GLOBAL NAVIGATION SATELLITE SYSTEMS, INERTIAL NAVIGATION, AND INTEGRATION

GLOBAL NAVIGATION SATELLITE SYSTEMS, INERTIAL NAVIGATION, AND INTEGRATION

THIRD EDITION

MOHINDER S. GREWALANGUS P. ANDREWSCHRIS G. BARTONE

A JOHN WILEY & SONS, INC., PUBLICATION

Copyright © 2013 by John Wiley & Sons, Inc. All rights reserved

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Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Grewal, Mohinder S. Global navigation satellite systems, inertial navigation, and integration / Mohinder S. Grewal, Angus P. Andrews, Chris G. Bartone. – Third edition. pages cm Includes index. Originally published under title: Global positioning systems, inertial navigation, and integration. ISBN 978-1-118-44700-0 (cloth) 1. Global Positioning System. 2. Inertial navigation. 3. Kalman filtering. I. Andrews, Angus P. II. Bartone, Chris G. III. Title. G109.5.G74 2013 910.285–dc23 2012032753

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

M.S.G. dedicates this book to the memory of his parents, Livlin Kaur and Sardar Sahib Sardar Karam Singh Grewal.

A.P.A. dedicates his contributions to his wife, Jeri, without whom it never would have happened.

C.G.B dedicates this work to his wife, Shirley, and two sons, Christopher and Stephen, for their never-ending support over the years.

Preface xxvii

Acknowledgments xxxi

AcronymsandAbbreviations xxxiii

1 Introduction, 1

1.1 Navigation, 11.1.1 Navigation-RelatedTechnologies, 11.1.2 NavigationModes, 2

1.2 GNSSOverview, 41.2.1 GPS, 4

1.2.1.1 GPSOrbits, 41.2.1.2 GPSSignals, 41.2.1.3 SelectiveAvailability(SA), 51.2.1.4 ModernizationofGPS, 6

1.2.2 GlobalOrbitingNavigationSatelliteSystem(GLONASS), 61.2.2.1 GLONASSOrbits, 61.2.2.2 GLONASSSignals, 61.2.2.3 NextGenerationGLONASS, 7

1.2.3 Galileo, 71.2.3.1 GalileoNavigationServices, 71.2.3.2 GalileoSignalCharacteristics, 81.2.3.3 Updates, 9

CONTENTS

vii

viii CONTENTS

1.2.4 Compass(BeiDou-2), 101.2.4.1 CompassSatellites, 101.2.4.2 Frequency, 10

1.3 InertialNavigationOverview, 101.3.1 TheoreticalFoundations, 101.3.2 InertialSensorTechnology, 11

1.3.2.1 SensorRequirements, 121.3.2.2 Motivation, 131.3.2.3 InertialSensorsPriortoNewton, 131.3.2.4 EarlyMomentumWheelGyroscopes

(MWGs), 141.3.2.5 GermanInertialTechnology:1930s–1945, 151.3.2.6 CharlesStarkDraper(1901–1987),“TheFather

ofInertialNavigation”, 191.3.2.7 AerospaceInertialTechnology, 201.3.2.8 DevelopmentsSincetheColdWar, 30

