Preface to the Third Edition	6
	References	9
	Preface to the Second Edition	10
	Preface to the First Edition	13
	Contents	17
	Abbreviations and Constants	24
	Abbreviations	24
	1 Introduction	28
	1.1 A Key Note on GPS	29
	1.1.1 GPS Modernization	31
	1.2 A Brief Message About GLONASS	34
	1.2.1 The Development of GLONASS	34
	1.3 Basic Information on Galileo	36
	1.3.1 The Development of Galileo	37
	1.4 Introduction of BeiDou	38
	1.4.1 The Development of BeiDou	39
	1.5 A Combined Global Navigation Satellite System	40
	References	41
	2 Coordinate and Time Systems	43
	2.1 Geocentric Earth-Fixed Coordinate Systems	43
	2.2 Coordinate System Transformations	47
	2.3 Local Coordinate System	48
	2.4 Earth-Centred Inertial Coordinate System	50
	2.5 IAU 2000 Framework	54
	2.6 Geocentric Ecliptic Inertial Coordinate System	58
	2.7 Time Systems	59
	References	62
	3 Satellite Orbits	63
	3.1 Keplerian Motion	63
	3.1.1 Satellite Motion in the Orbital Plane	66
	3.1.2 Keplerian Equation	70
	3.1.3 State Vector of the Satellite	72
	3.2 Disturbed Satellite Motion	75
	3.3 GPS Broadcast Ephemerides	75
	3.4 IGS Precise Ephemerides	77
	3.5 GLONASS Ephemerides	78
	3.6 Galileo Ephemerides	79
	3.7 BDS Ephemerides	79
	References	79
	4 GPS Observables	80
	4.1 Code Pseudoranges	80
	4.2 Carrier Phases	82
	4.3 Doppler Measurements	84
	References	86
	5 Physical Influences of GPS Surveying	87
	5.1 Ionospheric Effects	87
	5.1.1 Code Delay and Phase Advance	87
	5.1.2 Elimination of Ionospheric Effects	90
	5.1.3 Ionospheric Models	93
	5.1.4 Mapping Functions	97
	5.1.5 Introduction of Commonly Used Ionospheric Models	100
	5.2 Tropospheric Effects	104
	5.2.1 Tropospheric Models	105
	5.2.2 Mapping Functions and Parameterisation	109
	5.2.3 Introduction of Commonly Used Tropospheric Models	112
	5.2.4 Tropospheric Model for Airborne Kinematic Positioning	115
	5.2.5 Water Vapour Research with Ground-Based GPS Measurement	117
	5.3 Relativistic Effects	118
	5.3.1 Special Relativity and General Relativity	118
	5.3.2 Relativistic Effects on GPS	121
	5.4 Earth Tide and Ocean Loading Tide Corrections	123
	5.4.1 Earth Tide Displacements of GPS Stations	123
	5.4.2 Simplified Model of Earth Tide Displacements	125
	5.4.3 Numerical Examples of Earth Tide Effects	127
	5.4.4 Ocean Loading Tide Displacement	129
	5.4.5 Computation of the Ocean Loading Tide Displacement	132
	5.4.6 Numerical Examples of Loading Tide Effects	133
	5.5 Clock Errors	134
	5.5.1 Introduction of Commonly Used Clock Error Models	136
	5.5.2 Impact of Frequency Reference of a GPS Receiver on the Positioning Accuracy	138
	5.6 Multipath Effects	139
	5.6.1 GPS Altimetry, Signals Reflected from the Earth’s Surface	141
	5.6.2 Reflecting Point Positioning	141
	5.6.3 Image Point and Reflecting Surface Determination	143
	5.6.4 Research Activities in GPS Altimetry	144
	5.7 Anti-spoofing and Selective Availability Effects	145
	5.8 Antenna Phase Centre Offset and Variation	146
	5.9 Instrumental Biases	150
	References	151
	6 GPS Observation Equations and Equivalence Properties	157
	6.1 General Mathematical Models of GPS Observations	157
	6.2 Linearisation of the Observation Model	159
	6.3 Partial Derivatives of Observation Function	161
	6.4 Linear Transformation and Covariance Propagation	165
	6.5 Data Combinations	166
	6.5.1 Ionosphere-Free Combinations	168
	6.5.2 Geometry-Free Combinations	169
	6.5.3 Standard Phase–Code Combination	172
	6.5.4 Ionospheric Residuals	173
	6.5.5 Differential Doppler and Doppler Integration	174
	6.6 Data Differentiations	176
	6.6.1 Single Differences	177
	6.6.2 Double Differences	180
	6.6.3 Triple Differences	182
	6.7 Equivalence of the Uncombined and Combining Algorithms	184
	6.7.1 Uncombined GPS Data Processing Algorithms	185
	6.7.2 Combining Algorithms of GPS Data Processing	187
	6.7.3 Secondary GPS Data Processing Algorithms	192
	6.7.4 Summary	195
