Guochang Xu GPS. Theory, Algorithms and Applications. Second Edition. With 59 Figures. Sprin ger

Transcription

1 Guochang Xu GPS Theory, Algorithms and Applications Second Edition With 59 Figures Sprin ger

2 Contents 1 Introduction AKeyNoteofGPS A Brief Message About GLONASS Basic Information of Galileo A Combined Global Navigation Satellite System 5 2 Coordinate and Time Systems Geocentric Earth-Fixed Coordinate Systems Coordinate System Transformations Local Coordinate System Earth-Centred Inertial Coordinate System Geocentric Ecliptic Inertial Coordinate System Time Systems 17 3 Satellite Orbits Keplerian Motion Satellite Motion in the Orbital Plane Keplerian Equation State Vector of the Satellite Disturbed Satellite Motion GPS Broadcast Ephemerides IGS Precise Ephemerides GLONASS Ephemerides 35 4 GPS Observables Code Pseudoranges Carrier Phases Doppler Measurements 41 5 Physical Influences of GPS Surveying Ionospheric Effects Code Delay and Phase Advance Elimination of the Ionospheric Effects Ionospheric Models Mapping Functions 51

3 5.2 Tropospheric Effects Tropospheric Models Mapping Functions and Parameterisation Relativistic Effects Special Relativity and General Relativity Relativistic Effects on GPS Earth Tide and Ocean Loading Tide Corrections Earth Tide Displacements of the GPS Station Simplified Model of the Earth Tide Displacements Numerical Examples of the Earth Tide Effects Ocean Loading Tide Displacement Computation of the Ocean Loading Tide Displacement Numerical Examples of Loading Tide Effects Clock Errors Multipath Effects GPS-Altimetry, Signals Reflected from the Earth-Surface Reflecting Point Positioning Image Point and Reflecting Surface Determination Anti-Spoofing and Selective Availability Effects Antenna Phase Centre Offset and Variation Instrumental Biases 85 6 GPS Observation Equations and Equivalence Properties General Mathematical Models of GPS Observations Linearisation of the Observational Model Partial Derivatives of Observational Function Linear Transformation and Covariance Propagation Data Combinations Ionosphere-Free Combinations Geometry-Free Combinations Standard Phase-Code Combination Ionospheric Residuais Differential Doppler and Doppler Integration Data Differentiations Single Differences Double Differences Triple Differences Equivalence of the Uncombined and Combining Algorithms Uncombined GPS Data Processing Algorithms Combining Algorithms of GPS Data Processing Secondary GPS Data Processing Algorithms Summary Equivalence of Undifferenced and Differencing Algorithms Introduction Formation of Equivalent Observation Equations Equivalent Equations of Single Differences 125

4 Contents XV Equivalent Equations of Double Differences Equivalent Equations of Triple Differences Method of Dealing with the Reference Parameters Summary of the Unified Equivalent Algorithm Adjustment and Filtering Methods Introduction Least Squares Adjustment Least Squares Adjustment with Sequential Observation Groups Sequential Least Squares Adjustment Conditional Least Squares Adjustment Sequential Application of Conditional Least Squares Adjustment Block-Wise Least Squares Adjustment Sequential Solution of Block-Wise Least Squares Adjustment Block-Wise Least Squares for Code-Phase Combination Equivalently Eliminated Observation Equation System Diagonalised Normal Equation and the Equivalent Observation Equation Kaiman Filter Classic Kaiman Filter Kaiman Filter - A General Form of Sequential Least Squares Adjustment Robust Kaiman Filter Adaptively Robust Kaiman Filtering A Priori Constrained Least Squares Adjustment A Priori Parameter Constraints A Priori Datum Quasi-Stable Datum Summary Cycle Slip Detection and Ambiguity Resolution Cycle Slip Detection Method of Dealing with Cycle Slips A General Criterion of Integer Ambiguity Search Introduction Summary of Conditional Least Squares Adjustment Float Solution Integer Ambiguity Search in Ambiguity Domain Integer Ambiguity Search in Coordinate and Ambiguity Domains Properties of the General Criterion An Equivalent Ambiguity Search Criterion and its Properties Numerical Examples of the Equivalent Criterion Conclusions and Comments Ambiguity Function Maximum Property of Ambiguity Function 183

5 XVI Contents 9 Parameterisation and Algorithms of GPS Data Processing Parameterisation of the GPS Observation Model Evidence of the Parameterisation Problem of the Undifferenced Observation Model A Method of Uncorrelated Bias Parameterisation Geometry-Free Illustration Correlation Analysis in the Case of Phase-Code Combinations Conclusions and Comments Equivalence of the GPS Data Processing Algorithms Equivalence Theorem of GPS Data Processing Algorithms Optimal Baseline Network Forming and Data Condition Algorithms Using Secondary GPS Observables Non-Equivalent Algorithms Standard Algorithms of GPS Data Processing Preparation of GPS Data Processing Single Point Positioning Standard Un-Differential GPS Data Processing Equivalent Method of GPS Data Processing Relative Positioning Velocity Determination Kaiman Filtering Using Velocity Information Accuracy of the Observational Geometry Applications of GPS Theory and Algorithms Software Development Functional Library Data Platform A Data Processing Core Concept of Precise Kinematic Positioning and Flight-State Monitoring Introduction Concept of Precise Kinematic Positioning Concept of Flight-State Monitoring Results, Precision Estimation and Comparisons Conclusions Perturbed Orbit and its Determination Perturbed Equation of Satellite Motion Lagrangian Perturbed Equation of Satellite Motion Gaussian Perturbed Equation of Satellite Motion Perturbation Forces of Satellite Motion Perturbation of the Earth's Gravitational Field Perturbation of the Sun and the Moon as well as Planets Earth Tide and Ocean Tide Perturbations Solar Radiation Pressure Atmospheric Drag Additional Perturbations 265

6 Contents XVII Order Estimations of Perturbations Ephemerides of the Moon, the Sun and Planets Analysis Solution of the C 20 Perturbed Orbit Orbit Correction Principle of GPS Precise Orbit Determination Algebra Solution of the Variation Equation Numerical Integration and Interpolation Algorithms Runge-Kutta Algorithms Adams Algorithms Cowell Algorithms Mixed Algorithms and Discussions Interpolation Algorithms Orbit-Related Partial Derivatives Discussions Independent Parameterisation and A Priori Information Equivalence of the GPS Data Processing Algorithms 307 Appendix 1 IAU 1980 Theory of Nutation 309 Appendix 2 Numerical Examples of the Diagonalisation of the Equations 311 References 317 Subject Index 337