1.4 GNSS/INSIntegrationOverview, 301.4.1 TheRoleofKalmanFiltering, 301.4.2 Implementation, 311.4.3 Applications, 31

1.4.3.1 MilitaryApplications, 311.4.3.2 CivilianandCommercialApplications, 31

Problems, 32References, 32

2 FundamentalsofSatelliteNavigationSystems, 35

2.1 NavigationSystemsConsidered, 352.1.1 SystemsOtherthanGNSS, 352.1.2 ComparisonCriteria, 36

2.2 SatelliteNavigation, 362.2.1 SatelliteOrbits, 362.2.2 NavigationSolution(Two-DimensionalExample), 36

2.2.2.1 SymmetricSolutionUsingTwoTransmittersonLand, 36

2.2.2.2 NavigationSolutionProcedure, 402.2.3 SatelliteSelectionand

DilutionofPrecision(DOP), 412.2.4 ExampleCalculationofDOPS, 45

2.2.4.1 FourSatellites, 452.3 TimeandGPS, 46

2.3.1 CoordinatedUniversalTime(UTC)Generation, 462.3.2 GPSSystemTime, 462.3.3 ReceiverComputationofUTC, 47

CONTENTS ix

2.4 Example:UserPositionCalculationswithNoErrors, 482.4.1 UserPositionCalculations, 48

2.4.1.1 PositionCalculations, 482.4.2 UserVelocityCalculations, 50

Problems, 51References, 53

3 FundamentalsofInertialNavigation, 54

3.1 ChapterFocus, 543.2 BasicTerminology, 553.3 InertialSensorErrorModels, 59

3.3.1 Zero-MeanRandomErrors, 603.3.1.1 WhiteSensorNoise, 603.3.1.2 ExponentiallyCorrelatedNoise, 603.3.1.3 RandomWalkSensorErrors, 603.3.1.4 HarmonicNoise, 613.3.1.5 “1/f”Noise, 61

3.3.2 Fixed-PatternErrors, 613.3.3 SensorErrorStability, 62

3.4 SensorCalibrationandCompensation, 633.4.1 SensorBiases,ScaleFactors,andMisalignments, 63

3.4.1.1 CompensationModelParameters, 633.4.1.2 CalibratingSensorBiases,ScaleFactors,

andMisalignments, 643.4.2 OtherCalibrationParameters, 65

3.4.2.1 Nonlinearities, 653.4.2.2 SensitivitiestoOther

MeasurableConditions, 653.4.2.3 OtherAccelerometerModels, 66

3.4.3 CalibrationParameterInstabilities, 663.4.3.1 CalibrationParameterChanges

betweenTurn-Ons, 673.4.3.2 CalibrationParameterDrift, 67

3.4.4 AuxilliarySensorsbeforeGNSS, 673.4.4.1 AttitudeSensors, 673.4.4.2 AltitudeSensors, 68

3.4.5 SensorPerformanceRanges, 683.5 EarthModels, 68

3.5.1 TerrestrialNavigationCoordinates, 693.5.2 EarthRotation, 703.5.3 GravityModels, 70

3.5.3.1 GNSSGravityModels, 713.5.3.2 INSGravityModels, 713.5.3.3 LongitudeandLatitudeRates, 73

x CONTENTS

3.6 HardwareImplementations, 773.6.1 GimbaledImplementations, 783.6.2 FloatedImplementation, 803.6.3 CarouselingandIndexing, 81

3.6.3.1 AlphaWanderandCarouseling, 813.6.3.2 Indexing, 81

3.6.4 StrapdownSystems, 823.6.5 StrapdownCarouselingandIndexing, 82

3.7 SoftwareImplementations, 833.7.1 ExampleinOneDimension, 833.7.2 InitializationinNineDimensions, 84

3.7.2.1 NavigationInitialization, 843.7.2.2 INSAlignmentMethods, 843.7.2.3 GyrocompassAlignment, 85

3.7.3 GimbalAttitudeImplementations, 873.7.3.1 AccelerometerRecalibration, 873.7.3.2 VehicleAttitudeDetermination, 873.7.3.3 ISAAttitudeControl, 88

3.7.4 GimbaledNavigationImplementation, 893.7.5 StrapdownAttitudeImplementations, 90

3.7.5.1 StrapdownAttitudeProblems, 903.7.5.2 ConingMotion, 903.7.5.3 RotationVectorImplementation, 933.7.5.4 QuaternionImplementation, 953.7.5.5 DirectionCosinesImplementation, 963.7.5.6 MATLAB®Implementations, 97

3.7.6 StrapdownNavigationImplementation, 973.7.7 NavigationComputerandSoftwareRequirements, 99

3.7.7.1 PhysicalandOperationalRequirements, 1003.7.7.2 OperatingSystems, 1003.7.7.3 InterfaceRequirements, 1003.7.7.4 SoftwareDevelopment, 100

3.8 INSPerformanceStandards, 1013.8.1 FreeInertialOperation, 1013.8.2 INSPerformanceMetrics, 1013.8.3 PerformanceStandards, 102

3.9 TestingandEvaluation, 1023.9.1 LaboratoryTesting, 1023.9.2 FieldTesting, 103

3.10 Summary, 103Problems, 104References, 106

CONTENTS xi

4 GNSSSignalStructure,Characteristics,andInformationUtilization, 108

4.1 LegacyGPSSignalComponents,Purposes,andProperties, 1094.1.1 MathematicalSignalModelsfortheLegacy

GPSSignals, 1094.1.2 NavigationDataFormat, 112

4.1.2.1 Z-Count, 1144.1.2.2 GPSWeekNumber(WN), 1154.1.2.3 InformationbySubframe, 116

4.1.3 GPSSatellitePositionCalculations, 1174.1.3.1 EphemerisDataReferenceTimeStepand

TransitTimeCorrection, 1194.1.3.2 True,Eccentric,andMeanAnomaly, 1194.1.3.3 Kepler’sEquationforthe

