GPS satellite surveying

목차 (Table of Contents)

• CONTENTS
• Preface = xiii
• Frequently Used Abbreviations = xvii
• 1 INTRODUCTION = 1
• 1.1 The outcome of GPS positioning = 4
• 1.2 A performance review = 5
• 1.3 Some geodetic considerations = 10
• 2 ELEMENTS OF SATELLITE SURVEYING = 16
• 2.1 Goecentric coordinate systems and their motions = 16
• 2.1.1 Precession and nutation = 17
• 2.1.2 The conventional terrestrial reference system = 22
• 2.2 Time systems = 26
• 2.2.1 Time in orders of magnitude = 26
• 2.2.2 Astronomic time scales = 29
• 2.2.3 Atomic time = 33
• 2.2.3.1 Need for coordination = 34
• 2.2.3.2 Link to earth rotation = 35
• 2.2.4 Time and earth orintation services = 37
• 2.3 Satellite orbital motion = 38
• 2.3.1 Kepler elements = 38
• 2.3.2 Normal orbital theory = 41
• 2.3.3 Satellite visibility and topocentric motion = 49
• 2.3.4 Disturbed satellite motion = 53
• 2.3.4.1 Gravitational field of the earth = 54
• 2.3.4.2 Acceleration due to the sun and the moon = 55
• 2.3.4.3 Solar radiation pressure = 56
• 3 THE GLOBAL POSITIONING SYSTEM = 58
• 3.1 Space segment = 60
• 3.1.1 GPS satellites = 60
• 3.1.2 Orbital configuration = 62
• 3.1.3 Satellite transmissions = 65
• 3.1.3.1 Overview = 66
• 3.1.3.2 Space vehicle and GPS time systems = 67
• 3.1.3.3 GPS signal structure = 68
• 3.1.3.4 The bavigation messate = 72
• 3.2 Control segment and other support = 77
• 3.3 Receivers = 78
• 3.3.1 Some Fundamentals = 79
• 3.3.1.1 Bandwidth = 79
• 3.3.1.2 Power = 79
• 3.3.1.3 Filtering = 81
• 3.3.1.4 Frequency translation and multiplication = 81
• 3.3.1.5 Spread spectrum = 83
• 3.3.1.6 Cross-correlation = 83
• 3.3.1.7 Locking and tracking = 85
• 3.3.2 Modern geodetic receivers = 86
• 3.3.3 Pseudorange measurement accuracy = 87
• 3.3.4 Coping with antispoofing = 89
• 3.3.4.1 Squaring = 90
• 3.3.4.2 Code-aided squaring = 90
• 3.3.4.3 Cross-correlation = 90
• 3.3.4.4 Z tracking = 90
• 4 ADJUSTMENT COMPUTATIONS = 93
• 4.1 Elements = 94
• 4.1.1 Statistical nature of surveying measurement = 94
• 4.1.2 Elementary statistical concepts = 95
• 4.1.3 Observational errors = 97
• 4.1.4 Accuracy and precision = 97
• 4.2 Stochastic and mathematical models = 98
• 4.3 Propagation of mean and variance-covariance = 102
• 4.4 Mixed adjustment model = 108
• 4.4.1 Linearization = 109
• 4.4.2 Minimization and solution = 109
• 4.4.3 Cofactor matrices = 110
• 4.4.4 A posteriori variance of unit weight = 111
• 4.4.5 Iterations = 113
• 4.5 Observation equation and condition equation models = 114
• 4.6 Sequential solution = 115
• 4.7 Weighted parameters and conditions between parameters = 123
• 4.8 Minimal and inner constraint adjustments = 130
• 4.9 Statistics in least-squares adjustments = 135
• 4.9.1 Multivariate normal distribution = 135
• 4.9.2 Distribution of $$V^TPV$$ = 137
• 4.9.3 Testing $$V^TPV$$ and $$\Delta V^TPV$$ = 142
• 4.9.4 General linear hypothesis = 147
• 4.9.5 Ellipses as confidence regions = 149
• 4.9.6 Properties of standard ellipses = 155
• 4.9.7 Other measures of precision = 160
• 4.10 Reliability = 161
• 4.10.1 Redundancy numbers = 161
• 4.10.2 Controlling type Ⅱ error for a single blunder = 163
• 4.10.3 Internal reliability = 167
• 4.10.4 Absorption = 168
• 4.10.5 External reliability = 168
• 4.10.6 Correlated cases = 169
• 4.11 Blunder detection = 170
• 4.11.1 The $$\tau $$ test = 171
• 4.11.2 Data snooping = 173
• 4.11.3 changin weights of observations = 174
• 5 OEAST-SQUARES ADJUSTMENT EXAMPLES = 175