	6.8 Equivalence of Undifferenced and Differencing Algorithms	196
	6.8.1 Introduction	196
	6.8.2 Formation of Equivalent Observation Equations	197
	6.8.3 Equivalent Equations of Single Differences	199
	6.8.4 Equivalent Equations of Double Differences	203
	6.8.5 Equivalent Equations of Triple Differences	205
	6.8.6 Method of Dealing with the Reference Parameters	206
	6.8.7 Summary of the Unified Equivalent Algorithm	207
	References	208
	7 Adjustment and Filtering Methods	210
	7.1 Introduction	210
	7.2 Least Squares Adjustment	210
	7.2.1 Least Squares Adjustment with Sequential Observation Groups	212
	7.3 Sequential Least Squares Adjustment	214
	7.4 Conditional Least Squares Adjustment	216
	7.4.1 Sequential Application of Conditional Least Squares Adjustment	218
	7.5 Block-Wise Least Squares Adjustment	219
	7.5.1 Sequential Solution of Block-Wise Least Squares Adjustment	221
	7.5.2 Block-Wise Least Squares for Code–Phase Combination	223
	7.6 Zhou’s Theory: Equivalently Eliminated Observation Equation System	224
	7.6.1 Zhou–Xu’s Theory: Diagonalised Normal Equation and the Equivalent Observation Equation	227
	7.7 Kalman Filter	229
	7.7.1 Classic Kalman Filter	229
	7.7.2 Kalman Filter: A General Form of Sequential Least Squares Adjustment	231
	7.7.3 Robust Kalman Filter	232
	7.7.4 Yang’s Filter: Adaptively Robust Kalman Filtering	235
	7.7.5 Progress in Adaptively Robust Filter Theory and Application	239
	7.7.6 A Brief Introduction to the Intelligent Kalman Filter	241
	7.8 A Priori Constrained Least Squares Adjustment	241
	7.8.1 A Priori Parameter Constraints	242
	7.8.2 A Priori Datum	243
	7.8.3 Zhou’s Theory: Quasi-Stable Datum	245
	7.9 Summary	247
	References	249
	8 Cycle Slip Detection and Ambiguity Resolution	252
	8.1 Cycle Slip Detection	252
	8.2 Method of Dealing with Cycle Slips	254
	8.3 A General Criterion of Integer Ambiguity Search	254
	8.3.1 Introduction	254
	8.3.2 Summary of Conditional Least Squares Adjustment	255
	8.3.3 Float Solution	257
	8.3.4 Integer Ambiguity Search in Ambiguity Domain	258
	8.3.5 Integer Ambiguity Search in Coordinate and Ambiguity Domains	259
	8.3.6 Properties of Xu’s General Criterion	261
	8.3.7 An Equivalent Ambiguity Search Criterion and Its Properties	262
	8.3.8 Numerical Examples of the Equivalent Criterion	265
	8.3.9 Conclusions and Comments	267
	8.4 Ambiguity Resolution Approach Based on the General Criterion	268
	8.5 Ambiguity Function	270
	8.5.1 Xu’s Conjecture: Maximum Property of Ambiguity Function	271
	8.6 Ionosphere-Free Ambiguity Fixing	274
	8.6.1 Introduction	274
	8.6.2 Concept of Ionospheric Ambiguity Correction	276
	8.6.3 Determination of the Ionospheric Ambiguity Correction	279
	8.6.4 Integer Ambiguity Fixing Through Ambiguity-Ionospheric Equations	280
	8.6.5 Float Ambiguity Fixing	280
	8.7 PPP Ambiguity Fixing	280
	References	282
	9 Parameterisation and Algorithms of GPS Data Processing	285
	9.1 Parameterisation of the GPS Observation Model	285
	9.1.1 Evidence of the Parameterisation Problem of the Undifferenced Observation Model	286
	9.1.2 A Method of Uncorrelated Bias Parameterisation	287
	9.1.3 Geometry-Free Illustration	293
	9.1.4 Correlation Analysis in the Case of Phase–Code Combinations	294
	9.1.5 Conclusions and Comments	295
	9.2 Equivalence of the GPS Data Processing Algorithms	296
	9.2.1 Equivalence Theorem of GPS Data Processing Algorithms	297
	9.2.2 Optimal Baseline Network Forming and Data Condition	299
	9.2.3 Algorithms Using Secondary GPS Observables	301
	9.2.4 Simplified Equivalent Representation of GPS Observation Equations	302
	9.3 Non-equivalent Algorithms	309
	9.4 Reference Changing in GPS Difference Algorithm	309
	9.4.1 Changing Reference Satellite	309
	9.4.2 Changing Reference Station	310
	9.5 Standard Algorithms of GPS Data Processing	313
	9.5.1 Preparation of GPS Data Processing	313