EccentricAnomaly, 1204.1.3.4 SatelliteTimeCorrections, 121

4.1.4 C/A-CodeandItsProperties, 1224.1.4.1 TemporalStructure, 1244.1.4.2 AutocorrelationFunction, 1244.1.4.3 PowerSpectrum, 1254.1.4.4 DespreadingoftheSignalSpectrum, 1264.1.4.5 RoleofDespreadinginInterference

Suppression, 1274.1.4.6 Cross-CorrelationFunction, 128

4.1.5 P(Y)-CodeandItsProperties, 1294.1.5.1 P-CodeCharacteristics, 1294.1.5.2 Y-Code, 130

4.1.6 L1andL2Carriers, 1304.1.6.1 Dual-FrequencyOperation, 130

4.1.7 TransmittedPowerLevels, 1314.1.8 FreeSpaceandOtherLossFactors, 1314.1.9 ReceivedSignalPower, 132

4.2 ModernizationofGPS, 1324.2.1 AreastoBenefitfromModernization, 1334.2.2 ElementsoftheModernizedGPS, 1344.2.3 L2CivilSignal(L2C), 1354.2.4 L5Signal, 1364.2.5 M-Code, 1384.2.6 L1CSignal, 1394.2.7 GPSSatelliteBlocks, 1404.2.8 GPSIII, 141

4.3 GLONASSSignalStructureandCharacteristics, 1414.3.1 FrequencyDivisionMultipleAccess(FDMA)

Signals, 142

xii CONTENTS

4.3.1.1 CarrierComponents, 1424.3.1.2 SpreadingCodesandModulation, 1424.3.1.3 NavigationDataFormat, 1424.3.1.4 SatelliteFamilies, 143

4.3.2 CDMAModernization, 1434.4 Galileo, 144

4.4.1 ConstellationandLevelsofServices, 1444.4.2 NavigationDataandSignals, 144

4.5 Compass/BD, 1464.6 QZSS, 146Problems, 148References, 150

5 GNSSAntennaDesignandAnalysis, 152

5.1 Applications, 1525.2 GNSSAntennaPerformanceCharacteristics, 152

5.2.1 SizeandCost, 1535.2.2 FrequencyandBandwidthCoverage, 1535.2.3 RadiationPatternCharacteristics, 1555.2.4 AntennaPolarizationandAxialRatio, 1565.2.5 Directivity,Efficiency,andGainofaGNSSAntenna, 1595.2.6 AntennaImpedance,StandingWaveRatio,andReturn

Loss, 1605.2.7 AntennaBandwidth, 1615.2.8 AntennaNoiseFigure, 163

5.3 ComputationalElectromagneticModels(CEMs)forGNSSAntennaDesign, 164

5.4 GNSSAntennaTechnologies, 1665.4.1 Dipole-BasedGNSSAntennas, 1665.4.2 GNSSPatchAntennas, 166

5.4.2.1 Edge-Fed,LP,Single-FrequencyGNSSPatchAntenna, 168

5.4.2.2 Probe-Fed,LP,Single-FrequencyGNSSPatchAntenna, 170

5.4.2.3 DualProbe-Fed,RHCP,Single-FrequencyGNSSPatchAntenna, 171

5.4.2.4 SingleProbe-Fed,RCHP,Single-FrequencyGNSSPatchAntenna, 172

5.4.2.5 DualProbe-Fed,RHCP,MultifrequencyGNSSPatchAntenna, 175

5.4.3 Survey-Grade/ReferenceGNSSAntennas, 1765.4.3.1 ChokeRing-BasedGNSSAntennas, 1765.4.3.2 AdvancedPlanner-BasedGNSS

Antennas, 177

CONTENTS xiii

5.5 PrinciplesofAdaptablePhased-ArrayAntennas, 1805.5.1 DigitalBeamformingAdaptiveAntennaArray

Formulations, 1825.5.2 STAP, 1855.5.3 SFAP, 1855.5.4 ConfigurationsofAdaptablePhased-Array

