GPS. Theory, Algoritms and Applications, 2nd Edition
Год: 2007
Автор: Guochang Xu
Издательство: Springer-Verlag
ISBN: 978-3-540-72714-9
Формат: DjVu
Язык: Английский
Качество: eBook (изначально компьютерное)
Количество страниц: 353
Описание This reference and handbook describes theory, algorithms and applications of the Global Positioning System (GPS/Galileo). It is primarily based on source-code descriptions of the KSGsoft program developed by the author at the GFZ in Potsdam. The theory and algorithms are extended and verified for a new development of a multiple functional GPS/Galileo software. Besides the concepts such as the unified GPS data processing method and the numerical solution of the variation equations, as well as the general ambiguity search criteria reported in the first edition, there are several highlights reported. Such as the equivalent principle and its applications, the theory of independent parameterisation, the diagonalisation algorithm, etc. Mathematically rigorous, the book begins with the basics of coordinate and time systems and satellite orbits, as well as GPS observables, and deals with topics such as physical influences, observation equations and their parameterisation, adjustment and filtering, ambiguity resolution, data processing, and the determination of perturbed orbits.
Оглавление:
1 Introduction..............................................................................1
1.1AKeyNoteofGPS........................................................................2
1.2ABriefMessageAboutGLONASS.....................................................3
1.3BasicInformationofGalileo............................................................4
1.4ACombinedGlobalNavigationSatelliteSystem....................................5
2CoordinateandTimeSystems.......................................................7
2.1GeocentricEarth-FixedCoordinateSystems........................................7
2.2CoordinateSystemTransformations.................................................10
2.3LocalCoordinateSystem...............................................................11
2.4Earth-CentredInertialCoordinateSystem..........................................13
2.5GeocentricEclipticInertialCoordinateSystem....................................17
2.6TimeSystems.............................................................................17
3SatelliteOrbits..........................................................................21
3.1KeplerianMotion........................................................................21
3.1.1SatelliteMotionintheOrbitalPlane.........................................24
3.1.2KeplerianEquation..............................................................27
3.1.3StateVectoroftheSatellite.....................................................29
3.2DisturbedSatelliteMotion.............................................................31
3.3GPSBroadcastEphemerides...........................................................32
3.4IGSPreciseEphemerides...............................................................34
3.5GLONASSEphemerides................................................................35
4GPSObservables.......................................................................37
4.1CodePseudoranges......................................................................37
4.2CarrierPhases............................................................................39
4.3DopplerMeasurements.................................................................41
5PhysicalInfluencesofGPSSurveying.............................................43
5.1IonosphericEffects......................................................................43
5.1.1CodeDelayandPhaseAdvance...............................................43
5.1.2EliminationoftheIonosphericEffects......................................45
5.1.3IonosphericModels.............................................................48
5.1.4MappingFunctions..............................................................51
Contents
XIV
5.2TroposphericEffects.....................................................................55
5.2.1TroposphericModels............................................................56
5.2.2MappingFunctionsandParameterisation..................................59
5.3RelativisticEffects.......................................................................62
5.3.1SpecialRelativityandGeneralRelativity....................................62
5.3.2RelativisticEffectsonGPS.....................................................64
5.4EarthTideandOceanLoadingTideCorrections..................................67
5.4.1EarthTideDisplacementsoftheGPSStation..............................67
5.4.2SimplifiedModeloftheEarthTideDisplacements. . . . . . . . . . . . . . . . . . . . . . . .68
5.4.3NumericalExamplesoftheEarthTideEffects.............................70
5.4.4OceanLoadingTideDisplacement...........................................72
5.4.5 ComputationoftheOceanLoadingTideDisplacement. . . . . . . . . . . . . . . . . .75
5.4.6NumericalExamplesofLoadingTideEffects...............................75
5.5ClockErrors..............................................................................76
5.6MultipathEffects.........................................................................78
5.6.1 GPS-Altimetry, Signals Reflected from the Earth-Surface . . . . . . . . . . . . . . . . 79
5.6.2ReflectingPointPositioning...................................................80
5.6.3 ImagePointandReflectingSurfaceDetermination . . . . . . . . . . . . . . . . . . . . . . .81
5.7Anti-SpoofingandSelectiveAvailabilityEffects...................................82
