern selection method for a joint bounded-distance and encoding-based decoding algorithm of binary codes [Transactions Letters]. In: IEEE Transactions on Communications, vol. 58, no. 6, pp. 1601–1604 (2010) 10. Olah, C.: Understanding LSTM Networks (2015) 11. Hinton, G.E., Ruslan, R.S.: Reducing the dimensionality of data with neural networks. Sci. 313(5786), 504–507 (2006) 12. Zhuang, Y., et al.: Visible light positioning and navigation using noise measurement and mitigation. In: IEEE Transactions on Vehicular Technology, vol. 68, no. 11, pp. 11094–11106 (2019) 13. Han, J.B., Choi, L.: Large-scale indoor positioning using geomagnetic field with deep neural networks. In: ICC 2019 - 2019 IEEE International Conference on Communications (ICC). IEEE (2019) 14. Rizk, H., Torki, M., Youssef, M.: CellinDeep: robust and accurate cellular-based indoor localization via deep learning. IEEE Sens. J. 19(6), 2305–2312 (2018) 15. Bahl, P., Padmanabhan, V.N.: RADAR: an in-building RF-based user location and tracking system. In: Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No. 00CH37064), vol. 2. IEEE (2000)

Research on Space/ground Based Pulsar Timescale for PNT Qingyong Zhou1(B) , Ziqing Wei1 , Linli Yan2 , Pengfei Sun3 , Kun Jiang4 , and Yidi Wang5 1 Xi’an Institute of Surveying and Mapping, Xi’an 710054, China 2 School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China 3 National Time Service Center, CAS, Xi’an 710600, China 4 Beijing Institute of Communication and Tracking Technology, Beijing 100090, China 5 College of Aerospace and Material Engineering, National University of Defense Technology,

Changsha 410073, China

Abstract. The comprehensive Positioning Navigation Timing (PNT) system is a multi-source information fusion system with Global Navigation Satellite System (GNSS) as the core. The high-precision millisecond pulsar timing can enhance the long-term stability of the GNSS time benchmark and maintain a space-time benchmark for future deep-space users. In this paper, the method of establishing space and ground-based pulsar time is studied. The ground radio timing data from the International Pulsar Timing Array (IPTA), the X-ray timing data from the Neutron star Interior Composition Explorer (NICER) in space, and the simulation data from the 500-m spherical radio telescope (Five-hundred-meter Aperture Spherical radio Telescope, FAST) for three millisecond pulsars are used to analyze the stability of ground/space-based pulsar time. The research results show that the annual stability of the PSR J0437-4715 ground-based pulsar time based on IPTA data is 3.30 × 10–14 , and the 10-year stability is 1.23 × 10–15 , respectively; The existence of pulsar red noise could reduce the time stability of the pulsar; The annual stability of the PSR J1939+2134 ground-based pulsar time is 6.51 × 10–12 ; We find that the accuracy of the pulse Time of Arrival(TOA) is an important factor that restricts the stability of space-based pulsar time. Based on NICER space X-ray timing data, the stability of the pulsar time for PSR J1824-2452A is 1.36 × 10–13 in one year; Finally, the simulation analysis for FAST’s data without considering the influence of red noise is completed, and we find that the PSR J1939+2134 ground-based pulsar time based on FAST has an annual stability of 2.55 × 10–15 , a 10-year stability of 1.39 × 10–16 , and a 20-year stability of 5.08 × 10–17 . It demonstrates that powerful pulsar observation capabilities of FAST will help to improve the accuracy of ground-based pulsar time. Keywords: Positioning navigation timing · Pulsar time · Atomic time · Pulse TOA

1 Introduction Spatial location and time are the most important basic information in the era of interconnection of all things, especially time is the basis of modern high-precision measurement. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 628–636, 2021. https://doi.org/10.1007/978-981-16-3142-9_60

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The time measurement tool is atomic clock, which can achieve time measurement accuracy from nanosecond (10–9 s) to picosecond (10–12 s), and even femtosecond (10–18 s) and higher. In addition, the standard time and frequency signals generated by atomic clock can be carried on radio waves or light waves for long-distance transmission [1, 2]. A national time and frequency system with atomic clock as the core is of great significance for the protection of national life, economic operation and national security, and is an important national spatial information infrastructure. Relying on the Global Navigation Satellite Systems (GNSS), GNSS can provide high-precision and reliable positioning, navigation, timing (PNT) services in the world. The positioning accuracy can reach centimeter level, and the time service accuracy can reach 10 ns, which can meet the needs of most users on the earth’s surface and near earth space [3, 4]. As an advanced space-time benchmark service information system, GNSS has been widely integrated into human life and society. However, GNSS has weak radio signal, poor penetration and poor anti-interference, and cannot solve all users’ PNT services, such as users in deep space, underwater and other scenarios. In order to provide PNT services with stronger applicability, higher accuracy and robustness, USA designed its national PNT architecture in 2010 [5]. The PNT system will integrate the existing navigation resources, deeply integrate the navigation terminal, optimize the calculation theory, and provide continuous, unified and reliable PNT services for space, air, ground, water, underground and underwater users, aiming at building a new national PNT system in 2025. Since the discovery of the first pulsar in 1967, scientists have realized the application value of extremely stable pulsar rotation frequency in time reference [6–8]. Pulsars are a kind of high-speed rotating neutron stars, which have the most stable frequency in nature. The rotation of some millisecond pulsars is extremely stable, the rotation period rate is 10–19 –10–21 s/s, the annual stability is 3 × 10–14 , and the annual maximum deviation is only 1 µs in one year. It indicates that pulsar may become a new time and frequency resource in the future, which can provide an independent time benchmark based on remote natural objects and lasting for millions or even billions of years, called pulsar time (PT). The long-term stability of ground atomic time can be improved by using the long-term stability of pulsars. With the improvement of pulsar timing accuracy, pulsar timing also shows its good engineering application prospect. In December 2018, ESA announced the operation of a pulsar based clock (PulChron) project [9], which aims to use pulsars to monitor and improve the time stability of Galileo satellite navigation system. In January 2019, ESA scientists published their first result of PulChron in 55 days from December 2018 to January 2019. It was found that the integrated pulsar based on 18 ms pulsars of the European pulsar timing array deviated from UTC by 1–2 ns in two months, and its monthly stability was better than that of UTC. PT has the advantages of high stability, full autonomy and universal [7]. Under the framework of the comprehensive PNT, using pulsar timing information is expected to monitor and improve the long-term stability of GNSS time benchmark, and GNSS users can obtain more stable time benchmark information. For deep space users, pulsar, as a cosmic lighthouse, can provide high-precision autonomous navigation and time service. Meanwhile, if millisecond pulsars are observed in the space X-ray and ground radio frequency, it can realize high-precision time traceability between the earth and space.

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It can be seen that the millisecond pulsars can enhance the GNSS time benchmark and construct the deep space navigation time service system in the PNT system clock. At present, PNT related research focuses on architecture design, multi navigation source fusion and model elastic design, and the application research of new time frequency resource PT is relatively less. This paper mainly discusses the principle of PT and evaluate the stability of PT by using the measured data of IPTA\NICER and the simulation data of FAST.

2 Basic Principle of Pulsar Time Pulsar timing is the basic observation method of pulsar time scale research. Pulsar timing is the process of using radio telescope or space observation satellite to monitor the regular pulsar radiation and record pulse time of arrival. TOA refers to the time when the pulsar radiation pulse signal reaches the observation equipment. The pulsar signal is very weak, so the timing observation needs to stack the pulse profiles observed many times according to the timing model to get a high signal-to-noise ratio pulse profile as the standard profile. Then, the pulse arrival time of each observation can be obtained by cross-correlation between the integral pulse profile and the standard profile. The clock of the station or satellite is usually selected as the time reference for timing observation, and its time should be corrected to the international standard time system, such as the International Atomic Time (TAI) or terrestrial time (TT) standard time system, so as to ensure that the timing observation is based on the time system with the highest accuracy in the world. For the analysis of near earth pulsar observation events, we select an ideal inertial reference system, usually the solar centroid celestial reference system, so the TOA at the observation station is converted to the TOA at the barycenter of the solar system (SSB), and the time scale is also modified to barycentric coordinate time (TCB). Through the analysis of TOAs at SSB the timing model of pulsar can be obtained [10, 11]: 1 φ(t) = φ0 + v(t − t0 ) + v˙ (t − t0 )2 + · · · 2

(1)

Where, φ(t) is the pulse phase at the observational time t, φ0 is the pulse phase at the initial epoch t0 , and ν, ν˙ are the rotation frequency of pulsar and its derivative respectively. Timing model also can be called as pulsar rotation law, can accurately predict the time of arrival of the pulse. Pulsar time is a relative time scale, which is realized by measuring the difference between PT and reference atomic time clock. Whether the ground radio observation or space observation of pulsar, the TOA of the pulse obtained by timing observation is based on the atomic time. Firstly, the TOA of the pulse is calibrated by the station atomic clock, and then the arrival time of the pulse is traced to the international atomic time through the time comparison link. The timing residual is the difference between the predicted and observed time of arrival at the SSB. The predicted value is based on the timing model reflecting the pulsar rotation law, which represents the pulsar time (PT). The arrival time of the pulse obtained by radio observation is based on the atomic time (AT), so the timing residual includes the clock error between the pulsar time and

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the reference prime time. If various effects are completely corrected in pulsar timing processing, the timing residual is PT-AT. Now, BIPM provides two ways to realize TAI: quasi real time TT (TAI) and post event TT (BIPM). In this paper, TT (BIPM2015) is selected as the benchmark of space-based pulsar time research, and the stability of PT is analyzed by σz algorithm [12].

3 Time Stability Analysis of Space-Based Pulsars We select two millisecond pulsars PSR J1939+2134 and PSR J1824-2452A with strong X-ray and radio radiation, which are conducive to the comparison of space/ground-based pulsar time and the time reference is TT (BIPM2015). Two millisecond pulsars are the observation targets of IPTA and NICER. Intensive observation is carried out and the observation data are released. 3.1 TIME Stability Analysis of Ground Based Pulsars Based on IPTA Timing Data In 2019, IPTA have released the second batch of observation data of 65 pulsars including two types of data [14]. The first type of data inherits the form of the first batch of IPTA data, fitting the dispersion measure (DM) and white noise parameterization. The second type of data carries out red noise fitting on the basis of the first type. In this paper, the first type data of PSR J1939+2134 and PSR J1824-2452A are selected, and the red noise is not processed. The data period of PSR J1824-2452A is about 6 years, while that of PSR J1939+2134 is nearly 30 years. The planetary ephemeris is DE436, and the ground-based pulsar time of each pulsar is shown in Fig. 1. The expression of pulsar time is PT(I) - TT (BIPM2015). I represents the name of pulsar, also known as timing residuals. In Fig. 1, the upper figure is PT (PSR J1824-2452A) - TT (BIPM2015), and its root mean square error (RMS) is 2.39 µs. The lower figure is PT (PSR J1939+2134) TT (BIPM2015), and its RMS is 68.37 µs. It can be seen that there is obvious long-term timing noise, also known as red noise.

Fig. 1. The ground based pulsar time based on IPTA millisecond pulsar timing data (PSR J18242452A in the upper figure and PSR J1939+2134 in the lower figure, the same below)

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Fig. 2. The stability of ground-based pulsar constructed by IPTA pulsar timing data

The σz method is used to evaluate the pulsar time stability based on timing data of IPTA millisecond pulsar, as shown in Fig. 2. It can be seen that the time stability of ground-based pulsars constructed based on IPTA data increases slowly with the increase of time scale. It should be noted that when the time scale is larger than half of the observation period, it is estimated that the latest observation data will be used preferentially. It is estimated that the annual stability of PSR J1824-2452A ground-based pulsar is 2.32 × 10–13 and its 5-year stability is 1.10 × 10–13 , while that of PSR J1939+2134 ground-based pulsar is 6.51 × 10–12 , its 5-year stability is 2.42 × 10–12 and its 10-year stability is 2.05 × 10–12 . With the increase of time scale, the stability changes little. Statistics show that the average TOA accuracy of PSR J1939+2134 is 331 ns, while that of PSR J1824-2452A is 997 ns. Because of the quasi periodic red noise of PSR J1939+2134, its pulsar time stability is obviously restricted. 3.2 Time Stability Analysis of Space-Based Pulsars Based on the Observation Data of NICER Project NICER is an astrophysical space mission implemented by NASA on the international space station [14]. It is dedicated to solving the four basic force interaction mechanisms inside neutron stars. In this paper, we download the original observation data of nice from MJD 57933.0–58588.0 from NASA official website. Just like other space X-ray satellite case photon event data processing, it needs the following steps: (1) data extraction; (2) time file generation; (3) clock signal elimination and target photon screening; (4) TOA correction; (5) pulse profile generation and TOA calculation; (6) timing analysis. The processing analysis shows that the single observation accuracy of pulse TOA of PSR J1824-2452A is 9.16 µs, while that of PSR J1939+2134 is 15.57 µs. Through the timing analysis of TOA series, the timing residuals of each pulsar can be obtained, which is also the characterization of space-based pulsar time, as shown in Fig. 5. In Fig. 5, the upper figure shows PT(PSR J1824-2452A) - TT (BIPM2015) with RMS of 22.09 µs, and the lower figure shows PT(PSR J1939 + 2134)-TT(BIPM2015) with RMS of 18.16 µs (Fig. 4). Similarly, the time stability of space-based pulsars based on the observation data of nice can be obtained, as shown in Fig. 3.

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Fig. 3. The space based pulsar time estimation based on NICER millisecond pulsar timing data.

Fig. 4. The stability of ground-based pulsar time constructed by NICER timing data

It can be seen that the time stability of space-based pulsars constructed based on the data of nice is basically stable in a short time scale. The annual time stability of space-based pulsars of PSR J1824-2452A and J1939+2134 are 1.36 × 10–13 and 2.02 × 10–12 respectively. NICER was launched and installed on the international space station in September 2017. According to the latest international scientific data protection cycle, we can only download the observation data of two pulsars for about one and a half years during the research period, so the current results can not reflect the long-term stability of space-based pulsars. The effective area of the X-ray detector of nicer is about 1800 cm2 @1.5 keV However, the photon flux density of the two millisecond pulsars at 0.5–10 keV is in the order of 10–5 ph/cm2 /s. according to the calculation, the photon number of PSR J1824-2452A and PSR J1939+2134 received by nicer is 0.055 ph/s and 0.021 ph/s respectively [15], and the cumulative time of each observation is in the order of ks. Although the X-ray detector of NICER has a strong ability to suppress the spatial background noise, the background noise intensity received by the detector is 0.90 ph/s and 0.49 ph/s, which restricts the high-precision pulse TOA. It can be seen that the further improvement of space-based pulsar time stability requires large area and high sensitivity detectors, long observation time.