• 5.1 Introduction = 175
• 5.2 Adjustment of a simple network on the mapping plane = 178
• 5.3 Minimal constraint for network adjustment on the mapping plane = 187
• 5.4 Inner constraint for network adjustment on the mapping plane = 189
• 5.5 Adjustment of the complete network on the mapping plane = 195
• 5.6 Adjustment of the complate network with additional information = 198
• 5.7 Detection poor network geometry : the dangerous circle = 201
• 5.8 Closed traverse adjustment on the mapping plane = 203
• 5.9 Open traverse adjustment on the mapping plane = 206
• 5.10 Adjustment of leveling observations = 206
• 5.11 Stochastic models for distances and angles = 210
• 6 LINKS TO PHYSICAL OBSERVATIONS = 215
• 6.1 Geoid = 216
• 6.2 Ellipsoid of revolution = 223
• 6.3 Location of the ellipsoid and reductions of observations = 226
• 7 THE THREE-DIMENSIONAL GEODETIC MODEL = 233
• 7.1 The partial derivatives = 234
• 7.2 Additional remarks = 241
• 7.3 An example = 243
• 8 GPS OBSERVABLES = 247
• 8.1 Pseudoranges = 248
• 8.1.1 The namigation solution = 252
• 8.1.2 DOP factors = 253
• 8.2 Carrier phases = 255
• 8.2.1 Undifferenced carrier phase observable = 256
• 8.2.2 Single differences = 259
• 8.2.3 Double differences = 261
• 8.2.4 Triple differences = 262
• 8.2.5 Delta ranges = 263
• 8.3 Evaluation = 264
• 8.3.1 The clock eooro terms = 265
• 8.3.1.1 Receiver clocks = 266
• 8.3.1.2 The question of simultaneity = 266
• 8.3.1.3 Satellite colck corrections = 268
• 8.3.1.4 Residual satellite clock error = 270
• 8.3.2 Summary of undifferenced expressions = 270
• 8.3.3 Singularities = 272
• 8.3.4 A priori position errors = 275
• 8.3.5 Cancellation of commmon mode errors = 277
• 8.3.5.1 Navigation solution = 277
• 8.3.5.2 Relative positioning = 279
• 8.3.6 Connection to other systems = 279
• 8.3.6.1 The Doppler connection = 280
• 8.3.6.2 The VLBI connection = 282
• 8.3.7 Selective availability = 283
• 9 PROPAGATION MEDIA, MULTIPATH, AND PHASE CENTER = 286
• 9.1 The atmosphere in brief = 287
• 9.2 Elements of wave propagation = 290
• 9.3 Ionospheric effects on GPS observables = 294
• 9.3.1 Code delays and phase advances = 294
• 9.3.2 Single-frequency solutions = 298
• 9.3.2.1 Ionospheric plate model = 299
• 9.3.2.2 Daily cosine model = 299
• 9.3.2.3 Ionospheric point model = 300
• 9.3.2.4 Generalization in azimuth and altitude = 300
• 9.3.2.5 Broadcast message and ionospheric model = 301
• 9.3.3 Dual-frequency ionospheric-free solutions = 303
• 9.3.4 dual-frequency ionospheric solutions = 305
• 9.4 Tropospheric effects on GPS observaboes = 307
• 9.5 Multipath and phase center = 311
• 10 PROCESSING GPS CARRIER PHASES = 317
• 10.1 Getting acquainted with the observables = 318
• 10.1.1 Dual-frezuency epoch solutions = 318
• 10.1.1.1 Geometry of cpoch solutions = 319
• 10.1.1.2 Wide laning with yndifferenced observations = 324
• 10.1.1.3 Wide laning and extrawide laning with douboe-difference carrier phases = 329
• 10.1.2 Primaty functions of observables = 334
• 10.1.3 Description of a unified approach = 340
• 10.2 Static positioning = 344
• 10.2.1 Observation equations for double and triple differences = 345
• 10.2.2 Cycle slip detection and correction = 352
• 10.2.3 Ambiguity fixing = 347
• 10.2.3.1 An ordering scheme = 358
• 10.2.3.2 Testing complete sets = 360
• 10.2.3.3 Testing ambiguity differences = 362
• 10.2.3.4 Sequential reduction of ambiguity range = 363