5.8AntennaPhaseCentreOffsetandVariation.........................................82
5.9InstrumentalBiases.....................................................................85
6 GPSObservationEquationsandEquivalenceProperties . . . . . . . . . . . . . . . . . . .87
6.1GeneralMathematicalModelsofGPSObservations..............................87
6.2LinearisationoftheObservationalModel...........................................89
6.3PartialDerivativesofObservationalFunction.....................................90
6.4LinearTransformationandCovariancePropagation..............................94
6.5DataCombinations......................................................................95
6.5.1Ionosphere-FreeCombinations...............................................97
6.5.2Geometry-FreeCombinations.................................................98
6.5.3StandardPhase-CodeCombination........................................100
6.5.4IonosphericResiduals.........................................................101
6.5.5DifferentialDopplerandDopplerIntegration............................102
6.6DataDifferentiations..................................................................104
6.6.1SingleDifferences..............................................................105
6.6.2DoubleDifferences............................................................107
6.6.3TripleDifferences..............................................................110
6.7 EquivalenceoftheUncombinedandCombiningAlgorithms . . . . . . . . . . . . . . . . . 111
6.7.1UncombinedGPSDataProcessingAlgorithms...........................112
6.7.2CombiningAlgorithmsofGPSDataProcessing.........................114
6.7.3SecondaryGPSDataProcessingAlgorithms..............................119
6.7.4Summary........................................................................122
6.8 EquivalenceofUndifferencedandDifferencingAlgorithms. . . . . . . . . . . . . . . . . . . 122
6.8.1Introduction....................................................................122
6.8.2FormationofEquivalentObservationEquations. . . . . . . . . . . . . . . . . . . . . . . .123
6.8.3EquivalentEquationsofSingleDifferences...............................125
XV
Contents
6.8.4EquivalentEquationsofDoubleDifferences..............................128
6.8.5EquivalentEquationsofTripleDifferences...............................130
6.8.6MethodofDealingwiththeReferenceParameters. . . . . . . . . . . . . . . . . . . . . .130
6.8.7SummaryoftheUnifiedEquivalentAlgorithm..........................131
7AdjustmentandFilteringMethods..............................................133
7.1Introduction............................................................................133
7.2LeastSquaresAdjustment............................................................133
7.2.1 Least Squares Adjustment with Sequential Observation Groups . . . . . . 135
7.3SequentialLeastSquaresAdjustment..............................................137
7.4ConditionalLeastSquaresAdjustment............................................138
7.4.1 Sequential Application of Conditional Least Squares Adjustment . . . . 140
7.5Block-WiseLeastSquaresAdjustment.............................................141
7.5.1 Sequential Solution of Block-Wise Least Squares Adjustment . . . . . . . . 143
7.5.2 Block-Wise Least Squares for Code-Phase Combination . . . . . . . . . . . . . . . 145
7.6EquivalentlyEliminatedObservationEquationSystem. . . . . . . . . . . . . . . . . . . . . . . .146
7.6.1 Diagonalised Normal Equation and the Equivalent
ObservationEquation.........................................................148
7.7KalmanFilter...........................................................................150
7.7.1ClassicKalmanFilter..........................................................150
7.7.2 Kalman Filter -- A General Form of Sequential
LeastSquaresAdjustment....................................................151
7.7.3RobustKalmanFilter..........................................................152
7.7.4AdaptivelyRobustKalmanFiltering.......................................155
7.8APrioriConstrainedLeastSquaresAdjustment.................................159
7.8.1APrioriParameterConstraints.............................................159
7.8.2APrioriDatum.................................................................160
7.8.3Quasi-StableDatum...........................................................161
7.9Summary................................................................................163
8CycleSlipDetectionandAmbiguityResolution.............................167
8.1CycleSlipDetection...................................................................167
8.2MethodofDealingwithCycleSlips................................................168
8.3AGeneralCriterionofIntegerAmbiguitySearch...............................169
8.3.1Introduction....................................................................169
8.3.2 SummaryofConditionalLeastSquaresAdjustment. . . . . . . . . . . . . . . . . . . .170
8.3.3FloatSolution...................................................................171
8.3.4IntegerAmbiguitySearchinAmbiguityDomain. . . . . . . . . . . . . . . . . . . . . . . .172
8.3.5 Integer Ambiguity Search in Coordinate
andAmbiguityDomains.....................................................174
8.3.6PropertiesoftheGeneralCriterion........................................175
8.3.7 An Equivalent Ambiguity Search Criterion and its Properties . . . . . . . . 176
8.3.8NumericalExamplesoftheEquivalentCriterion. . . . . . . . . . . . . . . . . . . . . . . .178
8.3.9ConclusionsandComments.................................................181