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3.3 PT Stability Analysis Based on FAST Simulation Data High precision timing observation is the foundation of pulsar timing. At present, FAST is the world’s largest single aperture radio telescope, has greatly improved the pulsar observation sensitivity [16]. Due to the limited observation area of FAST and the strong red noise of PSR J1939+2134, FAST has not observed the two millisecond pulsars, and FAST has not released its millisecond pulsar timing results. In order to compare with the results calculated by IPTA and NICER, we simulate the 30-year observation data of two pulsars. The estimation of TOA observation accuracy takes into account the influence of phase noise at the same time [17]. The results show that the time of arrival accuracy of 1800s observed by FAST for PSR J1824-2452A and J1939+2134 is 1.532 µs and 37.9 ns respectively. In the data simulation of PSR J1939 + 2134, the presence or absence of red noise is considered. The ground-based PT based on FAST are obtained, as shown in Fig. 5. The RMS values of three ground-based PT are 1.56 µs, 39.49 ns and 89.33 µs respectively, which are PSR J1824-2452A, PSR J1939+2134 and PSR J1939+2134 without considering red noise effect. Similarly, the stability of three pulsars can be obtained, as shown in Fig. 6.

Fig. 5. The ground-based pulsar time based on FAST simulation timing data

It can be seen that, without considering the influence of red noise, the time stability of PSR J1824-2452A and PSR J1939+2134 pulsars increases with time, and tends to be stable when the time exceeds 15 years, which is related to the fixed timing observation accuracy of pulsars in the simulation. The annual stability of PSR J1824-2452A groundbased pulsar based on FAST is 1.02 × 10–13 , 5 × 10–15 and 2.27 × 10–15 , while that of PSR J1939+2134 ground-based pulsar is 2.55 × 10–15 , 1.39 × 10–16 and 5.08 × 10–17 . It can be seen that high-precision measurement of time of arrival is the most effective way to improve the stability of pulsar time. In this paper, the influence of red noise on the time of PSR J1939+2134 ground-based pulsar is also analyzed. The annual stability of PSR J1939+2134 ground-based pulsar considering red noise is 1.14 × 10–12 , 10-year

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Fig. 6. The stability of ground-based pulsar constructed by FAST simulation timing

stability is 1.66 × 10–12 and 20-year stability is 3.36 × 10–13 . It is found that the red noise will greatly reduce the pulsar time stability, and the strong red noise will cover up the contribution of high-precision pulse TOA measurement, but the pulsar time stability will also flatten with the increase of time scale.

4 Conclusion and Discussion The Comprehensive PNT system is an important part of national information infrastructure in the future, which can provide unified and high-precision space-time benchmark service for all kinds of users. As the core of the national PNT system, GNSS provides services to meet the most common needs, and provides time and space benchmark transfer services to other users’ navigation time service systems. In this paper, the method of ground/space-based pulsar time is studied. The stability of space-based pulsar time is analyzed by using IPTA ground radio, NICER space X-ray millisecond pulsar timing data and 30 years FAST simulation data. (1) Based on IPTA data, the annual stability of PSR J1824-2452A ground-based pulsar is 2.32 × 10–13 , and the 5-year stability is 1.10 × 10–13 . Affected by its red noise, the annual stability of PSR J1939+2134 ground-based pulsar is 6.51 × 10–12 , 5-year stability is 2.42 × 10–12 , and 10-year stability is 2.05 × 10–12 . (2) The accuracy of pulse TOA is an important factor restricting the time stability of space-based pulsars. The annual stability of space-based pulsars of PSR J1824-2452A and J1939+2134 are 1.36 × 10–13 and 2.02 × 10–12 , respectively. (3) By using the simulation data of FAST, it is confirmed that FAST can further improve the observation accuracy and is more conducive to the improvement of the time stability of ground-based pulsars. Without considering the influence of red noise, the annual stability of PSR J1824-2452A ground-based pulsar based on fast is 1.02 × 10–13 , 5.00 × 10–15 and 2.27 × 10–15 , while that of PSR J1939 + 2134 ground-based pulsar is 2.55 × 10–15 , 1.39 × 10–16 and 5.08 × 10–17 .

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Acknowledgments. This study is funded by the State Key Development Program for Basic Research of China (Grant No. 2020YFB0505800), the National Science Foundation of China (Grant No. 42004004,42074006, and 11903001), the Key Research Foundation of Education Ministry of Anhui Province (KJ2019A0787), the Doctor Foundation of Anhui Jianzhu University 2019 (2019QDZ14),and National Social Science Foundation of China(Grant No.2020-SKJJ-C-043).

References 1. Major, F.G.: The Quantum Beat-Principles and Applications of Atomic Clocks(Second Edition). Springer, NewYork (2007) 2. Zhai, Z.Z., Zhang, W.Q., Yong, C., Yang, P.H.: Basic Principle of Atomic Clock and Time Frequency Measurement Technology. Shanghai Science and Technology Literature Press, Shanghai (2008) 3. Yang, Y.X.: Comprehensive PNT system and its key technologies. J. Surveying Mapp. 45, 505–510 (2016) 4. Lu, J., Guo, X., Su, C.: Global capabilities of BeiDou Navigation Satellite System. Satellite Navigation 1(1), 1–5 (2020). https://doi.org/10.1186/s43020-020-00025-9 5. National Security Space Office. National positioning, navigation, and timing architecture implementation plan (2010). Available via DIALOG. https://rosap.ntl.bts.gov/view/dot/ 18293. Accessed 8 Mar 2021 6. Petit, G., Tavella, P.: Pulsars and time scales. Astron. Astrophys. 308, 290–298 (1996) 7. Taylor, J.H.: Millisecond pulsars: nature’s most stable clocks. Proc. IEEE 79, 1054–1062 (1991) 8. Hobbs, G., Guo, L., Manchester, R.N., Coles, W., et al.: A pulsar-based timescale from the international pulsar timing array. MNRAS. 491, 5951–5960 (2019) 9. Ricardo, P., Esteban, G., Pedro, R., et al.: PulChron: a pulsar time scale demonstration for PNT systems. In: Proceedings of the 2019 Precise Time and Time Interval Meeting, ION PTTI 2019, Reston, Virginia, 28–31 January 2019 10. Edwards, R.T., Hobbs, G.B., Manchester, R.N.: TEMPO2, a new pulsar timing package II. The timing model and precision estimates. MNRAS. 372, 1549–1574 (2006) 11. Zhou, Q.Y., Ji, J.F., Ren, H.F.: Timing equation in X-ray pulsar autonomous navigation. Acta Physica Sinica. 62, 139701 (2013). https://doi.org/10.7498/aps.62.139701 12. Matsakis, D.N., Taylor, J.H., Eubanks, T.M.: A statistic for describing pulsar and clock stabilities. Astron. Astrophys. 326, 924–928 (1997) 13. Perera, B.B.P., DeCesar, M.E., Demorest, P.B., et al.: The international pulsar timing array: second data release. MNRAS. 490, 4666–4687 (2019) 14. Dominick, M.R., Zaynab, G., Lauren, L., et al.: A NICER view of spectral and profile evolution for three X-Ray-emitting millisecond pulsars. APJ. 892, 150–164 (2020) 15. Deneva, J.S., Ray, P.S., Lommen, A., et al.: High-precision X-Ray timing of three millisecond pulsars with NICER: stability estimates and comparison with radio. APJ. 874, 160–184 (2019) 16. Nan, R.D., Wang, Q.M., Zhu, L.C., Zhu, W.B.: Pulsar observations with radio telescope FAST. Chin. J. Astron. Astrophys. 6, 304–310 (2006) 17. Zhou, Q.Y., Liu, S.W., Hao, X.L., et al.: Analysis of measurement accuracy of ephemeris parameters for pulsar navigation based on the X-ray space observation. Acta Physica Sinica. 65, 079701 (2016). https://doi.org/10.7498/aps.65.079701

Research on Positioning Method in the Lunar Space Linshan Xue1 , Xue Li2(B) , Weiren Wu1 , and Yikang Yang3 1 University of Electronic Science and Technology of China, Chengdu 611731, China 2 Chongqing University, Chong Qing 400044, China 3 Xi’an Jiaotong University, Xi’an 710049, China

Abstract. With the accomplish of Chang’e-5 mission, China’s Chang’e mission has entered the next stage, that is, the development and utilization of the moon and the construction of the lunar station. However, in this stage of lunar surface exploration mission, the accuracy of positioning cannot meet the requirement. In the paper, we provide the telemetry, tracking, command (TT&C) and communication links in the lunar space at the lunar station. Then, the high accuracy positioning method is given. The method mainly positioning by ranging and angle measurement. The ranging completes the acquisition of radial parameters of transceiver nodes, and the angle measurement acquire the tangential parameters. In order to obtain high precision positioning results, BOC (5, 1) modulation system and dual one-way ranging (DOWR) are used to measure the distance, and L-type interferometer is used to measure the angle. Besides, we design the angle measurement algorithm to increase the number of transmitter that can be measured by the interferometer. Under the condition of carrier to noise ratio of 60 dBHz, the ranging accuracy is 0.947 ns, and the angle measurement accuracy is higher than 0.02 rad. Keywords: Lunar base · TT&C · Positioning · Ranging · Angle measurement

1 Introduction As the nearest celestial body to the earth, the moon will be used as a relay station for deep space exploration in the future. Since the 1970s, the United States, the Soviet Union and other countries have been carrying out exploration of the moon to show the strength of nation. With the end of the cold war, the exploration of the moon has gradually changed from a political mission to a scientific mission [1]. Since the launch of Chang’e-1 on October 24, 2007, China’s Lunar Exploration Mission has been carried out step by step. As of December 18, 2020, the five Chang’e exploration missions have been successful. In the future, manned landing on the moon and the construction of lunar sur-face stations will also be carried out. After completing the first phase of Chang’e exploration missions, China will gradually start the construction of lunar station. However, the lunar polar resource exploration, manned lunar landing and the construction of lunar station put forward higher requirements for navigation and positioning tasks. And the high-precision lunar navigation and positioning function is a vital part of © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 637–645, 2021. https://doi.org/10.1007/978-981-16-3142-9_61

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manned lunar exploration. Although very long baseline interferometry (VLBI) observation can achieve high precision positioning of 10 m magnitude, there are many nodes on the moon surface during the construction of the moon base which will lead to the lack of the spectrum resources and VLBI resources. Besides, the combination of inertial navigation system (INS) and image navigation are used in most missions. However, the error of INS will drift with time, it is impossible to achieve high-precision navigation and positioning [2]. This paper analyzes the high-precision positioning methods in the construction of the lunar station. Firstly, the scene of this stage is designed, including the distribution of each node on the lunar surface and the allocation of related links. Then, the BOC & single carrier mode is used to position the lunar surface unit. BOC signal is used for ranging, and single carrier signal is carried at the central frequency of integrated signal for angle measurement. If the results of angle measurement and range measurement are obtained, the lander or rover on the lunar surface can be located. After obtaining its body coordinate system, it is converted to the moon fixed coordinate system through the lunar stations or lander at a fixed position on the lunar surface.

2 The Scene and Link Design of Lunar Station There are two methods to position the lunar unit. One is to locate the lunar surface unit through the TT & C links between earth and moon. The method has a large number of TT & C units on the ground which has complete functions and strong controllability. However, the control unit far away from the moon, with prolonged time and large signal attenuation. The second method is to position the lunar surface unit through the near moon unit or the lunar surface unit (including the lunar relay satellite, rover, etc.), which has the advantages of strong autonomy, short distance from the unit and high measurement accuracy, but the disadvantage is that it needs strong autonomy. In this paper, the positioning of the near moon unit is carried out through the earth moon TT & C link and the orbit information of the near moon unit. And the unit on the moon surface can be positioned by near moon unit. The link designs in the two scenarios are as follows [3]. The earth and nearby nodes are mainly as follows . 1) Mission Center: it provides command of the whole task; 2) Deep space TT & C network: it provides ground TT & C support and completes high-speed data receiving and sending on the ground. 3) VLBI measurement station: it mainly finish the TT & C of spacecraft; 4) Earth relay satellite system: it is the system in earth orbit that provides relay services for spacecraft data transmission; 5) Beidou navigation satellite system: to a certain extent, it is the communication relay for the space units near the moon (Fig. 1). The moon and its nearby nodes are as follows: 1) Lunar station: it is the main node of the lunar surface and serves as the center of the whole trunk communication;

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Ka Uplink control/ranging Downlink telemetry/ranging/DOR

S Control/Telemetry/Data transmission

Laser Uplink&Downlink

S Uplink control/ranging Downlink telemetry/ranging/DOR/data transmission

lunar rover

Ka Downlink Lunar station S/Ka band link S band uplink telemetry/data transmission S band downlink telemetry/ranging/DOR

Lander

Ka band uplink telemetry/ranging Ka band downlink telemetry/ranging/DOR

Rover

Fig. 1. Design of links between earth and moon

2) Relay satellite system: it is located in the orbit around the moon, providing data relay services for lunar orbiting spacecraft and landing facilities; 3) Lunar orbiting space station: it is the smallest platform in lunar orbit. Its main purpose is to improve the capability of deep space exploration as a test site; 4) Lunar Rover: it provides large-scale exploration vehicle within the scope of the moon, it is necessary to establish links on the ground to ensure the security of the mission. 5) Lunar surface lander/ascender: it is a spacecraft used to land and rise on the lunar surface and rendezvous with the lunar orbiting space station; 6) Astronaut: the executor of space science exploration activities (Fig. 2).

Moon orbiter

DSG

Lunar astronauts

Lunar station

Lander S band uplink telemetry/data transmission S band downlink telemetry/ranging/DOR Ka band uplink telemetry/ranging Ka band downlink telemetry/ranging/DOR UHF communication link

Fig. 2. Design of links near moon

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The functions of lunar station can be generally divided into the following parts: 1) Scientific exploration and the related experimental functions. 2) Ensuring the basic survival of relevant personnel. The above units need to carry out data links with the lunar relay satellite, the ground, the astronauts and each other at the same time, so they need to be equipped with standard S band TT & C, navigation system, Ka band TT & C, navigation system, Ka/laser high-speed data transmission system and UHF local communication system. Considering there are many lunar surface units and the bandwidth resource is scarce, S/Ka band is used for TT & C data transmission. For example, the relay satellite needs to establish TT & C data transmission links with large instruments on the lunar surface. In addition, data transmission is needed between large lunar units (such as manned spacecraft, lunar orbital space station and lunar base).

3 Design of Lunar Positioning Signal The lunar surface communication unit should equip standard S band TT & C system, navigation system and UHF communication system. Besides, it must have sufficient redundant communication capability and emergency communication capability. The lunar rover and the lander use the lunar surface UHF communication link to realize data exchange. When the lunar unit cannot observe more than three navigation units at the same time, the system uses single point ranging and angle measurement are used for positioning. Here, the lunar rover and lander are taken as examples to illustrate. First, we can achieve data exchange between lunar rover and lander by lunar UHF communication link. Then, UHF duplex communication terminals with BOC modulation and single carrier modulation are configured on lunar rover and lander respectively. The DOWR is used to eliminate the clock error and pseudo range to further improve the positioning accuracy. The angle is measured by carrier phase differential interferometry [4]. 3.1 Signal Model In the paper, the binary offset carrier (BOC) signal and single carrier signal transmit at the same frequency. Due to the BOC signal can free the bandwidth of the center frequency, the single carrier can transmit at the same time for angle measurement. The BOC signal can be expressed as (3.1): s(t) = d (t) · g(t) · c(t)

(3.1)

Here, d (t) is navigation data. g(t) represents the PN sequence which the frequency can be expressed as fc . c(t) is the subcarrier sequence which the frequency can be expressed as fs . And the fc and fs are multiple of 1.023 MHz. (3.2) is the relationship between them.  fs = m × 1.023 MHz (3.2) fc = n × 1.023 MHz In the paper, the BOC signal adopts BOC (5, 1) signal. The main lobe range is 4.092 MHz–6.138 MHz. In addition, BOC (5, 1) has excellent anti-multipath ability.

