BDS/GPS Dual-Mode Software Receiver: Principles and Implementation Technology

Preface
Introduction
Contents
1 Positioning, Coordinate System, and Time Standard
	1.1 The Question Raised
		1.1.1 Basic Purpose and Basic Positioning System
		1.1.2 The Workings of a Clock
		1.1.3 A Modified System
		1.1.4 Summary of the Modified System
	1.2 Common Coordinate Systems
		1.2.1 Earth Centered Inertial Frame
		1.2.2 The Geodetic Frame
		1.2.3 The ECEF Coordinate System
		1.2.4 The ENU or NED Coordinate System
		1.2.5 The Body Frame Coordinate System
	1.3 The Time System
		1.3.1 Solar Time and Sidereal Time
		1.3.2 Dynamical Time
		1.3.3 Atomic Time and Coordinated Universal Time (UTC)
		1.3.4 GPS Time (GPST)
		1.3.5 BeiDou Time (BDT)
	References
2 Brief Introduction to the GPS and BeiDou Satellite Navigation Systems
	2.1 The History of the GPS System
	2.2 The Construction of the GPS System
	2.3 The GPS Modernization Plan
	2.4 An Overview of BDS
	References
3 GPS and the Signal Format and Navigation Message of BDS-2
	3.1 The GPS Signal
		3.1.1 The Generation Mechanism of the GPS Signal
		3.1.2 The C/A Code Generator
		3.1.3 Autocorrelation and Cross-Correlation of C/A Codes
	3.2 The BeiDou Signal
		3.2.1 BDS Signal Structure
		3.2.2 BDS Pseudo-Random Code Generator
		3.2.3 Autocorrelation and Cross-Correlation of BDS Pseudo-Random Codes
	3.3 Navigation Messages
		3.3.1 The GPS Navigation Message
		3.3.2 The BDS Navigation Message
	3.4 Time Relationships Among Various Satellite Signals
	References
4 Capture and Tracking of the Signal
	4.1 Signal Acquisition
		4.1.1 The Concept of Signal Acquisition
		4.1.2 Signal Capture Based on the Time Domain Correlator
		4.1.3 Signal Acquisition Based on the Matched Filter
		4.1.4 Signal Capture Based on FFT
		4.1.5 Signal Acquisition Combing Short-Time Correlation Matched Filter and FFT
		4.1.6 Signal Capture Based on Data Blocking and Frequency Compensation
		4.1.7 Threshold Setting for Signal Capture
		4.1.8 Coherent Integration and Non-coherent Integration
	4.2 Signal Tracking
		4.2.1 The Basic Phase-Locked Loop
		4.2.2 Thermal Noise Performance Analysis of the Linear Phase-Locked Loop
		4.2.3 Carrier Tracking Loop
		4.2.4 The Pseudo-Code Tracking Loop
		4.2.5 Problems in Tracking Loop Implementation and Debugging
		4.2.6 Bit Synchronization
		4.2.7 Sub-frame Synchronization
	References
5 Dual Mode Observation Extraction and Error Analysis
	5.1 Pseudo-Range Observation
	5.2 Carrier Phase Observation
	5.3 Doppler Frequency and Integral Doppler Observation
	5.4 Analysis of Measurement Error Features
		5.4.1 Satellite Clock Error
		5.4.2 Ephemeris Error
		5.4.3 Ionospheric Delay
		5.4.4 Tropospheric Delay
		5.4.5 The Multipath Effect
		5.4.6 Receiver Errors
	5.5 Differential GNSS Technology
	References
6 Calculating a Satellite’s Position and Velocity
	6.1 Satellite Orbit Theory
	6.2 GPS Satellites and BDS MEO/IGSO Satellites
	6.3 BDS GEO Satellite
	6.4 Interpolation Calculation of Satellite Position and Velocity
	6.5 Precise Ephemeris and Ephemeris Expansion
	References
7 Position, Velocity, and Time Solutions
	7.1 The Least-Squares Solution
		7.1.1 Basic Principles
		7.1.2 Weighted Least-Squares
		7.1.3 Calculation of Speed and Clock Drift Using Doppler Observations
		7.1.4 Satellite Elevation and Azimuth
		7.1.5 Geometric Dilution of Precision
		7.1.6 Receiver Autonomous Integrity Monitoring (RAIM)
	7.2 Maximum Solution Separation
	7.3 Kalman Filtering
		7.3.1 Recursive Least-Squares
		7.3.2 The Basic Kalman Filter
		7.3.3 From Continuous Time Systems to Discrete Time Systems
		7.3.4 The Extended Kalman Filter
		7.3.5 Several KF Models Commonly Used in Receivers
		7.3.6 Technical Processing in the Implementation of Kalman Filtering
	7.4 Summary of the Least-Squares and Kalman Filtering Solutions
	References
8 RF Front-End
	8.1 Transmission and Reception of Satellite Signals
	8.2 Noise Figure of the Cascaded System
	8.3 Bandpass Sampling
	8.4 IF Sampling and RF Sampling Schemes
		8.4.1 IF Sampling Scheme
		8.4.2 RF Sampling Scheme
	8.5 Automatic Gain Control (AGC) and Quantization Bit Width
	8.6 The Relationship Between RF Carrier-to-Noise Ratio and Baseband Signal-to-Noise Ratio
		8.6.1 Case Analysis of the RF Front-End Frequency Scheme
	References
9 Implementation of BDS/GPS Dual-Mode Software Receivers
	9.1 Signal Source for Dual-Mode Software Receivers
	9.2 Software Modules and Program Interfaces for Dual-Mode Receivers
	9.3 Data Processing in Dual-Mode Receivers
Appendix A Basic Matrices and Vector Operations
A.1 The Inverse Matrix and Its Properties
A.2 Eigenvalues and Eigenvectors of the Matrix
A.3 Quadratic Form and Fixed Matrices
A.4 Several Important Matrix Decompositions
A.5 Preliminary Matrix Analysis
Appendix B Conversion and Rotation of the Cartesian Coordinate System
Appendix C Mean and Variance of NBP and WBP
Appendix D Derivations Related to the Elliptical Orbit of the Satellite
Appendix E The Klobuchar Model with Ionospheric Delay