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