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The bandwidth of integrated signal is less than 15 MHz, and the signal transmission and reception can be realized by digital signal processing. Besides, the RF channel is easy to realize and miniaturize. The integrated signal can be expressed as (3.3) sIF (t) = s(t) cos(2π fIF t) + cos(2π fIF t)

(3.3)

Here, sIF (t) is intermediate frequency (IF) signal. fIF is the frequency of IF signal. cos(2π fIF t) is the single carrier signal which used to angle measurement. In the paper, we adopt 14.96 MHz as IF. The power spectrum of the transmitted signal are shown in Fig. 3.

Fig. 3. Normalized power spectrum of transmitted signal. (a) Normalized power spectrum of base-band BOC (5, 1) signal; (b) Normalized power spectrum of intermediate frequency signal

3.2 Angle Measurement Signal Receiving Algorithm The position of antenna array elements is shown in Fig. 4. D

C

θ O

φ A

ϕ

B

Fig. 4. Diagram of orthogonal baseline phase interferometer

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In the lunar surface positioning system, the two-dimensional linear interferometer is used to measure the angle. The distance between the baseline OA and OC are equal, and the distance between the baseline AB and CD are equal. The UHF frequency is used for interference angle measurement on lunar surface. Considering that the ambiguity of carrier phase will exist when the length of the second baseline is larger than half wavelength of the signal, two groups of cross prime baselines are needed to solve the ambiguity. In this case, the traditional five antenna interferometer can only measure the angle of a single signal. Therefore, compared with the spatial spectrum algorithm, the interferometer system has a great disadvantage in measuring the arrival direction of multiple signals at the same time. The disadvantage means it cannot locate multiple targets on the lunar surface at the same time. Moreover, when the number of nodes near the moon is limited, it is impossible to ensure that the nodes can establish ranging links with more than four nodes at any time. Therefore, it is necessary to locate multiple nodes through a single interferometer antenna. The receiver distinguishes the nodes by frequency division. The receiver receives signals of different frequency points at different times. The frequency switching modes are provided, such as Table 1. Table 1. The frequency switching method of antenna Time Antenna O

A

B

C

D

T1

f1

f2

f3

f4

f5

T2

f5

f1

f2

f3

f4

T3

f4

f5

f1

f2

f3

T4

f3

f4

f5

f1

f2

T5

f2

f3

f4

f5

f1

Because the microwave switch will switch each antenna element, so each channel cannot track the signal stably. In this case, the receiver should recapture and track the signal frequently, which will eventually affect the accuracy of signal ranging and angle measurement. In this paper, when there is no corresponding frequency signal input, the external extrapolation method is used to keep the tracking loop stably. Thus, the tracking loop can ensure long-term ranging and interferometer measurement without losing lock. The dual frequency point switching methods of antenna array element have their own advantages. The switching mode in Table 1 ensures each frequency point has corresponding signal reception at each time, and will not cause the loop locking due to the sudden change of Doppler frequency. The tracking loop extrapolation algorithm is as follows: 1) At the end of the period when each antenna element has received signal, the carrier phase offset, and pseudo code phase offset in the carrier tracking loop and pseudo

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code tracking loop are input into the simulate transmission signal module. And the analog transmission signal is offset according to the values; 2) When there is no signal input, the output of simulate transmitting signal module is imported into the tracking loop. The angle measurement method is as follows: 1) Extract the carrier phase in the carrier tracking loop. If the baseline length is greater than half wavelength, the integer ambiguity should be solved according to the Chinese remainder theorem as (3.4). e(N1 , N2 ) = d1 · (N2 λ +

φ2 φ1 λ) − d2 · (N1 λ + λ) 2π 2π

(3.4)

Here, d1 is the length of OA. d2 is the length of OB. N1 , N2 are integer ambiguity. φ1 represents the carrier phase difference of OA. φ2 represents the carrier phase difference of OB. λ is the wavelength of signal. 2) Searching the integer N1 , N2 when minimum e of baseline OAB and OCD. Through (3.5, 3.6), the angle measurement of baseline OAB and the angle measurement of baseline OCD can be calculated.   φ2_OB N2_OB λ+ 2π λ (3.5) φ = arccos d2  θ = arccos

φ2_OD λ 2π

N2_OD λ+ d2

 (3.6)

Here, N2_OB , N2_OD are the integer ambiguities of antenna OB and OD’s carrier phase difference. φ2_OB , φ2_OD are the part which less than 2π in the antenna OB and OD’s carrier phase difference. 3) The pitch angle is π2 − θ , and the formula of azimuth angle is shown in (3.7)   cos φ (3.7) ϕ = arccos cos θ

4 Simulation and Error Analysis In order to realize the positioning of lunar spacecraft, the main measurement error comes from the process of ranging and angle measurement. Among them, BOC signal acquisition and tracking algorithm has been more mature in foreign and domestic, this paper mainly focuses on the simulation of multi-target interferometer measurement algorithm. 4.1 The Simulation of Angle Measurement Algorithm The signal frequencies are set as f1 = 100 MHz, f2 = 200 MHz, f3 = 400 MHz, f4 = 550 MHz, f5 = 800 MHz. For interferometer, the length of baseline OA and OC

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is 0.233 m, and the length of baseline OB and OD is 0.747 m. The carrier to noise ratio is 60 dBHz and the switching time of frequency is 0.15 s. With the increase of time, the impact of frequency switching is gradually reduced. Finally, the angle measurement error obtained by different frequencies is shown in Fig. 5. With the increase of frequency, the angle measurement error decreases gradually.

Fig. 5. The angle measurement error of different frequency (a) 100 MHz; (b) 200 MHz

4.2 Error Analysis The main sources of receiver ranging error are thermal noise error and dynamic stress error. The dynamic stress error can be eliminated by carrier to pseudo code technique. Therefore, this paper only analyzes the ranging error caused by thermal noise. The theoretical calculation formula is as (4.1).    4F2 d 2F1 d 2 BLD 2(1 − d ) + (4.1) σRanging = Tchip CNR Tcoh · CNR Here, Tchip (ns) is the code length of each chip. d is the code interval between leading/immediate/lagging of code tracking loop. BLD (Hz) is bandwidth of the code tracking loop filter. Tcoh is the integral and dump time. F1 is the code loop correlator factor. F2 is the code loop discriminator factor. CNR is the carrier to noise ratio. In the system, due to we adopts the BOC (5, 1) to ranging, the parameters are as follows: Tchip = 977 ns, d = 1/4, F1 = 0.5, F2 = 1, Bn = 10 Hz, Tcoh = 1 ms. And the thermal noise can be calculated as σRanging = 0.947 ns. The angle measurement process uses the carrier phase difference received by each antenna. And the phase noise of five receiving antennas has strong coherence. In the case of multi baseline carrier phase difference, the carrier phase jitter caused by the phase noise can cancel. Thus, the angle measurement accuracy is directly determined by the carrier phase measurement error (under the condition that the carrier integer ambiguity is ignored). If we adopt third-order PLL, the thermal noise error is as (4.2). BLF 1  )]0.5 σtPLL = [  (1 + C N0 2T · C N0

(4.2)

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We choose BLF = 10 Hz, T = 1 ms. And the carrier phase error is σtPLL = 0.003 rad when CNR = 60 dBHz. And the angle measurement error can be calculated as (4.3). σθ =

λ σtPLL d2

(4.3)

5 Conclusion This paper introduces the plan of lunar exploration in China, that is, the mission of building the lunar station initially. Then, the data transmission and TT & C links in the moon-earth space and near moon space are planned in the process of the mission. Aiming at the problem of insufficient lunar surface positioning accuracy, a high-precision positioning system for the future lunar station is proposed. We adopt DOWR to ranging and interferometer to angle measurement. And The integrated signal of ranging and side angle is designed. For integrated signal, BOC (5, 1) signal is used for ranging. In this system, it can effectively reduce the multi-path interference of the lunar surface. The angle measurement signal adopts single carrier and time division switching to realize multi-target high-precision angle measurement on interferometer. At the end of the paper, the error in the process of ranging and angle measurement is analyzed and simulated.

References 1. Zhaoyu, P., Jizhong, L., Qian, W., et al.: Overview of lunar exploration and international lunar research station. Chin. Sci. Bull. 65(24), 2577–2586 (2020) 2. Xiaojiang, Y., Tian, R., Qijia, D., et al.: Radio-based high precision navigation meth-ods for lunar exploration. In: China Satellite Navigation Conference, Chengdu (2020) 3. Wu, W.R., Liu, J.Z., Tang, Y.H., et al.: China lunar exploration program. J. Deep Space Explor. 6(5), 405–416 (2019) 4. Lee, J.-H., Woo, J.-M.: Interferometer direction-finding system with improved DF accuracy using two different array configurations. IEEE Antennas Wirel. Propag. Lett. 14, 719–722 (2015)

Parameter Estimation of Pulsar Position Based on Least Square Shi Chen1 , Li-rong Shen1(B) , Yong-qiang Shi2 , Xiao-ping Li1 , Zhe Su3 , and Hai-feng Sun1 1 School of Aerospace Science and Technology, Xidian University, Xi’an, China

[email protected]

2 Beijing Institute of Control Engineering, Beijing 100080, China 3 Institute of Space Electronic Information Technology, Xi’an 710100, China

Abstract. The pulsar position parameters error is one of the main factors affecting the accuracy of X-ray pulsar autonomous navigation and pulsar time keeping. There is a nonlinear relationship between pulsar position parameters and pulsar timing residuals. Based on the above issues, this paper established a mathematical model for parameter estimation of pulsars’ right ascension and declination errors, analyzed the pulsar timing residuals caused by different planetary ephemeris, and studied the influence of the errors of right ascension and declination of pulsars on the timing residuals. On this basis, the pulsar position parameters are estimated by the least square method. And the simulation experiment and analysis are carried out. The results show that, based on the proposed method, using DE430 planetary ephemeris, when the timing residual is 0.1 us, the accuracy of pulsar position estimation accuracy is about 0.03 mas, which shows the effectiveness of the proposed method. Keywords: Pulsar · Timing residuals · Position error

1 Introduction In recent years, with the development of space science and technology, deep space exploration has become a hot topic of concern in all countries. X-ray pulsar based navigation (XPNAV) has been widely studied by scholars all over the world for its superior characteristics, which can provide autonomous navigation information such as position, velocity, attitude and time for near earth, deep space and even interplanetary spacecraft. In 2016, the institute of high energy physics Chinese academy of sciences and technology and engineering center for space utilization Chinese academy of sciences analyzed the data of Crab pulsar for one month observed by using the gamma-ray burst polarization detector on ‘Tiangong2’. The orbit determination of tiangong2 is carried out, and the error is about 20 km (3σ), which verifies the feasibility of autonomous navigation based on X-ray pulsar [1]. In 2017, NASA successfully carried out the project of ‘Space X-ray Timing and Navigation Technology Detector (SEXTANT)’ on the international space station, which confirmed that millisecond pulsar can be used to accurately determine © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 646–655, 2021. https://doi.org/10.1007/978-981-16-3142-9_62

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the position of high-speed moving objects in space. The highest positioning accuracy of this experiment is 4.8 km (1σ), which proved the feasibility of XPNAV technology [2]. In 2019, the Chinese Academy of Sciences announced that the X-ray pulsar navigation experiment was carried out by using China’s first astronomical satellite “Insight”, and the positioning accuracy reached 10 km (3σ), which further verified the feasibility of pulsar autonomous navigation [3]. Millisecond pulsars play an important role in pulsar timing and X-ray pulsar based navigation, and have been widely studied in recent years. The long-term stability of 15 years of PSR B1855+09 is better than that of the atomic time maintained by USNO, it is close to the PTB atomic time standard maintained by German Institute of Technical Physics. This result will be improved in the future [4]. The accuracy of TOA measurement of the of millisecond pulsar will also improve the accuracy of pulsar positioning and the large planet calendar. The accurate establishment of pulsar timing model is the key of XPNAV, which determines the accuracy of XPNAV. The timing model can be divided into single pulsar timing model and binary pulsar timing model. Among them, the parameters of pulsar timing model include pulsar rotation frequency, frequency derivatives, pulsar right ascension/declination, right ascension/declination of pulsar proper motions, etc. On the basis of single pulsar timing model parameters, the binary pulsar timing model includes Kepler parameters, which has more parameters and more complex models. In the aspect of pulsar timing model research, in 1985, Davids studied the timing model and residual model considering gravitational delay [5]. In 1986, Hellings studied the relativistic effect that must be considered when converting the TOA measured by ground station to the natural coordinates of pulsar, and analyzed the influence factors such as proper motion and parallax [6]. In 1990, Fosterhe and Backer studied the model of estimating pulsar parameters by using the information of pulse TOA measurement, which established the parameter support for the establishment of timing model [7]. In the same year, Doroshenko and Kopeikin systematically analyzed the whole process of pulse TOA processing by constructing the coordinate systems of mass center, geocentric and station center [8]. In 2006, Hobbs, Edwards and others studied the pulsar timing software tempo2, and gave the timing model and the fitting method of each parameter [9]. Based on the Hellings model, Sheikh built a time conversion model for pulsar navigation [10]. Zhou Qingyong analyzed the pulsar timing model and rotation stability [11]. Wang Yidi studied the pulsar dynamic signal processing method, and proposed a prediction method of pulsar timing noise based on time series analysis, and compensated the system error which affects the pulsar navigation [12]. Li Liang and Wang Guangli studied the feasibility of pulsar navigation of measurement acquisition, integer ambiguity, scope of application from the perspective of astrometry [13]. Planetary ephemeris error is a major factor affecting the navigation and timing accuracy of pulsars. Accurate pulsar position is the premise of pulsar navigation. When the right ascension or declination error of pulsar reaches 1 milliarcsecond, the maximum positioning error can reach 700 m [14].Thus, it is necessary to estimate the error of the right ascension and declination of the pulsar, so as to realize the high-precision estimation and update of the pulsar position and provide the parameter support for XPNAV. In the aspect of pulsar position estimation, Sun Shouming analyzed the influence of pulsar position error on different navigation algorithms, studied the principle of pulsar

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position error estimation and established relevant mathematical models [14]. Sun Xiong used grid method to traverse and search the position of pulsars based on the whitened residuals [15], which can improve the accuracy of right ascension and declination of pulsar to a certain extent. However, the grid method needs a lot of points and large calculation, it presents a great challenge to on orbit computing resources. Meanwhile, the determination of initial position parameters and the determination of mesh size need to be further studied. In order to estimate the error of right ascension and declination of pulsar with high accuracy in a small amount of computation, a pulsar timing parameter estimation model is established in this paper. The nonlinear problem is transformed into a linear problem, the pulsar position parameter estimation model based on least square method is derived. And the influence of different planetary ephemeris on timing residuals is analyzed based on experiments. On this basis, the least square method is used to estimate the position of pulsars under different timing residual accuracy, which verifies the effectiveness of the proposed method.

