GPS Satellite
Surveying
GPS
Satellite Surveying
Alfred Leick
3rd Edition, 2004, 435 pages
Publisher: J. Wiley & Sons
ISBN 0-471-05930-7
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Errata (PDF, 28 Kb)
PREFACE xiii
ACKNOWLEDGMENTS
xvii
ABBREVIATIONS
xix
NOTATION
xxiii
1
INTRODUCTION
1.1 Historical Perspective / 3
1.2 Geodetic Aspects / 8
2 GEODETIC REFERENCE
SYSTEMS
2.1 Conventional Terrestrial
Reference System / 13
2.1.1 Polar Motion / 13
2.1.2 Tectonic Plate
Motion / 15
2.1.3 Solid Earth Tides /
18
2.1.4 Ocean Loading / 19
2.2 Conventional Celestial
Reference System / 19
2.2.1 Transforming
between ITRF and ICRF / 22
2.2.2 Time Systems / 25
2.3 Datum / 29
2.3.1 Geoid / 29
2.3.2 Ellipsoid of
Revolution / 35
2.3.3 Geoid Undulations
and Deflections of the Vertical / 36
2.3.4 Reductions to the
Ellipsoid / 40
2.3.5 The 3D Geodetic
Model / 44
2.3.5.1
Partial Derivatives / 46
2.3.5.2
Reparameterization / 48
2.3.5.3
Implementation Considerations / 49
3 SATELLITE SYSTEMS
3.1 Motion of Satellites /
53
3.1.1 Kepler
Elements / 54
3.1.2 Normal Orbital
Theory / 55
3.1.3 Satellite
Visibility and Topocentric Motion / 65
3.1.4 Perturbed
Satellite Motion / 66
3.1.4.1
Gravitational Field of the Earth / 67
3.1.4.2
Acceleration due to the Sun and the Moon / 69
3.1.4.3
Solar Radiation Pressure / 69
3.1.4.4
Eclipse Transits and Yaw Maneuvers / 70
3.2 GPS Global Positioning
System / 72
3.2.1 General
Description / 72
3.2.2 Satellite
Transmissions at 2002 / 75
3.2.2.1
Signal Structure / 76
3.2.2.2
Navigation Message / 81
3.2.3 GPS
Modernization / 83
3-2.3.1
Civil L2C Codes / 84
3-2.3.2 Civil
L5 Code / 85
3.2.3.3
M-Code / 85
3.3 GLONASS / 86
3.4 Galileo / 90
4 LEAST-SQUARES ADJUSTMENTS
4.1 Elements / 93
4.1.1 Statistical
Nature of Surveying Measurement / 93
4.1.2 Elementary
Statistical Concepts / 94
4.1.3 Observational
Errors / 95
4.1.4 Accuracy and
Precision / 95
4.2 Stochastic and Mathematical
Models / 96
4.3 Variance-Covariance
Propagation / 99
4.4 Mixed Adjustment Model / 104
4.4.1 Linearization /
104
4.4.2 Minimization and
Solution / 105
4.4.3 Cofactor
Matrices / 106
4.4.4 A Posteriori
Variance of Unit Weight / 107
4.4.5 Iterations / 109
4.5 Observation and Condition
Equation Models / 110
4.6 Sequential Solution / 112
4.7 Weighted Parameters and
Conditions / 118
4.8 Minimal and Inner
Constraints / 124
4.9 Statistics in
Least-Squares Adjustment / 129
4.9.1 Multivariate
Normal Distribution / 129
4.9.2 Distribution of vTv
/ 131
4.9.3 Testing vTPv
and vTPv / 135
4.9.4 General Linear
Hypothesis / 138
4.9.5 Ellipses as
Confidence Regions / 141
4.9.6 Properties of
Standard Ellipses / 146
4.9.7 Other Measures of
Precision / 150
4.10 Reliability / 151
4.10.1 Redundancy
Numbers / 151
4.10.2 Controlling
Type-11 Error for a Single Blunder / 153
4.10.3 Internal
Reliability / 157
4.10.4 Absorption / 157
4.10.5 External
Reliability / 158
4.10.6 Correlated Cases /
159
4.11 Blunder Detection / 159
4.11.1 The T Test / 160
4.11.2 Data Snooping /
161
4.11.3 Changing Weights
of Observation / 162
4.12 Examples / 162
4.13 Kalman Filtering / 167
5 PSEUDORANGE AND CARRIER PHASE
OBSERVABLES
5.1 Pseudoranges and Carrier
Phases / 171
5.2 Differencing / 175
5.3 Initial Evaluation / 177
5.3.1 Satellite
Clock Corrections / 177
5.3.2 Topocentric
Range / 178
5.3.3 Cycle Slips /
179
5.3.4 Singularities /
181
5.3.5 Impact of a
Priori Position Errors / 183
5.3.6 Cancellation of
Common Mode Errors / 185
5.3.6.1
Point Positioning / 185
5.3.6.2
Relative Positioning / 186
5.4 Satellite Code Offsets /
186
6 TROPOSPHERE AND
IONOSPHERE
6.1 Overview / 189
6.2 Tropospheric Refraction
and Delay / 194
6.2.1 Model Zenith
Delay Functions / 197
6.2.2 Model Mapping
Functions / 197
6.2.3 Horizontal
Gradient Model / 199
6.2.4 Precipitable
Water Vapor / 200
6.3 Tropospheric Absorption