Antennas, 1855.5.5 RelativeMeritsofAdaptablePhased-Array

Antennas, 1865.6 ApplicationCalibration/CompensationConsiderations, 187Problems, 189References, 190

6 GNSSReceiverDesignandAnalysis, 193

6.1 ReceiverDesignChoices, 1936.1.1 GlobalNavigationSatelliteSystem(GNSS)Application

tobeSupported, 1936.1.2 SingleorMultifrequencySupport, 194

6.1.2.1 Dual-FrequencyIonosphereCorrection, 1946.1.2.2 ImprovedCarrierPhaseAmbiguity

ResolutioninHigh-AccuracyDifferentialPositioning, 194

6.1.3 NumberofChannels, 1956.1.4 CodeSelections, 1956.1.5 DifferentialCapability, 196

6.1.5.1 CorrectionsFormats, 1976.1.6 AidingInputs, 198

6.2 ReceiverArchitecture, 1996.2.1 RadioFrequency(RF)FrontEnd, 1996.2.2 FrequencyDown-ConversionandIFAmplification, 201

6.2.2.1 SNR, 2026.2.3 Analog-to-DigitalConversionand

AutomaticGainControl, 2036.2.4 BasebandSignalProcessing, 204

6.3 SignalAcquisitionandTracking, 2046.3.1 HypothesizeabouttheUserLocation, 2056.3.2 HypothesizeaboutWhichGNSSSatellitesAre

Visible, 2056.3.3 SignalDopplerEstimation, 2066.3.4 SearchforSignalinFrequencyandCodePhase, 206

6.3.4.1 SequentialSearchinginCodeDelay, 2086.3.4.2 SequentialSearchinginFrequency, 2096.3.4.3 FrequencySearchStrategy, 2096.3.4.4 ParallelandHybridSearchMethods, 210

xiv CONTENTS

6.3.5 SignalDetectionandConfirmation, 2106.3.5.1 DetectionConfirmation, 2116.3.5.2 CoordinationofFrequencyTuningand

CodeChippingRate, 2136.3.6 CodeTrackingLoop, 213

6.3.6.1 CodeLoopBandwidthConsiderations, 2176.3.6.2 CoherentversusNoncoherentCode

Tracking, 2176.3.7 CarrierPhaseTrackingLoops, 218

6.3.7.1 PLLCaptureRange, 2216.3.7.2 PLLOrder, 2216.3.7.3 UseofFrequency-LockLoops(FLLs)for

CarrierCapture, 2216.3.8 BitSynchronization, 2226.3.9 DataBitDemodulation, 222

6.4 ExtractionofInformationforUserSolution, 2236.4.1 SignalTransmissionTimeInformation, 2236.4.2 EphemerisDataforSatellitePosition

andVelocity, 2246.4.3 PseudorangeMeasurementsFormulation

UsingCodePhase, 2246.4.3.1 PseudorangePositioningEquations, 226

6.4.4 MeasurementsUsingCarrierPhase, 2266.4.5 CarrierDopplerMeasurement, 2286.4.6 IntegratedDopplerMeasurements, 229

6.5 TheoreticalConsiderationsinPseudorange,CarrierPhase,andFrequencyEstimations, 2316.5.1 TheoreticalErrorBoundsforCodePhase

Measurement, 2326.5.2 TheoreticalErrorBoundsforCarrierPhase

Measurements, 2336.5.3 TheoreticalErrorBoundsforFrequency

Measurement, 2346.6 High-SensitivityA-GPSSystems, 235

6.6.1 HowAssistingDataImprovesReceiverPerformance, 2366.6.1.1 ReductionofFrequencyUncertainty, 2366.6.1.2 DeterminationofAccurateTime, 2376.6.1.3 TransmissionofSatelliteEphemeris

Data, 2386.6.1.4 ProvisionofApproximateClient

Location, 2386.6.1.5 TransmissionoftheDemodulatedNavigation

BitStream, 2396.6.1.6 Server-ProvidedLocation, 240

CONTENTS xv

6.6.2 FactorsAffectingHigh-SensitivityReceivers, 2406.6.2.1 AntennaandLow-NoiseRFDesign, 2406.6.2.2 DegradationduetoSignalPhase