2 Pulsar Timing Model Pulsars have the effect of slow rotation. The pulsar timing model describes the transformation of its rotation characteristics with time. In inertial reference frame, the mathematical expression of pulsar signal phase model is as follows [16] (t) = 0 +

n  1 (k−1) f (t − t0 )k k!

(1)

k=1

Here the observation time t is the Barycentric Dynamical Time (TDB) or Barycentric Coordinate Time (TCB) at Solar System Barycentric (SSB) or pulsar, (t) is the phase of pulsar signal at time t, 0 denotes an accumulated initial phase at reference epoch t 0 .The parameter f (k−1) means the k-order frequency derivative, and if k = 0, f (0) = f0 [16]. The pulsar timing model can accurately predict the phase information of pulsar signal at a certain time, and can provide accurate phase prediction information for pulsar navigation. Based on the pulsar phase model which establishes at the center of mass (SSB) of the solar system, we compared the cumulative profile with the standard profile at SSB, and can obtain the phase difference between the center of mass of the solar system and the spacecraft. Then the time difference between the arrival of pulsar signal to SSB and spacecraft can be obtained. Using it as the basic measurement of navigation, we combined with the state model of spacecraft and navigation filtering method, the autonomous navigation of spacecraft based on pulsar can be realized [17]. 2.1 Timing Residuals The position error of pulsar reflected in the timing model is mainly reflected in the timing residual. The relationship between pulsar position error and timing model is nonlinear. Therefore, we transformed the nonlinear problem into a linear problem, solved the timing

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residual, and calculated the position error of pulsar to obtain more accurate parameters of right ascension, declination and rotation. It is a feasible way to improve the precision of timing model and pulsar navigation. The expression of pulsar signal converted from spacecraft to SSB can be written as [8] ˜tSSB = tSC +

n˜ · (rSC/E + rE ) + δt c

(2)

Where tSC is time of arrival of pulse to spacecraft, n˜ is pulsar position vector which obtains right ascension and declination, rSC/E is the position of the earth relative to SSB, δt includes the Shapiro delay effect produced by the planets and celestial bodies in the solar system, the bending of light path caused by the solar gravitational field and the gravitational delay. The position error of pulsar can be expressed as n˜ = n − n, by substituting it into formula (2), we can get ˜tSSB = tSC +

n · (rSC/E + rE ) n · (rSC/E + rE ) − + δt c c

(3)

Then, the timing residual of the pulse arriving at SSB caused by pulsar position error is as follows: t = tSSB − ˜tSSB =

n · (rSC/E + rE ) c

(4)

It can be seen from formula (4) that due to the influence of pulsar position errors, in actual navigation, there have timing residuals as shown in formula (4), which will lead to spacecraft positioning error based on XPNAV. 2.2 Solution of Pulsar Right Ascension and Declination Based on Least Square In order to solve the problem of timing residual caused by pulsar position errors, it’s very important to study the calculation method of pulsar position error. The timing residuals are obtained from formula (4), the pulsar position errors are obtained by the least square analysis of timing residuals. The solution principle is shown in Fig. 1

Fig. 1. Principle of pulsar position error estimation

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The right ascension of pulsars is α, and the declination is δ, and the unit vector of  T pulsar direction is n = cos δ cos α cos δ cos α sin δ . Then the position of the pulsar ˜ the position error is (α, δ) which satisfied with errors is (α, ˜ δ),  α = α˜ + α (5) δ = δ˜ + δ Substituting formula (5) into the expression of pulsar unit vector. By first-order Taylor expansion, the first-order term is obtained and the second-order term is ignored, then it can get the formula as follows [12] ⎡ ⎤ ⎡ ⎤ cos δ˜ cos α˜ − cos δ˜ sin α.α ˜ − sin δ˜ cos α.δ ˜ ⎦ n = ⎣ cos δ˜ sin α˜ ⎦ + ⎣ cos δ˜ cos α.α (6) ˜ − sin δ˜ sin α.δ ˜ ˜ ˜ sin δ cos δ.δ ⎡ ⎤ ˜ − cos δ˜ sin αα ˜ − sin δ˜ cos αδ ⎦ n = ⎣ cos δ˜ cos αα (7) ˜ − sin δ˜ sin αδ ˜ ˜ cos δδ By substituting formula (7) into formula (4), the relationship between pulsar timing residuals and the errors of right ascension and declination of pulsar can be obtained,

T

 1 ˜ sc/y ) α − cos δ˜ sin α(r ˜ sc/x ) + cos δ˜ cos α(r (8) ti = ˜ sc/z ) − sin δ˜ cos α(r ˜ sc/x ) − sin δ˜ sin α(r ˜ sc/y ) δ c cos δ(r Where, ti is the timing residual of an observation, rsc/x is the component of position vector of spacecraft relative to SSB in x direction, rsc/y 、rsc/z is the component of spacecraft position vector relative to SSB in y and z directions. Through multiple observations, multiple sets of timing residuals can be obtained, and the pulsar position can be solved by the least square method. Its mathematical model can be expressed as 1 δ T = AX c Among them, the above parameters can be expressed as ⎡ ⎤ ⎡ ⎤ R1 t1

 ⎢ R2 ⎥ ⎢ t2 ⎥ α ⎢ ⎥ ⎢ ⎥ δ T = ⎢ . ⎥, A = ⎢ . ⎥, X = , δ ⎣ .. ⎦ ⎣ .. ⎦ tn Rn T

˜ sc/y ) − cos δ˜ sin α(r ˜ sc/x ) + cos δ˜ cos α(r R= ˜ sc/z ) − sin δ˜ cos α(r ˜ sc/x ) − sin δ˜ sin α(r ˜ sc/y ) cos δ(r

(9)

(10)

The position error of pulsar can be deduced based on the least square method [12] X = c(AT A)−1 AT δ T

(11)

Where X is the position error of pulsar to be estimated, δ T is timing residual, A is the cosine matrix with pulsar position error.

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3 Experiment and Analysis It can be seen from Eq. (8) that the timing residual is related to the position error of pulsar and the position of spacecraft relative to SSB. Based on this, this paper discusses the influence of these factors on the timing residuals from two aspects: the earth position error and the pulsar position error. We select B0531+21 pulsar as the estimation object. Its right ascension is 83.63°, and its declination is 22.01°. On this basis, we combined with timing residuals, based on the least square method proposed in this paper, to solve the right ascension and declination errors of pulsars. 3.1 The Influence of Planetary Ephemeris on Timing Residuals Planetary ephemeris records the position list information of one or more celestial bodies at a specific time every day, which plays an important role in deep space navigation, interplanetary exploration [18]. A series of planetary ephemeris have developed by NASA’s Jet Propulsion Laboratory (JPL), including DE421, DE430 and others. Based on two different planetary ephemeris, this paper analyzed the position errors of the planets recorded by the two ephemeris. Firstly, using the two sets of planetary ephemeris DE421 and DE430, this paper analyzes the difference of the earth’s position in the two planetary ephemeris, the results are shown in Fig. 2. Among them, the calculation time range is from January, 2005 to January, 2015, and the step is 1 day. 400 DE430 -DE421

300

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Fig. 2. Different ephemeris of DE430 and DE421 position of the earth

We use two planetary ephemeris. DE421 includes ranging and VLBI measurements of the Mars probe, new ranging and VLBI measurements of the Venus probe, and the latest estimates of planetary mass, lunar laser ranging, and two-month CCD measurements of Pluto, covering the 1900–2050 time range.DE430 covers the time interval from January 1, 1550 to January 22,2650, and has the most accurate lunar ephemeris. Figure 2 shows the position errors of the earth in DE430 and DE421 ephemeris, which

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shows a periodic trend in the past decade. Among them, the maximum difference of the two groups of ephemeris is 300 m, and with the increase of time, the difference of the ephemeris increases slightly. As can be seen from Fig. 3, the maximum pulsar timing residual caused by the difference of the earth position of the two ephemeris is 1 μs. -6

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Fig. 3. Timing residual difference of DE430 and DE421

3.2 Effect of Pulsar Position Error on Timing Residuals In pulsar navigation, the influence of the error of right ascension and declination on the navigation accuracy can be reflected from the influence of the error of right ascension and declination on the timing residual. Figure 4 and 5 show the calculated timing residuals when the errors of right ascension and declination of PSR B0531+21 are 20 mas, 2 mas and 0.2 mas. -8

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-7

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Fig. 5. Timing residuals corresponding to different declination errors

It can be seen that the errors of right ascension and declination reflected in the timing residuals are annual periodic terms, which are mainly due to the periodic change of the timing residuals introduced by the earth’s revolution. In general, with the increase of the error of the right ascension and declination, the pulsar timing residual becomes larger. Here, due to the influence of the selected pulsar azimuth, the timing residual caused by the declination error is greater than that caused by the error of the right ascension in the same case. Compared with Fig. 3 and Fig. 5, the magnitude of timing residuals caused by 20 mas declination error is equivalent to that of pulsar timing residuals caused by different planetary ephemeris, both of which are in the order of 1 μs. 3.3 Calculation and Analysis of Right Ascension and Declination Errors of Pulsars In this section, we study the estimation of pulsar position error based on least square method under different timing residuals. The planetary ephemeris used in the calculation is DE430, which starts from January 1, 2005 and lasts for three years. A total of 500 groups of pulse arrival times are calculated. The arrival time of the pulse is the simulation data, the time limit is three years, and the random number between them is taken as the pulse TOA, and the errors of right ascension and declination are all set at 1.8 mas. The mean value is obtained by 500 operations, and the position errors and its mean square deviations of pulsars with different timing residuals accuracy are calculated based on the least square method. The results are shown in Table 1, where RA is error of right ascension, DEC is error of declination. In this paper, the earth position given by different planetary ephemeris of DE421 and DE430 is different, which will lead to the deviations of pulsar position and introduce timing residual errors, which are not considered in this paper and need further research in the future. It can be seen from Table 1 that the proposed method can accurately estimate the right ascension and declination parameters of pulsars. In general, with the decrease of the accuracy of timing residuals, the position estimation error of pulsars increases significantly, that is, the higher the accuracy of each timing residuals, the smaller the

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Timing residual accuracy (μs) Mean value of RA error (mas) Mean value of DEC error (mas)

0.1

0.5

1

3

8

30

50

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−0.01

0.00

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0.03

0.00

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−0.01

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Mean square error of RA (mas)

0.002

0.05

0.08

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0.47

Mean square error of DEC (mas)

0.032

0.83

2.39

4.82

4.49

15.94

4.26 52.5

position estimation error of pulsars. When the timing residual is 0.1 μs, the position estimation accuracy of pulsar is about 0.03 mas; when the timing residual is 50 μs, the position estimation accuracy of pulsar is about 53 mas. This shows that the accuracy of the arrival time of the pulsar directly affects the accuracy of the pulsar position estimation. It can be seen from the table that the mean error of right ascension and declination is not 0, which is mainly due to the truncation error introduced in the linearization of the model. In addition, based on the least square pulsar position estimation proposed in this paper, the calculation accuracy of the right ascension error is higher than that of the declination error, which may be related to the azimuth estimation of the target object and the linearization truncation of the model. The right ascension and declination of the PSR B0531+21 used in this paper are 83.63° and 22.01° respectively, and the propagation path of the pulsar signal caused by the declination error of the pulsar is longer than that caused by the right ascension error of the same value, so it will cause large timing residual. Table 1 shows the strong correlation between pulsar position and timing residuals. A large number of simulation studies will be conducted to explore the reasons.

4 Conclusions In order to solve the problem of large amount of calculation in the existing estimation methods of pulsar position parameters estimation, this paper deduces the relationship model between pulsar position parameters and timing model, and transforms the nonlinear problem into linear problem. On this basis, we give the least square estimation method of pulsar position parameters. Based on the simulation experiment, we analyze the earth position difference of different ephemeris and its influence on timing residuals. Finally, we estimate the position parameters of the pulsar under different timing residuals. The results show that the difference of the earth position calculated by DE430 and DE421 ephemeris results in a timing residual error of 1 μs. The timing residual accuracy has a significant impact on the estimation of pulsar position parameters. When the timing residual is 0.1 μs, the pulsar position estimation accuracy is about 0.03 mas; when the timing residual is 50 μs, the pulsar position estimation accuracy is about 53 mas. Found by Space Optoelectronic Measurement & Perception Laboratory of BICE No. LabSOMP-2020–06.

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References 1. Wei, Z., Jun, X., Qinglong, H., Xiao, C.: Survey of autonomous celestial navigation technology for deep space. J. Flight Control Detect. 2. Haiming, W.: NASA completes the world’s first space validation of X-ray pulsar navigation. J. Space Sci. 38(3), 277–278 (2018) 3. Fangjun, L., Shuangnan, Z.: HXMT--China’s first X-ray astronomical satellite. J. Phys. (06), 341–347 (2017) 4. Tinggao, Y., Chongxia, Z.: Progress in timing observation of millisecond pulsars. Prog. Astron. (01), 1–9 (2005) 5. Davis, M.M., Taylor, J.H., Weisberg, J.M., Backer, D.C.: High-precision timing observations of the millisecond pulsar psr1937+21. Nature 315, 547–550 (1985) 6. Hellings, R.: Relativistic effects in astronomical timing measurements. Astron. J. 91, 650–665 (1986) 7. Foster, R., Backer, D.: Constructing a pulsar timing array. Astron. J. 361, 300–308 (1990) 8. Doroshenko, Q., Kopeikin, S.M.: High-precision pulse timing for single pulsars. Sov. Astron. 34(5), 496–501 (1990) 9. Edwards, R.T., Hobbs, G.B., Manchester, R.N.: TEMPO2, a new pulsar timing package. I: The timing model and precision estimates. arXiv: astro-ph/0607664v1 10. Sheikh, S.I., Hellings, R.W., Matzner, R.A.: High-order pulsar timing for navigation. In: Proceedings of the 63rd Annual Meeting of the Institute of Navigation, Cambridge (2007) 11. Qingyong, Z.: Research of Timing model and rotation stability of Pulsars. Information Engineering University, Zhengzhou (2011) 12. Yidi, W.: X-ray pulsar-based navigation: signal processing and positioning algorithms. National University of Defense Technology. 13. Liang, L., Guangli, W., Li, G.: Astrometric considerations for pulsar navigation. J. Deep Space Explor. 5(03), 235–240 (2018) 14. Shouming, S.: Study on autonomous navigation method of spacecraft based on X-ray pulsars. National University of Defense Technology (2011) 15. Xiong, S.: Research on frequency search and timing model of X-ray Pulsars. Xidian University (2018) 16. Sun, H.F., Sun, X., Fang, H.Y., et al.: Building X-ray pulsar timing model without the use of radio parameters. Acta Astronautica. 143 (2017) 17. Sheikh, S.I.: The use of variable celestial X-ray sources for spacecraft navigation (2005) 18. Min, F., Guangliang, D., Xuemei, D.: J. Aircr. TT & C. 31, 11 (2012)