8.4AmbiguityFunction...................................................................182
8.4.1MaximumPropertyofAmbiguityFunction..............................183
Contents
XVI
9 ParameterisationandAlgorithmsofGPSDataProcessing . . . . . . . . . . . . . . . 187
9.1ParameterisationoftheGPSObservationModel................................187
9.1.1 Evidence of the Parameterisation Problem of the Undifferenced
ObservationModel............................................................187
9.1.2AMethodofUncorrelatedBiasParameterisation. . . . . . . . . . . . . . . . . . . . . . .189
9.1.3Geometry-FreeIllustration..................................................195
9.1.4 Correlation Analysis in the Case of Phase-Code Combinations . . . . . . . 195
9.1.5ConclusionsandComments.................................................197
9.2EquivalenceoftheGPSDataProcessingAlgorithms............................198
9.2.1 Equivalence Theorem of GPS Data Processing Algorithms . . . . . . . . . . . . 198
9.2.2 Optimal Baseline Network Forming and Data Condition . . . . . . . . . . . . . . 200
9.2.3AlgorithmsUsingSecondaryGPSObservables..........................201
9.3Non-EquivalentAlgorithms..........................................................203
9.4StandardAlgorithmsofGPSDataProcessing....................................203
9.4.1PreparationofGPSDataProcessing.......................................203
9.4.2SinglePointPositioning......................................................204
9.4.3StandardUn-DifferentialGPSDataProcessing..........................209
9.4.4EquivalentMethodofGPSDataProcessing..............................211
9.4.5RelativePositioning...........................................................212
9.4.6VelocityDetermination.......................................................212
9.4.7KalmanFilteringUsingVelocityInformation............................215
9.5AccuracyoftheObservationalGeometry.........................................217
10ApplicationsofGPSTheoryandAlgorithms..................................219
10.1SoftwareDevelopment................................................................219
10.1.1FunctionalLibrary.............................................................219
10.1.2DataPlatform...................................................................223
10.1.3ADataProcessingCore.......................................................225
10.2 Concept of Precise Kinematic Positioning and Flight-State Monitoring . . . . . 226
10.2.1Introduction....................................................................226
10.2.2ConceptofPreciseKinematicPositioning................................229
10.2.3ConceptofFlight-StateMonitoring........................................233
10.2.4Results,PrecisionEstimationandComparisons. . . . . . . . . . . . . . . . . . . . . . . . .235
10.2.5Conclusions.....................................................................240
11PerturbedOrbitanditsDetermination........................................243
11.1PerturbedEquationofSatelliteMotion............................................243
11.1.1LagrangianPerturbedEquationofSatelliteMotion . . . . . . . . . . . . . . . . . . . .244
11.1.2GaussianPerturbedEquationofSatelliteMotion . . . . . . . . . . . . . . . . . . . . . . .246
11.2PerturbationForcesofSatelliteMotion............................................249
11.2.1PerturbationoftheEarth'sGravitationalField...........................249
11.2.2PerturbationoftheSunandtheMoonaswellasPlanets . . . . . . . . . . . . . . 254
11.2.3EarthTideandOceanTidePerturbations.................................255
11.2.4SolarRadiationPressure.....................................................258
11.2.5AtmosphericDrag.............................................................262
11.2.6AdditionalPerturbations.....................................................265
XVII
Contents
11.2.7OrderEstimationsofPerturbations........................................267
11.2.8EphemeridesoftheMoon,theSunandPlanets..........................267
11.3 Analysis Solution of the C
--20PerturbedOrbit.....................................271
11.4OrbitCorrection.......................................................................277
11.5PrincipleofGPSPreciseOrbitDetermination...................................281
11.5.1AlgebraSolutionoftheVariationEquation...............................283
11.6NumericalIntegrationandInterpolationAlgorithms. . . . . . . . . . . . . . . . . . . . . . . . . . .284
11.6.1Runge-KuttaAlgorithms......................................................284
11.6.2AdamsAlgorithms.............................................................289
11.6.3CowellAlgorithms.............................................................291
11.6.4MixedAlgorithmsandDiscussions........................................293
11.6.5InterpolationAlgorithms.....................................................294
11.7Orbit-RelatedPartialDerivatives...................................................294
12Discussions.............................................................................305
12.1IndependentParameterisationandAPrioriInformation . . . . . . . . . . . . . . . . . . . . . .305
12.2EquivalenceoftheGPSDataProcessingAlgorithms............................307
Appendix 1
IAU1980TheoryofNutation......................................................309
Appendix 2
Numerical Examples of the Diagonalisation of the Equations . . . . . . . . . . . 311
References.............................................................................317
SubjectIndex..........................................................................337
Дооформил B62