	9.5.2 Single Point Positioning	314
	9.5.3 Standard Un-differential GPS Data Processing	319
	9.5.4 Equivalent Method of GPS Data Processing	322
	9.5.5 Relative Positioning	323
	9.5.6 Velocity Determination	324
	9.5.7 Kalman Filtering Using Velocity Information	327
	9.6 Accuracy of the Observational Geometry	328
	9.7 Introduction to the Real-Time Positioning System	330
	9.7.1 Network RTK	330
	9.7.2 PPP-RTK	333
	References	333
	10 Applications of GPS Theory and Algorithms	335
	10 Applications of GPS Theory and Algorithms	335
	10.1.1 Functional Library	335
	10.1.2 Data Platform	340
	10.1.3 A Data Processing Core	342
	10.1.3 A Data Processing Core	343
	10.1.3 A Data Processing Core	345
	10.3.1 Introduction	346
	10.3.2 Concept of Precise Kinematic Positioning	348
	10.3.2.1 Combining the Static References with IGS Station	348
	10.3.2.2 Earth Tide and Loading Tide Corrections	348
	10.3.2.3 Multiple Static References for Kinematic Positioning	349
	10.3.2.4 Introducing Height Information as a Condition	351
	10.3.2.5 Creation of a Kinematic Tropospheric Model	351
	10.3.2.6 Higher-Order Ionospheric Effect Correction	352
	10.3.2.7 A General Method of Integer Ambiguity Fixing	352
	10.3.3 Concept of Flight-State Monitoring	352
	10.3.4 Results, Precision Estimation, and Comparisons	355
	10.3.4.1 Multiple Static References for Kinematic Positioning	357
	10.3.4.2 Ambiguity of Multiple Static References as a Condition for Kinematic Positioning	357
	10.3.4.3 Multiple Kinematic GPS for Flight-State Monitoring and Its Comparison with INS	359
	10.3.4.4 Static GPS Data Kinematic Processing	360
	10.3.4.5 Doppler Velocity Comparisons	360
	10.3.5 Conclusions	360
	References	361
	11 Perturbed Orbit and Its Determination	363
	11.1 Perturbed Equation of Satellite Motion	363
	11.1.1 Lagrangian Perturbed Equation of Satellite Motion	364
	11.1.2 Gaussian Perturbed Equation of Satellite Motion	367
	11.2 Perturbation Forces of Satellite Motion	370
	11.2.1 Perturbation of the Earth’s Gravitational Field	370
	11.2.1.1 The Earth’s Gravitational Field	370
	11.2.1.2 Perturbation Force of the Earth’s Gravitational Field	373
	11.2.2 Perturbations of the Sun, the Moon, and the Planets	375
	11.2.3 Earth Tide and Ocean Tide Perturbations	376
	11.2.4 Solar Radiation Pressure	380
	11.2.5 Atmospheric Drag	384
	11.2.6 Additional Perturbations	387
	11.2.7 Order Estimations of Perturbations	389
	11.2.8 Ephemerides of the Moon, the Sun, and Planets	390
	11.3 Analysis Solution of the \overline{C}_{20} Perturbed Orbit	394
	11.4 Orbit Correction	401
	11.5 Principle of GPS Precise Orbit Determination	405
	11.5.1 Xu’s Algebraic Solution to the Variation Equation	407
	11.6 Numerical Integration and Interpolation Algorithms	409
	11.6.1 Runge–Kutta Algorithm	409
	11.6.2 Adams Algorithms	413
	11.6.3 Cowell Algorithms	416
	11.6.4 Mixed Algorithms and Discussions	418
	11.6.5 Interpolation Algorithms	419
	11.7 Orbit-Related Partial Derivatives	420
	References	429
	12 Singularity-Free Orbit Theory	431
	12.1 A Brief Historical Review of the Singularity Problem	431
	12.2 On the Singularity Problem in Orbital Mechanics	434
	12.2.1 Basic Lagrangian and Gaussian Equations of Motion	434
	12.2.2 Solving Algorithm for the Singularity Problem	439
	12.2.3 Xu’s Criteria for Singularity	440
	12.2.4 Derivation of Lagrange-Xu Equations of Motion	441
	12.2.5 Derivation of Gauss Equations from Lagrange Equations	451
	12.2.6 Derivation of Gauss-Xu Equations of Motion	453
	12.3 Bridge Between Analytical Theory and Numerical Integration	456
	References	457
	13 Discussions	460
	13.1 Independent Parameterisation and A Priori Information	460
	13.2 Equivalence of the GPS Data Processing Algorithms	462
	13.3 Other Comments	463
	Appendix A: IAU 1980 Theory of Nutation	465
	Appendix B: Numerical Examples of the Diagonalisation of the Equations	469
	References	475
	Index	502