Analysis and Suggestions on the Resilience of GNSS Timing Longxia Xu1,2(B) , Feng Zhu1,2 , and Xiaohui Li1,2,3 1 National Time Service Center, Chinese Academy of Sciences, Xi’an, China

[email protected]

2 Key Laboratory of Precision Navigation Positioning and Timing, Chinese Academy

of Sciences, Xi’an, China 3 University of Chinese Academy of Sciences, Beijing 100049, China

Abstract. Time is widely used in almost all the critical fields. Among the 16 key fields identified in the U.S. Department of Homeland Security’s presidential policy directive No. 21, 11 industries, including communications, mobile phones, power distribution, finance and information technology, rely on accurate timing and time synchronization technology. Therefore, timing system is very important for the national economy, society and security. This paper focuses on resilient timing and time synchronization of satellite navigation systems, and analyzes the failure timing events caused by satellite navigation systems and the external factors (such as jamming and spoofing). On the basis of introducing the latest development of resilient timing of satellite navigation system and the next generation of PNT system at home and abroad, the definition of resilient timing is preliminarily analyzed. Combined with the development of Chinese Beidou satellite navigation system and PNT, some useful suggestions on resilient timing and time synchronization are given. Keyword: GNSS · Timing · Resilience · Time synchronization · Jamming

1 Introduction Satellite navigation systems provide positioning, navigation and timing (PNT) information for users. Accurate measuring of time offset is the basis of GNSS to provide the services of positioning and navigation. Based on the measured time offset, the pseudoranges which are the essential for positioning is determined. Presently, timing of satellite navigation systems is widely used in all kinds of fields. Eleven of the sixteen key industries [1] given by the U.S. Department of Homeland Security presidential policy directive No 21, such as communications, mobile phones, power distribution and finance, all dependent on accurate timing and time synchronization technology. The weak signals of satellite navigation systems are easy to be cheated by jamming. Being considered the wide application of GNSS timing and the existed problems [2], resilience is chosen as another index for evaluating GNSS performance after accuracy, integrity, continuity and availability. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 656–665, 2021. https://doi.org/10.1007/978-981-16-3142-9_63

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This paper analyzes the existing problems in resilient timing of GNSS in the aspects of GNSS anomalies and external factors, such as jamming and spoofing. Based on the latest development of international GNSS and plan of PNT system, the definition and meaning of resilient timing is preliminarily given and analyzed. According to the stateof-the-art of China, some suggestions are given on GNSS resilient timing and time synchronization.

2 Existing Problems of GNSS Timing The degradation or interruption of GNSS service performance are mainly caused by two factors. One is the anomalies from satellite navigation systems and the other is the external influences, such as jamming and spoofing. 2.1 GNSS Anomalies GPS Anomalies On January 26 of 2016, the UTC time parameters broadcast in GPS navigation message showed a singular deviation of 13.7 µs [3, 4]. An artificial mistake had triggered in the software of ground master station when satellite 23 was removed from the constellation. Comparing the broadcast ephemeris of GPS with the IGS precise ephemeris products, Li Heng analyzed the performance of GPS SIS from 2000 to 2010 [5, 6]. There are up to 3275 GPS SISURE abnormal events (i.e. SISURE exceeds 4.2*URA) occurred in the past ten years which are failed to provide the service of promised performance to users. With the improvement of GPS SIS performance, the number of abnormal events are getting less. Galileo Anomalies On January 18 of 2017, nine atomic clocks on the in-orbit satellites of Galileo stopped operating due to malfunction, including one rubidium clock and six passive hydrogen clocks. According to the analysis of ESA [7], the malfunction of rubidium clocks are related to short-circuited while that of hydrogen clocks are mainly caused by long-time shutdown. The hardware failure of ground control station of Galileo system directly led to the non-update of broadcast ephemeris during the period of May 14, of 2017 to May 16 of 2017 [8]. At the periods of 14:00–15:00 and 17:00 UTC on July 10 of 2019, Galileo experienced a three-hour interruption and all ephemeris were not updated on time resulting in the service interruption. From UTC 01:50 on July 12 of 2017, Galileo was failed to update satellite its navigation messages. Users experienced the degradation of Galileo service performance to its completely interruption [9]. It is found that a malfunction was occurred in the Galileo ground control center of PTF. This directly affected the prediction of satellite clock and orbit, and cannot generate navigation messages on time. An abnormal was detected in Galileo system time on December 14 of 2020 [10]. Since December 14 of 2020, the time

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parameters broadcasted by some Galileo satellites shown irregular jumps which resulted in the incorrect system time were received in user terminals. GLONASS Anomalies Due to the upload of incorrect ephemeris to all GLONASS satellites, the normal service was interrupted for up to 11 h on April 2 of 2014 [11]. The system did not return to normal until the ground control station of northern hemisphere uploaded correct data to all satellites. The Russian SDCM system pointed out that the longest on orbit operation satellite launched in 2006 failed at 15:45 of Moscow time on August 1 of 2019 [12, 13]. Other Systems Four rubidium atomic clocks in IRNSS failed on June 28 of 2017 [14] which was similar to that of Galileo satellite clocks in early June and resulted in the difficulty of providing service. On June 30 of 2015 and December 31 of 2016, BDS-2 had display errors during the adjustments of leap second [15]. Conclusion of GNSS Anomalies From the above GNSS anomaly events, it can be seen that GNSS anamolies mainly comes from the space segment, control segment and transmit link. Table 1 summarized the reasons and behaviours of anomalies of GNSS. The space segment anomalies mainly comes from the payload, satellite clock and time-frequency generation module. In addition, the complex space environment can also cause satellites malfunction, such as the unexpected change of pseudo-random code sequence caused by SEU [16]. Anomalies originated from the control segment are mainly caused by software and hardware failures, such as equipments malfunction and software bugs, which essentially belongs to human factors. As the navigation signal transmit from satellites to receivers, it is inevitably affected by space weather, such as ionosphere scintillation, electromagnetic storm [17]. This kind of bad space weather makes navigation signal unable to pass through the atmosphere and finally results in the degradation or even interruption of normal service. Table 1. Failures of GNSS Sources

Reasons

Space segment

Satellite clock failure/payload failure No signal or non-update of caused by space weather etc. navigation message or partial bad parameters, degradation or Malfunction of hardware/bugs in interruption of services software etc.

Control segment Transmit link

Ionosphere scintillation/Electromagnetic storm /Coronal Mass Ejection /jamming etc.

Behaviour

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2.2 Jamming and Spoofing The GNSS navigation signal is distributed to the ground from an altitude of more than 20000 km and the signal is very weak and vulnerable when reached ground. It is easy to be interfered and cheated by jamming and spoofing. Jammers transmit high power jamming signal which makes GNSS receivers unable to receive the real GNSS signal. Spoofing jammers are used intentionally to generate or relay fake signals with the same parameters as that of GNSS to block the normal receiving and leading the GNSS terminals obtain incorrect positions and time information. Jamming aimed at GNSS timing involves the space segment, control segment and user terminals. Space jamming mainly includes intentionally physical destroying of GNSS satellites, or blocking the normal communication link of time service. Jamming to the control segment are mainly physical destructions or interferences which interrupts the control of master station to satellites and makes GNSS unable to operate normally. The implementation of local suppression or electronic spoofing on user terminals can make users unable to obtain the correct GNSS time information or obtain with large time errors. The concept of “time warfare” is proposed by the US Air Force Strategy and Technology Center in May 2017. Following the definition of “navigation warfare”, the “time warfare” can be defined as preventing the enemy from using GNSS time service and ensuring that the normal use of GNSS timing for friendly targets while without affecting the normal utilization of GNSS time information outside the war zone. To cope with the coming time warfare, jamming and spoofing, it needs not only strengthen the GNSS system by techniques, such as improving the robustness of the satellite navigation systems, building a wide-area distributed jamming & spoofing monitoring network. In addition, strict anti-jamming laws and regulations should be formulated to weaken the impact of jamming and spoofing on GNSS timing.

3 Progress of GNSS Resilient Timing Excessive dependence on GNSS will cause serious economic losses and even threaten the safety of life. In view of the wide application of GNSS in all kinds of fields and its fatal weakness [18], it is urgent to develop the backup timing systems to improve the resilience of timing. America The United States issued a series of administrative orders to ensure the resilience of PNT. On August 15 of 2019, the U.S. Department of Defense issued the “Department of defense PNT strategy - ensuring the PNT advantage of U.S. military” [19] which requires the provision of resilient PNT services for joint forces. On February 12 of 2020, U.S. president signed the executive order “enhancing national resilience through responsible use of positioning, navigation and timing services” which requires that key infrastructure relying on GPS be free from interference and manipulation. In December 2018, U.S. president signed the “national timing resilience and security act of 2018” [21] which requires to build a terrestrial, resilient and reliable backup timing system for GPS within two years.

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The law requires the backup timing system be a terrestrial which uses radio signals to broadcast time information that synchronized to UTC and able to penetrate underground and inside buildings. The timing signal is required to have good resilience, difficult to be disrupted or degraded and expandable to provide position, navigation and timing and able to work in concert with similar systems such as eLoran. At the same time, the construction of eLoran is restarted to improve the security and reliability of timing. In order to cope with the impact of the “time warfare”, DARPA planned precise timing and time synchronization related projects in PNT system, including: 1) Quantum Assisted Sensing and Readout (QuASAR) project; 2) Ultrafast Laser Science and Engineering (PULSE) project; 3) Micro technology of Positioning, Navigation and Timing (Micro-PNT); 4) Spatial, Temporal and Orientation Information in Contested Environments (STOIC) project. The U.S. plan of PNT about timing can be summarized into four aspects. Firstly, developing high-precision optical atomic clocks that are independent of laboratory conditions and can be applied to various mobile platforms. Secondly, researching high-precision time and frequency synchronization technology to meet the comparison requirements of optical atomic clocks. Thirdly, developing of low power consumption, miniaturization, high integration and stability of chip scale atomic clocks. Lastly, developing the clock system of ultra-stability, robustness and multi-function in contested environments. All these measures are aim to provide navigation, positioning and timing services that are better than GPS or equivalent to its performance, and become an effective backup of GNSS. ESA ESA has been paying close attention to the vulnerability of space-based PNT signal, and is committed to improve the resilience of satellite navigation signals. The timing and time synchronization based on Galileo are taken as an independent service as positioning and navigation by European Union. The European’s ten-year plan - H2020 funded a series of projects on GNSS timing and time synchronization, among which Galileo timing service extension and consolidation (EGALITE) project [22] had researched and developed Galileo time service and mainly concerned on the integrity of timing. The following part will give a brief introduction on this. (1) Galileo navigation message broadcast timing augmentation flags EGALITE project proposed the safety architecture of Galileo timing at system level shown in Fig. 1 [23]. Each Galileo satellite distributes timing augmentation flags for the whole constellation. The timing augmentation flags are calculated based on the data from global converged timing integrity monitor stations (TIMS). Raw data from TIMS are streamed in real time to Galileo service center and processed to generate Galileo (GPS) timing flags. Timing augmentation flags are sent to control center for uplink to satellites and broadcast by Galileo satellites. According to the maximum tolerable error (MTE) of timing, the service is divided into three levels: 10ns (Service Level 1), 100ns (Service Level 2) and 1000ns (Service Level 3). The timing flag of each satellite takes 2 bits in navigation messages. (0 0) means don’t use the satellite for timing for service level 3, 2 and 1. (1 0) indicates don’t use the satellite for timing for service level 2 and 1. (0 1)

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Galileo satellites

pseudorange & navigation message GPS/Galileo Timing flags

GPS/Galileo Timing flags

Galileo control center receivers Timing Integrity Monitor Stations raw data

Galileo service center

Fig. 1. Safety Architecture of GNSS timing

indicates don’t use the satellite for timing for service level 1. (1 1) means use the satellite for timing for any service level. Users can easily know the timing performance of each satellite by receiving the timing flags and therefore have free selection of satellites for timing. The Galileo Authenticated Robust Timing System (GEARS) project [24] developed a timing system to verify a new Galileo navigation signals which added with anti-spoofing authentication information to improve the ability of anti-jamming of Galileo signals. This design can protect Galileo from threats and ensure the accuracy and reliability of timing in challenging environment. It also provides backup for navigation signal and timing reference when Galileo is unavailable. (2) Robust GNSS timing and time synchronization service As a part of European H2020, DEMETRA project [25] has developed a complete set of GNSS timing services including certified time steering, time monitoring and steering, receiver calibration, time integrity and time synchronization. Figure 2 shows the GNSS based robust time synchronization service system given in literature [26]. This system supports time synchronization by common view (CV), all in view (AV) and carrier phase (CP). The accuracy of time synchronization in world wide is several nanosecond. Due to the use of dual frequency observations of multiconstellations, TRAIM algorithm and augmentation information, this service system is not easy to be affected by interference and spoofing, and thus can provide users with robust and resilient timing and time synchronization service. (3) Backup timing systems The DEMETRA project also realizes the alternative backups [25] of GNSS. The standard time coded information is broadcasted via European Radio and TV links. The best performances with FM Radio is about 2ms. This project also provide the service that disseminating time with trusted NTP and the accuracy is below 10ms. The time and frequency distribution over fiber links realizes time distribution of subnanosecond. Besides, this projects also allows to synchronize user stations by means of a geostationary satellite with accuracy of better than 100ns. This service provides technological redundancy to GNSS which increases the robustness of Galileo. All these

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GNSS satellites

LSS PTF

SSP

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GNSS RTRX CV

GNSS RTRX CV

GNSS RTRX AV

GNSS RTRX CP

REF / UTC(k)

USER3

USER2

USER1

TSP GMS ESOC

Fig. 2. Robust time synchronization system based on GNSS

methods can be used as the backup of GNSS to enhance the resilience and robustness of GNSS time service. (4) Policy and others The UK invested 36 million pounds to build the National Time Center (NTC) to provide a more resilient timing system for national emergency response services and others in February 2020 [27], so that the UK will not be affected by the failure of GNSS. The NTC will adopt the terrestrial technology to enhance the resilience and safety of British timing systems as an important backup of GNSS. Based on the atomic clocks distributed in different places, a clock set is established to keep a stable time scale to ensure that users can obtain accurate UTC time without GNSS. Prospect of Chinese Resilient Timing System China has launched a plan of constructing a PNT system by 2035. This plan aims to build a unique, three-dimensional intersect and resilient timing system worldwide in the future which is mainly composed of BeiDou Satellite navigation system (BDS), time & frequency system of space station, terrestrial radio timing system and fiber timing links. The high-precision terrestrial timing system being under construction will form effective backup of GNSS from two aspects of fiber links and eLoran timing. As far as the eLoran timing, three stations broadcasting eLoran signal system will be built in west of China to realize the national coverage of terrestrial radio timing signal. The timing accuracy will be improved from 1 µs to 100 ns with the application of differential technology. In terms of fiber time synchronization, a backbone network which connecting Beijing, Shanghai, Xi’an and other cities will be established based on the communication optical fiber. The whole length will be more than 20000 km which will be the world’s longest and more precise optical timing backbone network. The accuracy of fiber time

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synchronization will be better than 100 ps and that of frequency accuracy will reach E-19. Through the construction of this new timing system, combined with the existed BDS, BPL, BPM, BPC and other timing systems, China will finally build an integrated, multisource complementary, reliable and resilient timing system which providing users with multi-level, multi-dimensional, safety, reliable and resilient time service.