Variations, 2406.6.2.3 SignalProcessingLosses, 2416.6.2.4 MultipathFading, 2416.6.2.5 SusceptibilitytoInterferenceandStrong

Signals, 2416.6.2.6 TheProblemofTimeSynchronization, 2426.6.2.7 DifficultiesinReliableSensitivity

Assessment, 2426.7 Software-DefinedRadio(SDR)Approach, 2426.8 PseudoliteConsiderations, 243Problems, 244References, 246

7 GNSSDataErrors, 250

7.1 DataErrors, 2507.2 IonosphericPropagationErrors, 251

7.2.1 IonosphericDelayModel, 2527.2.2 GNSSSBASIonosphericAlgorithms, 254

7.2.2.1 L1L2ReceiverandSatelliteBiasandIonosphericDelayEstimationsforGPS, 256

7.2.2.2 KalmanFilter, 2597.2.2.3 SelectionofQandR, 2617.2.2.4 CalculationofIonosphericDelayUsing

Pseudoranges, 2627.3 TroposphericPropagationErrors, 2637.4 TheMultipathProblem, 264

7.4.1 HowMultipathCausesRangingErrors, 2647.5 MethodsofMultipathMitigation, 266

7.5.1 SpatialProcessingTechniques, 2677.5.1.1 AntennaLocationStrategy, 2677.5.1.2 GroundPlaneAntennas, 2677.5.1.3 DirectiveAntennaArrays, 2677.5.1.4 Long-TermSignalObservation, 267

7.5.2 Time-DomainProcessing, 2697.5.2.1 Narrow-CorrelatorTechnology

(1990–1993), 2697.5.2.2 Leading-EdgeTechniques, 2707.5.2.3 CorrelationFunctionShape-Based

Methods, 2717.5.2.4 ModifiedCorrelatorReference

Waveforms, 271

xvi CONTENTS

7.5.3 MultipathMitigationTechnology(MMT)Technology, 2727.5.3.1 Description, 2727.5.3.2 Maximum-Likelihood(ML)Multipath

Estimation, 2727.5.3.3 TheTwo-PathMLEstimator(MLE), 2737.5.3.4 AsymptoticPropertiesofMLEstimators, 2747.5.3.5 TheMMTMultipathMitigationAlgorithm, 2747.5.3.6 TheMMTBasebandSignalModel, 2747.5.3.7 BasebandSignalVectors, 2757.5.3.8 TheLog-LikelihoodFunction, 2757.5.3.9 Secondary-PathAmplitudeConstraint, 2777.5.3.10 SignalCompression, 2777.5.3.11 PropertiesoftheCompressedSignal, 2797.5.3.12 TheCompressionTheorem, 280

7.5.4 PerformanceofTime-DomainMethods, 2817.5.4.1 RangingwiththeC/A-Code, 2817.5.4.2 CarrierPhaseRanging, 2827.5.4.3 TestingReceiverMultipathPerformance, 283

7.6 TheoreticalLimitsforMultipathMitigation, 2837.6.1 Estimation-TheoreticMethods, 283

7.6.1.1 OptimalityCriteria, 2847.6.2 MinimumMean-SquaredError(MMSE)Estimator, 2847.6.3 MultipathModelingErrors, 284

7.7 EphemerisDataErrors, 2857.8 OnboardClockErrors, 2857.9 ReceiverClockErrors, 2867.10 SAErrors, 2887.11 ErrorBudgets, 288Problems, 289References, 291

8 DifferentialGNSS, 293

8.1 Introduction, 2938.2 DescriptionsofLocal-AreaDifferentialGNSS(LADGNSS),

Wide-AreaDifferentialGNSS(WADGNSS),andSpace-BasedAugmentationSystem(SBAS), 2948.2.1 LADGNSS, 2948.2.2 WADGNSS, 2948.2.3 SBAS, 294

8.2.3.1 Wide-AreaAugmentationSystem(WAAS), 294

8.2.3.2 EuropeanGlobalNavigationOverlaySystem(EGNOS), 298

8.2.3.3 OtherSBAS, 299

CONTENTS xvii

8.3 GEOwithL1L5Signals, 2998.3.1 GEOUplinkSubsystemType1(GUST)ControlLoop

Overview, 3028.3.1.1 IonosphericKalmanFilters, 3038.3.1.2 RangeKalmanFilter, 3038.3.1.3 CodeControlFunction, 3048.3.1.4 FrequencyControlFunction, 3048.3.1.5 L1L5BiasEstimationFunction, 3058.3.1.6 L1L5BiasEstimationFunction, 3058.3.1.7 CarrierFrequencyStability, 306