/ 201
6.3.1 The Radiative
Transfer Equation / 202
6.3.2 Absorption Line
Profiles / 204
6.3.3 General
Statistical Retrieval / 207
6.3.4 Calibration of
WVR / 209
6.4 Ionospheric Refraction /
211
6.5 Ionospheric Code Delays
and Phase Advances / 215
6.6 Ionospheric Solutions /
219
6.6.1 Single
Frequencies and the Broadcast Ionospheric Model / 219
6.6.2 Ionospheric-Free
Functions / 221
6.6.3 Ionospheric
Functions / 222
6.6.4 Discriminating
Small Cycle Slips / 223
6.6.5 Multipath
Equations / 224
6.6.6 Generalizing the
Dual-Frequency Phase Function / 225
6.6.7 Global
Ionospheric Models / 226
7 PROCESSING PSEUDORANGES AND
CARRIER PHASES
7.1 The IGS and Its Products
/ 229
7.2 Antenna Corrections / 230
7.2.1 Phase Windup
Correction / 231
7.2.2 Satellite Antenna
Phase Center Offset / 233
7.2.3 Receiver Antenna
Phase Center Offset and Variation / 234
7.2.4 Multipath / 237
7.3 Geometry-Free Solutions /
244
7.4 Point Positioning / 250
7.4.1 Linearized Solution
and DOPs / 251
7.4.2 Closed Solution /
253
7.5 Precise Point Positioning /
254
7.6 Real-Time Precise Point
Positioning / 256
7.7 Relative Positioning / 259
7.7.1 Using Pseudoranges
/ 259
7.7.2 Double-Difference
Float and Triple-Difference Solutions / 261
7.7.3 Independent
Baselines / 265
7.7.4 Ambiguity Function
/ 267
7.7.5 Initialization on
the Ground / 270
7.7.6 GLONASS Carrier
Phase Processing / 271
7.7.7 Relative
Positioning within CORS / 276
7.8 Ambiguity Fixing / 277
7.8.1 Early Efforts /
279
7.8.2 LAMBDA / 282
7.8.3 Discernibility /
290
7.9 Real-Time Relative
Positioning / 293
7.9.1 Carrier Phase and
Pseudorange Corrections / 293
7.9.2 Local Network
Corrections / 295
7.9.3 WADGPS / 299
8 NETWORK
ADJUSTMENTS
8.1 GPS Vector Networks / 302
8.2 Transforming Nearly
Aligned Coordinate Systems / 304
8.3 Combination through
Rotation and Scaling / 306
8.4 GPS Network Examples / 308
8.4.1 Montgomery County
Geodetic Network / 308
8.4.2 SLC Engineering
Survey / 312
8.4.3 Orange County
Densification / 312
9 TWO-DIMENSIONAL GEODETIC
MODELS
9.1 The Ellipsoidal Model /
322
9.1.1 Reduction of
Observations / 322
9.1.1.1
Angular Reduction to Geodesic / 322
9.1.1.2
Distance Reduction to Geodesic / 325
9.1.2 Direct and
Inverse Solutions on the Ellipsoid / 326
9.1.3 Network
Adjustment on the Ellipsoid / 328
9.2 The Conformal Mapping
Model / 330
9.2.1 Reduction of
Observations / 331
9.2.2 The Angular
Excess / 332
9.2.3 Direct and
Inverse Solutions on the Map / 333
9.2.4 Network
Adjustment on the Map / 334
9.2.5 The At
and As Functions / 335
9.2.6 Similarity
Revisited / 337
APPENDIXES
A GENERAL BACKGROUND
A. 1 Spherical Trigonometry /
340
A.2 Rotation Matrices / 344
A.3 Linear Algebra / 345
A.3.1 Determinants and
Matrix Inverse / 345
A.3.2 Eigenvalues and
Eigenvectors / 347
A.3.3 Diagonalization /
348
A.3.4 Quadratic Forms /
349
A.3.5 Matrix Partitioning
/ 352
A.3.6 Cholesky Factor /
353
A.4 Linearization / 356
A.5 Statistics / 358
A.5.1 One-Dimensional
Distributions / 358
A.5.2 Distribution of
Sums and Variables / 362
A.5.3 Hypothesis Tests /
364
B THE ELLIPSOID
B.1 Geodetic Latitude,
Longitude, and Height / 368
B.2 Computations on the
Ellipsoidal Surface / 373
B.2.1 Fundamental
Coefficients / 373
B.2.2 Gauss
Curvature / 376
B.2.3 Elliptic Arc / 376
B.2.4 Angle / 377
B.2.5 Isometric Latitude
/ 378
B.2.6 Differential
Equation of the Geodesic / 379
B.2.7 The Gauss
Midlatitude Solution / 382
B.2.8 Angular Excess /
384
B.2.9 Transformation in a
Small Region / 384
C CONFORMAL MAPPING
C.1 Conformal Mapping of Planes
/ 387
C.2 Conformal Mapping of
General Surfaces / 392
C.3 The Isometric Plane / 393
C.4 Popular Conformal Mappings
/ 395
C.4.1 Equatorial
Mercator / 395
C.4.2 Transverse Mercator
/ 396
C.4.3 Lambert Conformal /
399
C.4.4 SPC and UTM / 403
REFERENCES
AUTHOR INDEX
SUBJECT INDEX