4 Reflection on Resilient Timing Resilient timing refers to the ability to provide time service with the normal performance when a timing system is failure or subject to external interference. There are two requirements for timing systems. First of all, users should be provided with a warning in time when the timing system is failure or its performance is degraded or interrupted. This ensure that users can keep acquiring time information by switching timing systems or by local time keeping. Secondly, when being cheated by external interference, the timing system should have the ability to detecting and identify the interference so that not be affected by the interference. As far as the GNSS is concerned, the following two aspects should be considered for resilient timing: (1) Improving the resilience of GNSS timing at the system level. It is suggested that the integrity or robust informations should be broadcast to enhance the timing performance of GNSS in information. It also can improve the resilience of GNSS timing by broadcasting authentication or encryption new signal. To deal with the influence of atmosphere on timing signal, it is recommended to monitor the transmission link of timing signal, such as detect the influence of solar and ionospheric anomalies on GNSS timing. It is required that the timing terminals can receive multi-constellation and multifrequency navigation signals, and has its local time source to keep time independently. In addition, the function of interference detecting and recognition is inevitable. This can be implemented through algorithm in terminal software to eliminate the influence of interference and ensure the accuracy and safety of timing. (2) Developing other timing systems. To solve the vulnerability of GNSS timing essentially, the backup timing system must be developed. This includes developing new type of atomic clocks and the corresponding time synchronization techniques, building territorial radio timing systems and other timing systems. An integrated timing system is formed to realize the complementary of mutual timing system and meeting the requirement of users for different precision in various environments. Acknowledgment. This paper is supported by the National Natural Science Foundation of China (Grant No 12073033) and the Youth Innovation Promotion Association of Chinese Academy of Sciences (Grant No 1188000XLX).

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References 1. Presidential Policy Directive 21/PPD-21. http://www.whitehouse.gov/the-press-office/2013/ 02/12/presidential-policy-directive-critical-infrastructure-security-and-resil 2. Banerjee, P.: Timing in GNSS its importance and challenges. In: International Conference on Microwave and Photonics. IEEE (2016) 3. GPS Experiences UTC Timing. IIF Satellite Launcher Problems. https://insidegnss.com/gpsexperiences-utc-timing-iif-satellite-launcher-problems/ 4. Mujunen, A., Aatrokoski, J., Tornikoski, M., Tammi, J.: GPS time disruptions on 26 January 2016. SCIENCE + TECHNOLOGY, 2. Aalto University publication series (2016) 5. Heng, L., Gao, G.X., Walter, T., Enge, P.: GLONASS signal-in-space anomalies since 2009. In: Proceedings of the 25th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2012), September 2012, Nashville, TN (2012) 6. Heng, L., Gao, G.X., Walter, T., Enge, P.: GPS signal-in-space anomalies in the last decade, data mining of 400,000,000 GPS navigation message. In: Proceedings of the Institute of Navigation GNSS conference (ION GNSS 2010), September 2010, Portland, Oregon (2010) 7. European GNSS service center. https://www.gsc-europa.eu/galileo/system. 8. https://www.gsc-europa.eu/sites/default/files/sites/all/files/Galileo-service-notice-02-v1.3. pdf. 9. https://www.gsc-europa.eu/sites/default/files/sites/all/files/Galileo-service-notice-01_v1.1. pdf. 10. http://www.ntsc.ac.cn/xwzx_/kyjz/202012/t20201223_5837101.html. 11. https://www.glonass-iac.ru/ 12. http://sputniknews.cn/ 13. https://www.gpsworld.com/glonass-gone-then-back/ 14. http://www.gnss-world.cn/wxdh/gnss/208.html. 15. Bin, T., Jin-long, L., Jun-fei, S., Hai-bo, H.: Analysis of some BeiDou timing clock display error in the process of leap second. Navig. Positioning Timing. 4(3), 72–76 (2017) 16. Qu, B., Wei, J., Zhang, S., Bi, L.: Effect analysis of single event upset for C/A code generator. In: CSNC (2013) 17. Mao-he, Y., Mao-you, L., Jiang-yan, S.: Analysis on the influence of space electromagnetic environment disturbance on the satellite navigation system. In: CSNC (2017) 18. https://www.blog.adva.com/en/a-timely-reminder-of-gnss-vulnerability. 19. DoD. Strategy for the Department of Defense positioning, navigation and timing (PNT) enterprise -ensuring a US military PNT advantage. https://rntfnd.org/wp-content/uploads/ DoD-PNT-Strategy.pdf. 20. Trump, D.J.: Executive order on strengthening national resilience through responsible use of positioning, navigation and timing services. https://www.whitehouse.gov/presidential-act ions/executive-order-strengthening-national-resilience-responsible-use-positioning-naviga tion-timing-services/. Accessed 12 Feb 2020 21. PUBLIC LAW 115–282. ACT of 2018 Frank lobiondo coast guard authorization. Accessed 4 Dec 2018 22. Píriz, R., Buendía, F., Martín, J.-R., et al.: Safety analysis for a new GNSS timing service via Galileo. In: 2nd International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2019), Miami, Florida, 16–20 September 2019, pp. 3359–3376 (2019) 23. Fidalgo, J., Píriz, R., Cezón, A., et al.: Proposal for the definition of a Galileo timing service, embedded real time software and systems. In: 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2019), Miami, Florida, 16–20 September 2019, pp. 827–839 (2019)

Analysis and Suggestions on the Resilience of GNSS Timing

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24. https://www.orolia.com/solutions/resilient-timing 25. Tavella, P.: The H2020 European project DEMETRA: experimental time services based on European GNSS signals. In: EFTF-IFCS (2017) 26. Zelle, H., Veerman, H., Kirkko-Jaakkola, M., Honkala, S., et al.: European global navigation satellite system robust timing & synchronization service. In: EFTF-IFCS (2017) 27. National Timing Centre programme—Resilient time for the future. https://www.npl.co.uk/ntc.

Machine Measuring Method for Norm-Position of Targets Haitao Wu(B) Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing, China [email protected]

Abstract. Current methods for targets location in real-life scenarios are still based on the point-level location, which regard the target as a mass point and perform its position via 2D/3D coordinates. However, point-level location cannot describe the spatial structure or three-dimensional position of targets, which is not enough to provide location services that meet higher requirements in some special areas, such as scene regeneration and precision operation. In this paper, we propose a novel position measure called Norm-Position for this task. Norm-position describes the target location information by spatial structure and three-dimensional position, which no longer regards the target as a mass point. Norm-position measurement surveys the position of all surface points belonging to the same object. It does not only rely on traditional position measurement methods, but a novel machine measurement approach that combines key technologies such as high-precision positioning and timing based on Beidou navigation satellite, computer vision, lidar, artificial intelligence, 5G communications, big data, and cloud computing, to name a few. The presentation of norm-position measuring results is to calculate the three-dimensional coordinates, spatial structure and space occupation of multiple targets in the real scenes. In this paper, we also present a machine measuring method for norm-position and verify its effectiveness. Finally, we discuss the potentials of norm-position measurement in practical applications such as realscene information management, unmanned precision operation and reverse control engineering. Keywords: Norm-position. real-life scene · Multiple targets · Machine measurement

1 Introduction High-precision positioning technology can provide basic location-based services for applications such as autonomous driving [1], automatic navigation [2], security monitoring [3] and emergency rescue [4] etc. On 23 June 2020, China successfully launched the 55th BDS navigation satellite and the final Beidou-3 satellite of Beidou navigation network was launched for global coverage. On 31st July 2020, President Xi Jinping announced the official commissioning of the BeiDou-3 global navigation satellite system, starting a new phase in China’s satellite navigation applications. With the promotion of BDS time service and positioning technology, high-precision position measurement © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 666–680, 2021. https://doi.org/10.1007/978-981-16-3142-9_64

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technology, computer vision and artificial intelligence [5], 5G [6], blockchain [7] and other key technologies are more closely integrated and more widely used in smart cities [8], smart agriculture [9], smart logistics [10] and other fields. The real-time and accurate measurement of the spatial position of multiple targets in real scenes helps realize deep integration of location information and attribute information of multiple targets and promotes accurate identification and dynamic management of spatial objects. Therefore, realizing real-time and accurate positioning of spatial objects is one of the most basic and important issues in location application scenarios. At present, there are two categories of positioning technologies, i.e. outdoor positioning and outdoor positioning, based on different application scenarios. Outdoor positioning is generally used in outdoor and other openair scenarios and its main positioning technologies include satellite positioning [11] and base station positioning [12]. Satellite positioning receives satellite signals sent from the Global Navigation Satellite System (GNSS) through the receiver to resolve the current location (latitude and longitude). The current mainstream global satellite navigation systems mainly include the Chinese BeiDou navigation satellite system (BDS), the U.S. Global Positioning System (GPS), the Russian GLONASS system and the European GALILEO system. As another important technology for outdoor positioning, the base station positioning is achieved by using the “three-point positioning” to resolve the position with the support from the base stations established by mobile communication operators. Since 1996, the United States, Japan, the European Union and other countries or organizations have successively legislated to require mobile operators to provide positioning services. In recent years, with the popularization and application of 5G, a lot of results have been achieved in the research on positioning based on 5G cellular networks [13], such as 5G applications in high-precision positioning of urban trains [14]. The outdoor positioning technologies represented by satellite positioning and base station positioning have become more mature, but are still affected by factors such as blocking and multipath effects, which makes indoor application impossible and has therefore given rise to the development of indoor positioning technology. In 2006, China launched the “Xihe” plan, proposing to achieve sub-meter level indoor positioning accuracy during the 13th Five-Year Plan period. In recent years, a variety of location measurement technologies have emerged for indoor positioning, which can be divided into wireless positioning technologies and non-wireless positioning technologies. Typical wireless positioning technologies include WIFI [15], bluetooth [16], Ultra Wide Band (UWB) [17], and Radio Frequency Identification (RFID) [18], while non-wireless positioning technologies are mainly based on vision [19], inertial components [20], geomagnetic [21], ultrasonic [22] and other technologies. These indoor positioning technologies are also widely used in the commercial market, for example, UWB positioning is widely used in industrial, logistics, and smart city scenarios and companies such as Apple, Huawei, and Xiaomi are gradually adding UWB modules to their smartphones to achieve high-precision positioning of mobile devices. Although there are currently more mature positioning technologies for both indoor and outdoor target position measurement, there still exists a common problem: positioning by regarding the target as a mass point. These positioning methods equate the target with a mass point in 2D or 3D space, i.e., they do not consider information such as the

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spatial structure and spatial occupation of the target. This type of positioning method is widely used in applications that involve the provision of only location-based services of targets, but proves hard to meet the requirements of applications such as 3D sensing of targets, real-world scene twinning and reverse control. For example, if a person is equated to a mass point in the center of the body for position measurement, the 3D position information of the same person is the same when the person is standing up and standing upside down, but the position of the person in space is completely different; similarly, the position information obtained through point positioning is the same for two cubic products of different sizes in an industrial production line, but the spatial occupation of the two targets is actually different. The point position alone cannot provide accurate operation information for the control equipment. Therefore, a comprehensive three-dimensional measurement of the target is needed and the spatial structure and spatial occupation information of the target can be accurately described by measuring the position of all surface points of the target. Based on this, this paper proposes the machine measurement of the norm position of the spatial object to describe the three-dimensional position, spatial structure and spatial occupation of the target.

2 Norm Position 2.1 Definition of Norm Position The norm position defined in this paper is the set of positions of all surface points belonging to the same target object. The norm position no longer presents the target as a mass point, but instead describes the target location information by spatial structure and spatial occupation. The norm-position measurement is equivalent to locating all the points that make up the target and the combination of the positions of all surface points belonging to the same target (i.e. the target norm position information), through which the three-dimensional structure of the target in three-dimensional space will be restored. Compared with the traditional target point positioning method, the norm position of spatial objects has the following characteristics: (1) Target materialization. Unlike the positioning method that treats the target as a mass point, the norm position measurement treats each target as an entity of a different category of object, which has preserved the structured and semantic characteristics of the entity. (2) Position structuring. Norm-position measurement is about the measurement of the coordinates of all constituent points on the surface of an entity and is able to construct the spatial form of the target based on the coordinates of surface points. Although the point cloud scan of the object can reconstruct the three-dimensional structure and spatial location of the target, the norm position measurement of the object is not equivalent to the point cloud scan of the object; what makes it different from the results of point cloud scan of the target is that the norm position measurement also includes the semantic features of the target. (3) Target-scene association. The norm position measurement obtains the target information directly from the real scenes, while using the spatial position of reference points in the scene to obtain the spatial position information of the target; on the other hand, the norm position of each target in the scene can be used to restore the real scenes.

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2.2 Key Technologies for Norm-position Machine Measurement The norm-position measurement of spatial objects is different from the traditional object position measurement in that it is a kind of realistic target monolithic, structured and semantic machine measurement based on multi-technology fusion. The core technologies supporting the machine measurement of spatial object norm position include the following: (1) BDS-based high-precision positioning and time services. For the machine measurement of spatial object norm position, BDS-based high-precision positioning and time service technology can provide position and time reference frame, which is the basis for norm position measurement. Using BDS-based high-precision point positioning [23] and the differential positioning based on BeiDou ground –based augmentation-based system [24], the centimeter-level position information of outdoor targets can be obtained. Based on BDS-based time service technology, a unified timestamp of multiple targets and devices in the scene is established to achieve nanosecond-level time synchronization [25]. (2) Instance segmentation and 3D perception of targets. Through multi-camera acquisition of RGB images or RGB-D images in the scene, the 3D structure of the target is reconstructed and restored through machine vision technology to sense the spatial occupation of multiple targets, such as realized by SFM algorithm [26]; instance segmentation of targets based on deep learning, such as realized by Mask R-CNN [27], the individual targets in the scene are monolithized and semanticized to obtain the individual attribute information of each target. The artificial intelligence technology represented by deep learning is the main technical means used to acquire the semantic information for norm position measurement. (3) Indoor and outdoor positioning based on multi-sensor fusion. BDS-based highprecision positioning technology can accurately obtain the location information of outdoor targets. However, indoor applications of BDS-based high-precision positioning have certain limitations due to the influence of indoor blocking and multipath effects. For indoor positioning, other sensors such as UWB, Bluetooth, vision sensors, LIDAR, WIFI, etc. are required for positioning. Based on the deep integration of Beidou and other positioning, sensing and measurement technologies, multi-source positioning models such as “Beidou+UWB+vision” [28] and “Beidou+vision+inertial navigation” [29] can be built to make up for the limitations of single location measurement technology and realize the sensing of the position of indoor and outdoor targets. (4) High-speed transmission and information connectivity based on 5G and IoT. Realizing norm position measurement of multiple targets in real scenes requires real-time acquisition and transmission of on-site radio signals, images, videos and other data. For the concurrent transmission of large amounts of data, the transmission method requires higher bandwidth and transmission rate. For example, according to the average bit rate of 5 Mbps for each channel of HD video, 1 Gbps of bandwidth is required for real-time transmission of 200 channels of the video. At the same time, the need for information exchange between different targets in the process of norm position measurement also puts higher requirements on the real-time transmission of information. In recent years, the development of 5G technology has provided a solution for high-speed data transmission. 5G technology, with its high speed, low latency, high reliability and other characteristics