8.4 GUSClockSteeringAlgorithm, 3078.4.1 ReceiverClockErrorDetermination, 3088.4.2 ClockSteeringControlLaw, 310

8.5 GEOOrbitDetermination(OD), 3108.5.1 ODCovarianceAnalysis, 312

8.6 Ground-BasedAugmentationSystem(GBAS), 3168.6.1 Local-AreaAugmentationSystem(LAAS), 3168.6.2 JointPrecisionApproachandLanding

System(JPALS), 3178.6.3 EnhancedLong-RangeNavigation(eLoran), 318

8.7 Measurement/Relative-BasedDGNSS, 3198.7.1 CodeDifferentialMeasurements, 319

8.7.1.1 Single-DifferenceObservations, 3208.7.1.2 Double-DifferenceObservations, 320

8.7.2 CarrierPhaseDifferentialMeasurements, 3218.7.2.1 Single-DifferenceObservations, 3218.7.2.2 Double-DifferenceObservations, 3218.7.2.3 Triple-DifferenceObservations, 3228.7.2.4 CombinationsofL1andL2CarrierPhase

Observations, 3228.7.3 PositioningUsingDouble-Difference

Measurements, 3228.7.3.1 Code-BasedPositioning, 3228.7.3.2 CarrierPhase-BasedPositioning, 3228.7.3.3 Real-TimeProcessingversus

Postprocessing, 3238.8 GNSSPrecisePointPositioningServicesandProducts, 323

8.8.1 TheInternationalGNSSService(IGS), 3238.8.2 ContinuouslyOperatingReferenceStations

(CORSs), 3248.8.3 GPSInferredPositioningSystem(GIPSY)andOrbit

AnalysisSimulationSoftware(OASIS), 3248.8.4 Australia’sOnlineGPSProcessingSystem(AUPOS), 3258.8.5 ScrippsCoordinateUpdateTool(SCOUT), 3258.8.6 TheOnlinePositioningUserService(OPUS), 325

xviii CONTENTS

Problems, 325References, 326

9 GNSSandGEOSignalIntegrity, 328

9.1 Introduction, 3289.1.1 RangeComparisonMethod, 3299.1.2 Least-SquaresMethod, 3309.1.3 ParityMethod, 331

9.2 SBASandGBASIntegrityDesign, 3329.2.1 SBASErrorSourcesandIntegrityThreats, 3339.2.2 GNSS-AssociatedErrors, 334

9.2.2.1 GNSSClockError, 3349.2.2.2 GNSSEphemerisError, 3359.2.2.3 GNSSCodeandCarrierIncoherence, 3359.2.2.4 GNSSSignalDistortion, 3359.2.2.5 GNSSL1L2Bias, 3369.2.2.6 EnvironmentErrors:Ionosphere, 3369.2.2.7 EnvironmentErrors:Troposphere, 336

9.2.3 GEO-AssociatedErrors, 3369.2.3.1 GEOCodeandCarrierIncoherence, 3369.2.3.2 GEO-AssociatedEnvironmentErrors:

Ionosphere, 3379.2.3.3 GEO-AssociatedEnvironmentErrors:

Troposphere, 3379.2.4 ReceiverandMeasurementProcessingErrors, 337

9.2.4.1 ReceiverMeasurementError, 3379.2.4.2 IntercardBias, 3379.2.4.3 Multipath, 3389.2.4.4 L1L2Bias, 3389.2.4.5 ReceiverClockError, 3389.2.4.6 MeasurementProcessingUnpack/Pack

Corruption, 3389.2.5 EstimationErrors, 338

9.2.5.1 ReferenceTimeOffsetEstimationError, 338

9.2.5.2 ClockEstimationError, 3399.2.5.3 EphemerisCorrectionError, 3399.2.5.4 L1L2Wide-AreaReferenceEquipment

(WRE)andGPSSatelliteBiasEstimationError, 339

9.2.6 Integrity-BoundAssociatedErrors, 3399.2.6.1 IonosphericModelingErrors, 3399.2.6.2 FringeAreaEphemerisError, 3409.2.6.3 Small-SigmaErrors, 340