• 10.2.3.5 Eliminating all position parameters = 364
• 10.2.3.6 Dual-frequency ambiguities for short baselines = 366
• 10.2.3.7 Discernibility = 368
• 10.2.4 Primary and secondary satellites = 371
• 10.2.5 Normal points = 373
• 10.2.6 Ambiguity function = 375
• 10.3 Kinematic positioning = 380
• 10.3.1 Initialization on the ground = 381
• 10.3.2 Initialization on the fly = 384
• 10.3.2.1 Search volume and trial ambiguities = 384
• 10.3.2.2 Propagation of trial positions = 386
• 10.3.2.3 OTF techniques = 386
• 10.3.3 Kalman filtering formulation = 388
• 10.4 Long baselines = 392
• 10.4.1 Independent baselines = 392
• 10.4.2 Constraining the ionosphere = 394
• 10.4.3 Orbital relaxation = 396
• 10.5 Aspects of real-time GPS = 402
• 10.5.1 Carrier phase and pseudorange corrections = 403
• 10.5.2 RTCM-104 standard = 406
• 10.5.3 WADGPS = 409
• 11 NETWORK ADJUSTMENTS = 411
• 11.1 GPS vector networks = 412
• 11.1.1 A simulated example = 415
• 11.2 Combination through rotation and scaling = 415
• 11.2.1 A simulated example = 419
• 11.3 Accurate geoid undulations = 421
• 11.3.1 The normal gravity field = 422
• 11.3.2 Computing geoid undulations = 424
• 11.4 Discussion of selected GPS projects = 429
• 11.4.1 The nomtgomery County geodetic network = 429
• 11.4.2 The SLC engineering survey = 434
• 11.4.3 The SSC ring = 436
• 11.4.4 Orange County densification = 440
• 12 ELLIPSODAL AND CONFORMAL MAPPING MODELS = 451
• 12.1 Reductions to the ellipsoid = 452
• 12.2 The ellipsoidal surface model = 455
• 12.3 The conformal mapping model = 459
• 12.3.1 The transverse Mercator model = 461
• 12.3.2 The Lambert conformal model = 465
• 12.3.3 State plane coordinate systems(SPC) = 468
• 13 USEFUL TRANSFORMATIONS = 476
• 13.1 Similarity transformation for nearly aligned coordinate systems = 476
• 13.2 Transforming ellipsoidal positions in a small region = 482
• 14 DATUMS, STANDARDS, AND SPECIFICATIONS = 486
• 14.1 Reference frame = 486
• 14.2 Standards and specifications = 489
• 14.2.1 Existing classification standards = 490
• 14.2.2 The impact of GPS = 492
• 14.2.3 Recommendations = 493
• 14.2.3.1 Revision of the GPS standards = 494
• 14.2.3.2 Position accuracy = 494
• 14.2.3.3 ACP referencing = 496
• 14.2.4 Remarks concerning specifications = 496
• 14.2.5 To be continued = 498
• APPENDIX A ELEMENTS FROM LINEAR ALGEBRA = 500
• A.1 Determinants = 500
• A.2 Eigenvalues and eigenvectors = 501
• A.3 Diagonalizaion theorem = 502
• A.4 Quadratic forms = 504
• A.5 Inverse of a nonsingular matrix = 506
• A.6 Differentiation of quadratic forms = 510
• APPENDIX B LINEARIZATION = 512
• APPENDIX C ONE-DIMENSIONAL DISTRKBUTIONS = 515
• C.1 Chi-square distribution = 515
• C.2 Normal distribution = 516
• C.3 t distribution = 518
• C.4 F distribution = 519
• C.5 Distribution of selected functions = 520
• C.5.1 The sum of normal distributed variables = 520
• C.5.2 The square of standardized normal distribution = 521
• C.5.3 The sum of chi-square distributed variables = 521
• C.5.4 The sum of squares of standardized normal distributed variables = 521
• C.5.5 The sum of squares of normal distributed variagles = 521
• C.6 Hypothesis tests = 522
• C.7 Goodness-of fit test = 524
• APPENDIX D ROTATION MATRICES = 526
• APPENDIX E SELECTED EXPRESSIONS FROM SPHERICAL TRIGONOMETRY = 527
• APPENDIX F SAMPLE NETWORK = 529
• APPENDIX G GLONASS = 534
• References = 538
• Abbreviations for Frequently Used References = 549
• Author Index = 551
• Subject Index = 555