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[30], has become one of the key technologies involved in the norm position measurement of spatial objects. (5) Intelligent cloud computing technology based on massive data. For the real-time measurement of norm position of multi-target entities in real scenes, the accumulated scene information needs to be processed efficiently, which requires intelligent computing platforms with strong computing power support. For example, according to each highperformance server’s ability of processing 10 channels of high-definition videos in real time, the processing of 200 channels of video will require at least 20 servers with cloud computing capability. Therefore, the strong computing power and technology of the cloud-computing platform provides an important computing support to ensure real-time norm position measurement. 2.3 Resolution Methods for Norm Position Compared with the traditional object point positioning method, the norm position measurement of the target involves more items to be resolved as well as higher computational complexity and more computational volume. Therefore, it is necessary to optimize the position resolution method. Based on this, the paper proposes the following resolution methods for norm position measurement: (1) Using static targets to resolve norm position of dynamic targets. The targets in the real scenes include a large number of static targets in addition to dynamic targets. The absolute position of the static targets remains constant and the static targets can be used as a reference to quickly determine the norm position of the dynamic targets based on the motion state of the dynamic target in relation to the static target. At the same time, the relative motion between two moving targets can also be used to resolve the norm position of a certain object. (2) Using the targets whose structures are known to resolve the norm position of all of the target surface points. For the norm position measurement of some targets, after the semantic information of the target is identified, the spatial structure of the target can be obtained through semantic features, so that only the coordinates of some control points will need to be calculated and the spatial structure of the target is assembled to help obtain all of the position information of the target surface points. This resolution method is suitable for resolving the norm position of some targets whose structures are known, such as products in the industrial field. The norm positions of these industrial products can be obtained quickly because they have uniform standard structure dimensions. (3) Using the targets in the 2D image to resolve the norm position of targets in the 3D image. The 2D image of the scene is collected, the instance segmentation of the target in the image is conducted and the spatial coordinates of the surface points of the target are resolved through the mapping of pixel points in the image onto the coordinates of the 3D spatial points. A typical implementation method such as the EPnP algorithm [31] is used to resolve the actual spatial coordinates of the target points by utilizing the pixel coordinates of multiple points in the image.

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3 Study of Measurement Methods Based on the above-mentioned resolution methods, this paper designs a feasible method for machine measurement of the norm position of spatial objects: the RGB-D camera is used to capture the scene images and the instance segmentation of multiple targets in the space is realized based on YOLACT; on the basis of the instance segmentation result of each object, the depth information of each target is obtained through the depth map; combined with the pixel coordinates and depth information of the target, the PnP algorithm is used to calculate the 3D spatial coordinates of all surface points of the target. 3.1 Principles and Methods 3.1.1 Instance Segmentation of Targets Although Mask R-CNN, which is widely used in instance segmentation, has been able to achieve good results, it mainly focuses on detection accuracy, with poor real-time performance and the detection speed of less than 10 FPS. In order to ensure the realtime performance of instance segmentation, YOLACT algorithm [32] is used as the implementation path in this study.

Fig. 1. YOLACT architecture

The network structure of YOLACT is shown in Fig. 1: In this model, ResNet101+FPN is used as the backbone, and the instance segmentation is achieved by two branches, i.e. the prototype generation branch and the mask coefficient branch. The prototype generation branch Protonet is mainly implemented based on FCN to generate mask prototypes; the mask coefficient branch mainly implements mask coefficient prediction through anchor-based target detector. The two branches are calculated independently and then the mask synthesis is performed by the use of matrix multiplication and Sigmoid function and the segmentation results is exported finally.

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3.1.2 Principles of Position Resolution The pixel-level position of each target in the image can be obtained through the instance segmentation of the object. The 3D position of the target in the world coordinate system can be obtained by transforming the coordinate system for pixels. For the pixel coordinates (u, v), the transformation into the image coordinate system can be realized by the following equation: ⎞⎛ ⎞ ⎛ ⎞ ⎛  x u 1 dx 0 u0 ⎝ v ⎠ = ⎝ 0 1 dy v0 ⎠⎝ y ⎠ (1) 0 0 1 1 1 in which dx and dy are the actual physical dimensions of the pixels on the light-sensing components, u0 and v0 are the image plane centers and x and y are the image coordinates. The conversion relationship between the image coordinate system and the camera coordinate system can be calculated by the following equation: ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ Xc x fx 0 0 0 ⎜ ⎟ Yc ⎟ Zc ⎝ y ⎠ = ⎝ 0 fy 0 0 ⎠⎜ ⎝ Zc ⎠ 1 0 0 10 1

(2)

in which fx, fy are the focal lengths of the camera in x-axis and y-axis and Xc, Yc, Zc are the coordinate values of the target in the camera coordinate system. The conversion relationship between the camera coordinate system and the world coordinate system can be calculated according to the following equation: ⎞ ⎛ ⎞ Xw Xc ⎝ Yc ⎠ = R⎝ Yw ⎠ + T Zc Zw ⎛

(3)

where Xw, Yw, and Zw are the coordinate values of the target in the world coordinate system, R is a 3 × 3 rotation matrix, and T is a 3 × 1 translation matrix. The matrices R and T can be combined into one external reference matrix, and then Eq. (3) can be rewritten as ⎛ ⎞ ⎛ ⎞ Xc Xw

⎜ Yc ⎟ ⎜ Yw ⎟ R T ⎜ ⎟= ⎜ ⎟ (4) ⎝ Zc ⎠ 0 1 ⎝ Zw ⎠ 1 1 Based on Eqs. (1)–(4), the equation for conversion of the pixel point into the 3D spatial position can be obtained as: ⎛ ⎞ ⎛ ⎞ ⎛  ⎞ Xw

u fx dx 0 u0 0 ⎜ R T ⎜ Yw ⎟ ⎟ Zc ⎝ v ⎠ = ⎝ 0 fy dy v0 0 ⎠ 0 1 ⎝ Zw ⎠ 0 0 1 0 1 1

(5)

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In Eq. (5), the matrix consisting of the parameters of the camera itself is called the internal reference matrix, which can be obtained through camera calibration. According to Eq. (5), the pixel coordinates (u, v) of the target and the internal reference matrix of the camera are both known. In order to resolve the 3D coordinates (Xw, Yw, Zw) of the target in the world coordinate system, the depth value Zc of the target in the camera coordinate system and the external reference matrix need to be calculated. 3.1.3 Target Depth Acquisition The depth value of the target in the camera coordinate system can be obtained with the depth camera. To calculate the 3D position of each point on the target surface, this study uses a binocular camera to acquire depth information. The binocular camera is able to export aligned RGB-D images, i.e. the images in which each pixel point in the color image corresponds to the depth value at the same location in the depth map. In the measurement of depth values, depth is usually noisy and there are some pixel locations where depth values cannot be obtained due to target reflections and other reasons. In order to obtain stable depth values, a neighborhood window is used to estimate the depth value at each pixel location, i.e., for a target at coordinates (i, j), the depth value Z(i, j) can be calculated as: j + S x = i−S y = j−S ϕ(x, y) · Z(x, y) i + S x = i−S x = i−S y = j−S ϕ(x, y)

i + S Z(i, j) =

(6)

In this equation, S is the size of the neighborhood window. ϕ(x, y) is the sign function, which is calculated as: 1, Z(x, y) = 0 ϕ(x, y) = (7) 0, Z(x, y) = 0

3.1.4 Calculation of External Reference Matrix To calculate the external reference matrix of the camera, this study performs pose estimation of the camera by the use of PnP (Perspective-n-Point) algorithm. This method performs camera pose estimation by a set of n 3D points in the world coordinate system and their corresponding 2D coordinates in the image. Based on the known control point coordinates, the camera pose can be estimated by combining the internal parameters of the camera. There are many methods of resolution of PnP algorithm, such as P3P with three sets of point pairs, direct linear transformation, EpnP and UpnP etc. In this study, the EPnP (Efficient PnP) algorithm is used for pose estimation. For N sets of control points, let the image coordinates of the ith control point be v[i] and the world coordinates be cwi. According to the EPnP algorithm, there is the equation

2

2 N

N [j] [i] w w

= c β v − β v − c

k k i j k k

k=1 k=1

(8)

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Resolve β based on the known coordinates of the control point. Calculate the coordinates of the control point in the camera coordinate system based on β: cic =

N j=1

βk vk[i]

(9)

For the reference point, according to the EPnP algorithm, there is the equation   piw = 4j=1 αij cjw  (10) pic = 4j=1 αij cjc According to the above equation, the coordinates of the reference point in the camera coordinate system can be obtained. The center of gravity and matrix of the reference point in the world coordinate system and camera coordinate system are calculated separately as follows: w  po = 1n ni=1 piw  (11) poc = 1n ni=1 pic ⎛ cT ⎛ wT ⎞ ⎞ p1 − pocT p1 − powT ⎜ pcT − pcT ⎟ ⎜ pwT − pwT ⎟ o ⎟ o ⎟ ⎜ 2 ⎜ 2 , B = (12) A = ⎜ ⎜ ⎟ ⎟ .. .. ⎝ ⎝ ⎠ ⎠ . . pnwT − powT

pncT − pocT

Calculate the H matrix: H = BT A

(13)

H = UVT

(14)

Perform the SVD of the matrix H:

Then the rotation matrix R in the external reference matrix can be calculated as: R = UVT

(15)

The translation matrix T can be calculated as: T = poc − Rpow

(16)

3.1.5 Norm Position Measurement Based on the pixel-level segmentation of the target, all the pixel points of the target surface can be obtained and the actual 3D coordinates of each point on the surface of each target in space can be obtained based on the conversion relationship between pixel coordinates and 3D spatial coordinates. By managing the set of 3D coordinates of each point on the surface of each target, the spatial structure of the target and the actual spatial occupation can be obtained.

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3.2 Experimental Verification 3.2.1 Equipment and Implementation To test the effectiveness of the design method used in this study, a simple verification system has been built for the experiment. The scene image acquisition is performed by a binocular camera, ZED2, which has a maximum resolution of 4416 × 1242 and a frame rate of 15FPS at 2K resolution, a depth measurement range of 0.5–20 m, and USB 3.0 output. The processing system is Ubuntu 18.04 with 64 GB of RAM and NVIDIA GeForce RTX 2080Ti GPU with 11 GB of video memory and Python programming language. In this study, the verification system has been built indoors and the world coordinate system has been established in a right-handed right-angle coordinate system and the ZED2 camera is mounted on the top of the tripod with a height of 2.1 m, as shown in Fig. 2. After the fixation of the camera, the camera is calibrated. Four control points have been selected in the site to obtain the world 3D coordinates onsite and 2D coordinates in the image. The external reference matrix of the camera is obtained by the use of EPnP algorithm. At the same time, the internal reference matrix of the camera is obtained by utilizing Zhang Zhengyou’s method of camera calibration based on the checkerboard.

Fig. 2. ZED2 installation

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3.2.2 Results and Analysis Firstly, the accuracy and detection time of target detection were calculated to verify the effectiveness and real-time performance of target instance segmentation. Secondly, the accuracy of three-dimensional space point positioning was tested. Finally, the validity of the norm-position measurement was tested via the twin test of human body’s real spatial pose. In the first step, different targets were placed in the site, and instance segmentation was performed on the targets through YOLACT. In the experiment, each target was moved 20 times, and the segmentation detection results of each target in 20 groups of different positions were counted. In the experiment, a total of 193 targets were correctly segmented, 7 targets were missed, and the detection accuracy was 96.5%. As shown in Fig. 3, this method could correctly detect all the targets placed in the segmented scenarios. Figure 4 shows the undetected target in the scenario, which is the basketball in the field. The average detection time was 55 ms. The frame rate of ZED2 camera was 15FPS at 2K resolution, so the segmentation speed of YOLACT could match the real-time speed of ZED2 camera.

Fig. 3. Result of instance segmentation: all detected accurately

Fig. 4. Result of instance segmentation: basketball is omitted

Then the accuracy of 3D positioning was verified. Five targets were selected in the experiment, including a big ball, a basketball, a human, a water bottle and a chair, to measure their positioning accuracy. An error test was carried out on 20 measurements of those 5 targets. To measure the errors, the errors between the measured value and the actual value on three coordinates X, Y, and Z were respectively calculated, as well as the spatial Euclidean distance between the actual values and the measured values S. It was found from Fig. 5 that the positioning error on the Z-axis was the smallest, while the positioning error on the X-axis was the largest. The spatial positioning error was 22.75 cm. Finally, the validity of the norm-position measurement method was verified by regenerating the spatial position of human body. The pixel coordinates of the key points of the target human were obtained from the image with the algorithm of extracting human body key points [33]. According to the norm-position measurement method proposed in this study, each key point can be converted into three-dimensional coordinates, and human body pose can be quickly reconstructed in space. As shown in Fig. 6, real-time digital twin of human motion state and spatial pose can be made by measuring the human body’s norm-position.

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Fig. 5. Result of 3D location

Fig. 6. Result of digital twin based on norm-position

3.3 Discussion The norm-position measurement method designed in this study, combined with artificial intelligence and visual positioning technology, embodies its idea of solving problem “from a known to an unknown state, and from two-dimensional to three-dimensional,” and the feasibility of the method was verified by building a simple verification system. It needs to be clarified that the complexity of the real scenarios can largely increase the difficulty of the norm-position measurement, and cause huge challenges to the method. However, the innovation and iteration of various advanced measurement methods also provide strong technical support for the method. Challenges and opportunities coexist.

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The research on norm-position machine measuring method will attract more researchers’ attention.

4 Analysis of Applications 4.1 Real Scenario Information Management In the application of target management, it is usually necessary to manage the various elements of interest in the scenario. The attributes and position information of each target entity can be obtained by machine-measuring the norm-position of the spatial objects, which is helpful in the accurate management of the target elements. For example, in the application of real-time management of tourist information in scenic areas, measuring the norm-position of tourists to single them out and obtain their individual attributes and location information can help achieve the accurate management of tourists. At the same time, the norm-position information of tourists can also provide field information for the safety and emergency management of scenic areas, supporting scientific decisionmaking. 4.2 Unmanned Precision Operation In the modern industrial automatic production, the unmanned precision operation of machines has become an important sign of intelligent manufacturing. In the typical application scenario where the robot arm automatically identifies, locates and grabs goods, the simple point positioning can no longer meet the complex and diverse operation requirements. For example, the operation system needs to use different capturing schemes for different materials and product structures. At the same time, different parts of the same object can be very different. By measuring the norm-position of the goods, the space pose of the goods and the space coordinates of each point can be obtained, based on which the robot arm then selects the corresponding grabbing operation scheme, making the operation adaptive and precise. In unmanned precise operation scenarios, the norm-position machine measurement method mainly provides precise target space position and three-dimensional structure information for operation equipment, so as to realize targeted selection of operation methods. 4.3 Reverse Control of Targets The real-time scene can be reconstructed based on the digital twinning of the target and the three-dimensional regeneration of the scenario. Furthermore, the reverse control of the target in the real scenario can be realized by controlling the twin target in the regenerated scenario. Typically in autonomous driving, the norm-position information of the target vehicle and other vehicles can be obtained in real time.

Machine Measuring Method for Norm-Position of Targets

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References 1. Weijian, G., Jiangwei, C., Chunlei, L.: Research on autonomous vehicle positioning based on CORS network difference. For. Eng. 36(02), 101–106 (2020) 2. Mengyin, F., Wenjie, S., Yi, Y., et al.: Research on visual navigation and positioning technology of unmanned ground platform. Navig. Positioning Timing 2019(4), 1–11 (2019) 3. Lei, T., Tao, H., Xu, C.: YOLOv3 based UAV identification and localization tracking. Chin. J. Eng. 312(04), 67–72 (2020) 4. Peng, W., Wenxiang, L., Feixue, W.: Research on GNSS emergency assisted positioning and accuracy evaluation method. J. National Univ. Defense Technol. 4, 140–145 (2013) 5. Bin, W., Haiyan, L., Yulin, W.: Prospect of AI technologies in aerospace in the future. J. Command Control 6(4), 349–355 (2020) 6. Jun, O., Shijun, C., Xiaoming, H., et al.: Analysis of high-precision positioning technology for 5G mobile communication network. Mobile Commun. 43(9), 13–17 (2019) 7. Wei, X., Yongxiu, H., Yan, Z., Li, Z.: 3D self-positioning of power line carrier network nodes based on block chain. Computer Simul. 37(11), 119–123 (2020) 8. Caihua, L., Longya, L., Tingyong, S., Xi, C., Yuxiang, L.: Research on Beidou singlefrequency RTK positioning technology for smart city. Urban Geotech. Invest. Surveying 6, 76–80 (2020) 9. Man, Z., Yuhan, J., Shichao, L., et al.: Progress in the research of navigation technology for agricultural machinery. Trans. Chin. Soc. Agric. Mach. 51(4), 1–18 (2020) 10. Haiying, L., Qinzhen, L., Wei, Z.: Research on dynamic command and scheduling system of military logistics vehicle based on Beidou-3. Logistics Sci.-Technol. 44(1), 153–155 (2021) 11. Xiaohong, Z., Jiahuan, H., Xiaodong, R.: Latest Progress in PPP/PPP-RTK and comparison with Beidou /GNSS PPP in positioning performance. Acta Geodaetica et Cartographica Sinica 49(9), 1084–1100 (2020) 12. Ke, G., Zhigang, H., Yu, S., Peichen, S., Qiang, G., Huagang, X.: construction and scheme of positioning system based on ground base station. J. Beijing Univ. Aeronaut. Astronaut. 45(10), 2051–2057 (2019) 13. Ping, Z., Hao, C.: Review of researches on 5G-oriented positioning technologies. J. Beijing Univ. Posts Telecommun. 41(5), 1–12 (2018) 14. Lingfan, Z., Liu, L., Jiachi, Z., Jiahui, Q.: Discussion on high-precision positioning of urban train based on 5G cellular network. J. Navig. Positioning 8(5), 1–10 (2020) 15. Xiaoxen, G., Zishen, L., Liang, W., Ningbo, W.: A WiFi-RTT positioning method for smart phones based on semi-parameter estimation. Navig. Positioning Timing 7(6), 60–70 (2020) 16. Saizhou, J., Guoliang, C., Chao, Z., Xuan, W., Junpeng, W., Rui, W.: An adaptive bluetooth fingerprint positioning algorithm based on area optimization. Sci. Surveying Mapp. 45(8), 51–56 (2020) 17. Wen, O., Lixing, J., Haolong, L., Kai, Z., Xueqiang, L.: A UWB cooperative positioning method. J. Navig. Positioning. 8(4), 20-25+38 (2020) 18. Qingqing, L., Benxian, X.: RFID positioning based on a grid density peak clustering algorithm. J. Electron. Measur. Instrum. 32(10), 73–78 (2018) 19. Jiayu, G., Suzhe, Y., Bin, L.: A high-precision visual positioning method based on sub-pixel matching. Navig. Positioning Timing. 7(3), 54–61 (2020) 20. Pan, L., Yue, X., Heng, Z., Hong, L., Guoqing, Y.: MSCKF-based IMU and LIDAR tight coupling positioning method. Chin. J. Sci. Instrum. 41(08), 13–20 (2020) 21. Meng, S., Yunjia, W., Jiapeng, Z., Shenglei, X., Minghao, S.: A geomagnetic location algorithm based on fast dynamic time warping. Sci. Surveying Mapp. 45(08), 77–82 (2020) 22. Changyong, Z., Yanfang, W.: Design of ultrasonic positioning system based on dynamic time interval. Sci. Technol. Eng. 18(35), 169–173 (2018)

680

H. Wu

23. Song, Z., Yong, M., Wenting, Y., Jiasong, Z.: Analysis of PPP positioning accuracy and convergence speed of beidou system. J. Geodesy Geodyn. 41(2), 122–124 (2021) 24. Xingwei, L., Junbo, S., Dexiang, P., Chaoqian, X.: Design and implementation of differential positioning terminal of CORS system. Bull. Surveying Mapp. 12, 114–117 (2020) 25. Dazhong, Z., et al.: Accuracy analysis of single star timing of BDS. Bull. Surveying Mapp. 4, 7–10 (2019) 26. Seitz, S.M., Szeliski, R., Snavely, N.: Photo tourism: exploring photo collections in 3D. ACM Trans. Graphics 25(3), 835–846 (2006) 27. He, K., Gkioxari, G., Dollár, P., et al.: Mask R-CNN. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 2961–2969 (2017) 28. Zhi, Q., Aigong, X., Xin, S., et al.: An indoor positioning method based on monocular vision/UWB combination. J. Navig. Positioning. 24(4), 32-37+66 (2018) 29. Ding, C., Yuelong, M., Xuefeng, C., et al.: Autonomous positioning method of UAV based on IMU and monocular vision combination. J. Syst. Simul. 029(01), 9–14 (2017) 30. Li, X., Guo, C., Gupta, L., et al.: Efficient and secure 5G core network slice provisioning based on VIKOR approach. IEEE Access. 7, 150517–150529 (2019) 31. Lepetit, V., Moreno-Noguer, F., Fua, P.: EPnP: an accurate O(n) solution to the PnP problem. Int. J. Comput. Vis. 81(2), 155–166 (2009) 32. Bolya, D., Zhou, C., Xiao, F., et al.: YOLACT: real-time instance segmentation. In: Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 9157–9166 (2019) 33. Cao, Z., Simon, T., Wei, S.E., et al.: Realtime multi-person 2D pose estimation using part affinity fields. In: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE (2017)

Author Index

A Ai, Lun, 316 An, Xueying, 435 B Bai, Tao, 404 Bai, Yan, 424 Bi, Bo, 130 Bi, Shaojun, 496 Bian, Lang, 219 C Cai, Baigen, 366 Cai, Hongliang, 241 Cai, Si-zhe, 467 Cao, Xiaoxiang, 616 Cao, Zhiguo, 525 Chai, Hongzhou, 256 Chang, Xinuo, 546 Chen, Dong, 414, 616 Chen, Ke, 307 Chen, Qiuli, 327, 445, 496 Chen, Shi, 646 Chen, Wei, 467 Chen, Weiyi, 424 Chen, Yan, 104 Chen, Ying, 231 Cheng, Jian, 557 Chi, Chen, 467 Chu, Henglin, 33, 45, 55 Chu, Lei, 394 Cui, Hongzheng, 187 Cui, Xiaowei, 33, 45, 55, 75 Cui, Zhichao, 557

D Dai, Zhendong, 11 Deng, Xidan, 163 Deng, Zhongliang, 566, 576, 596 Ding, Yiming, 525 Ding, Yu, 327 Du, Jiqing, 356 F Fan, Shunxi, 174 Fan, Yi, 174 Fang, Chenghe, 241 Feng, Shaojun, 140 Feng, Xiaochao, 66 Fu, Haiyang, 104, 140 Fu, Xiao, 576 Fu, Yuanwen, 515 G Gao, Hui-li, 467 Gao, Shuai, 66 Gao, Yang, 33, 45, 55, 75 Gao, Yufang, 557 Geng, Changjiang, 241 Gong, Lei, 66 Gong, Wenbin, 505 Guan, Xujun, 394 Guo, Chi, 455 Guo, Jing, 163 Guo, Wenfei, 455 Guo, Xia, 219 H Hao, Xiaoming, 336 Hu, Enwen, 596

© Aerospace Information Research Institute 2021 C. Yang and J. Xie (Eds.): China Satellite Navigation Conference (CSNC 2021) Proceedings, LNEE 773, pp. 681–684, 2021. https://doi.org/10.1007/978-981-16-3142-9

682 Huai, Jianzhu, 414, 616 Huang, Jinquan, 92, 586 Huang, Zheng, 505 Huang, Zhigang, 22 Huang, Ziru, 384 J Jia, Weisong, 327, 445, 496 Jia, Xiaolin, 174 Jia, Xiaomin, 208 Jiang, Kun, 628 Jiang, Weijia, 566 Jin, Yaqiu, 140 K Kang, Chengbin, 347, 445, 496 Kuang, Jian, 535 Kun, Xu, 256 L Lei, Lei, 467 Li, Bin, 478 Li, Hongli, 478 Li, Jinfei, 384 Li, Junzheng, 307 Li, Min, 197 Li, Qi, 241 Li, Qipeng, 414 Li, Rui, 22, 150 Li, Taiyu, 535 Li, Tao, 394 Li, Teng, 3 Li, Wanling, 525 Li, Xiangjun, 92 Li, Xiaohui, 656 Li, Xiao-ping, 646 Li, Xiaoyue, 404 Li, Xing, 219 Li, Xingtong, 586 Li, Xinna, 307 Li, Xue, 637 Li, Zhendong, 347, 546 Liang, Wentao, 208 Lin, Baojun, 404 Liu, Bingcheng, 424 Liu, Cheng, 241 Liu, Fei, 336 Liu, Gang, 75 Liu, Haitao, 187 Liu, Jiang, 366 Liu, Jiehua, 566 Liu, Kuixing, 66 Liu, Lin, 445 Liu, Peilin, 11 Liu, Qiang, 11

Author Index Liu, Wenxiang, 92 Liu, Xiaohui, 92, 114, 586 Liu, Yanxu, 596 Liu, Yilong, 231 Liu, Ying, 92 Liu, Yuqi, 33 Liu, Zhijia, 347 Lu, Debiao, 366 Lu, Jun, 231 Lu, Mingquan, 75 Lu, Shan, 289, 298 Lu, Xiaochun, 424 Luo, Rui, 487 Luo, Yarong, 455 Lv, Jing, 356 Lv, Qiaochu, 435 M Ma, Fujian, 197 Ma, Qian, 66 Ma, Yinhu, 241 Mao, Yue, 174 Meng, Yansong, 219 Min, Wang, 256 N Nie, Xin, 197 Niu, Xiaoji, 535 P Pan, Yuqian, 546 Pang, Tao, 163 Pei, Ling, 394 Q Qi, Hang, 596 Qi, Wenlong, 256 Qi, Xin, 66 Qiu, Mobo, 606 Qu, Pingping, 163 R Ren, Hongyi, 22 Ren, Yiwen, 270 Ruan, Lang, 356 S Shao, FengWei, 505 She, Chengli, 187 Shen, Fei, 208 Shen, Li-rong, 646 Shi, Yong-qiang, 646 Su, Ranran, 208 Su, Zhe, 646 Sui, Yun, 140

Author Index Sun, Hai-feng, 646 Sun, Jie, 270 Sun, Pengfei, 628 Sun, Tianyang, 241 T Tang, Chengkai, 289, 298 Tang, Chengpan, 231 Tang, Jingshi, 445, 496 Tang, Xiaomei, 114 Tang, Zuping, 270 Tian, Shiwei, 356, 557 W Wang, Binbin, 316 Wang, Changkun, 356 Wang, Denghui, 140 Wang, Dingjie, 435 Wang, Dongmin, 384 Wang, Ershen, 163 Wang, Feixue, 114 Wang, Guotai, 3 Wang, Haihong, 327, 445, 496 Wang, Hanhua, 576 Wang, Jian, 546 Wang, Junjun, 150 Wang, Junshuai, 336 Wang, Lei, 197 Wang, Mengyuan, 455 Wang, Qian, 3 Wang, Ruochen, 394 Wang, Shizhuang, 515 Wang, Sixin, 114 Wang, Wei, 231, 487 Wang, Xiang, 75 Wang, Xinlong, 336 Wang, Xuan, 208, 546 Wang, Yidi, 628 Wang, Yongsong, 606 Wang, Yue, 375 Wang, Yuetong, 566 Wang, Yuqi, 487 Wang, Zheng, 208 Wang, Zhengchun, 525 Wei, Haitao, 231 Wei, Jiaolong, 270 Wei, Kefan, 45, 55, 75 Wei, Ziqing, 628 Wu, Haitao, 666 Wu, Jie, 316, 435 Wu, Qi, 394 Wu, Weiren, 637 Wu, Xianbing, 174

683 X Xian, Deyong, 3 Xiang, Minzhi, 384 Xiao, Wei, 92 Xiao, Yamu, 586 Xiao, Yu, 366 Xie, Chao, 3 Xing, Juhong, 606 Xiong, Zhi, 525 Xu, Deyan, 174 Xu, Feng, 140 Xu, Jiawei, 375 Xu, Linfeng, 208 Xu, Longxia, 656 Xu, Qibing, 33 Xue, Linshan, 637 Y Yan, Linli, 628 Yang, Chong, 256 Yang, Guang, 424 Yang, Rong, 375 Yang, Tao, 366 Yang, Tiantian, 22 Yang, Xiansheng, 616 Yang, Yikang, 637 Yao, Jintao, 478 Ye, Junru, 104 Ye, Xiaozhou, 92 Ying, Rendong, 11 You, Lihua, 130 Yu, Jun, 187 Yu, Wenxian, 394 Yuan, Yuelin, 586 Z Zeng, Haiyu, 557 Zeng, Lingchuan, 424 Zhai, Yawei, 515 Zhan, Xingqun, 375, 515 Zhang, Guoyi, 231 Zhang, Jie, 347 Zhang, Jingcan, 150 Zhang, Juan, 289, 298 Zhang, Ruwei, 316 Zhang, Xu, 197, 327, 445 Zhang, Yi, 289, 298 Zhao, Dongqing, 384 Zhao, Hongsong, 606 Zhao, Xiaofang, 546 Zhao, Yifang, 241 Zheng, Chong, 208 Zheng, Jinjun, 445, 496 Zheng, Kang, 174 Zheng, Ruifeng, 280

684 Zheng, Xinyu, 566, 576 Zhou, Peiyuan, 187 Zhou, Qingyong, 628 Zhu, Feng, 656

Author Index Zhuang, Jianlou, 347 Zhuang, Yuan, 414, 616 Zhuang, Zhaowen, 114 Zuo, Yong, 92