CONTENTS xix

9.2.6.4 MissedMessage:OldButActiveData(OBAD), 340

9.2.6.5 TimetoAlarm(TTA)Exceeded, 3409.2.7 GEOUplinkErrors, 340

9.2.7.1 GEOUplinkSystemFailstoReceiveSBASMessage, 340

9.2.8 MitigationofIntegrityThreats, 3409.2.8.1 MitigationofGNSSAssociatedErrors, 3419.2.8.2 MitigationofGEO-AssociatedErrors, 3439.2.8.3 MitigationofReceiverandMeasurement

ProcessingErrors, 3439.2.8.4 MitigationofEstimationErrors, 3449.2.8.5 MitigationofIntegrity-Bound-Associated

Errors, 3459.3 SBASExample, 3469.4 Summary, 3479.5 Future:GIC, 348Problem, 348References, 348

10 KalmanFiltering, 350

10.1 Introduction, 35010.1.1 WhatIsaKalmanFilter?, 35110.1.2 HowDoesItWork?, 352

10.1.2.1 PredictionandCorrection, 35310.1.3 HowIsItUsed?, 353

10.2 KalmanFilterCorrectionUpdate, 35410.2.1 DerivingtheKalmanGain, 354

10.2.1.1 ApproachestoDerivingtheKalmanGain, 35510.2.1.2 GaussianProbabilityDensityFunctions, 35510.2.1.3 PropertiesofLikelihoodFunctions, 35610.2.1.4 SolvingforCombinedInformationMatrix, 35810.2.1.5 SolvingforCombinedArgmax, 35910.2.1.6 NoisyMeasurementLikelihoods, 36010.2.1.7 GaussianMaximum-LikelihoodEstimate

(MLE), 36210.2.1.8 EstimateCorrection, 36410.2.1.9 KalmanGainMatrixforMLE, 364

10.2.2 EstimateCorrectionUsingtheKalmanGain, 36410.2.3 CovarianceCorrectionforUsingMeasurements, 365

10.3 KalmanFilterPredictionUpdate, 36510.3.1 StochasticSystemsinContinuousTime, 365

10.3.1.1 White-NoiseProcesses, 36510.3.1.2 StochasticDifferentialEquations, 365

xx CONTENTS

10.3.1.3 SystemsofFirst-OrderLinearDifferentialEquations, 367

10.3.1.4 RepresentationinTermsofVectorsandMatrices, 368

10.3.1.5 EigenvaluesofDynamicCoefficientMatrices, 369

10.3.1.6 MatrixExponentialFunction, 37110.3.1.7 ForwardSolution, 37110.3.1.8 Time-InvariantSystems, 371

10.3.2 StochasticSystemsinDiscreteTime, 37210.3.2.1 Zero-MeanWhiteGaussian

NoiseSequences, 37210.3.2.2 GaussianLinearStochasticProcessesin

DiscreteTime, 37210.3.3 StateSpaceModelsforDiscreteTime, 37310.3.4 DynamicDisturbanceNoise

DistributionMatrices, 37410.3.5 PredictorEquations, 374

10.4 SummaryofKalmanFilterEquations, 37510.4.1 EssentialEquations, 37510.4.2 CommonTerminology, 37510.4.3 DataFlowDiagrams, 376

10.5 AccommodatingTime-CorrelatedNoise, 37710.5.1 CorrelatedNoiseModels, 378

10.5.1.1 AutocovarianceFunctions, 37810.5.1.2 RandomWalks, 37810.5.1.3 ExponentiallyCorrelatedNoise, 37910.5.1.4 HarmonicNoise, 37910.5.1.5 SelectiveAvailability(SA), 37910.5.1.6 SlowVariables, 380

10.5.2 EmpiricalModelingofSensorNoise, 38010.5.2.1 SpectralCharacterization, 38110.5.2.2 ShapingFilters, 381

10.5.3 StateVectorAugmentation, 38210.5.3.1 CorrelatedDynamicDisturbanceNoise, 38210.5.3.2 CorrelatedSensorNoise, 38310.5.3.3 CorrelatedNoiseinContinuousTime, 383

10.6 NonlinearandAdaptiveImplementations, 38410.6.1 AssessingLinearApproximationErrors, 384

10.6.1.1 StatisticalMeasuresofAcceptability, 38410.6.1.2 SamplingforAcceptabilityTesting, 385

10.6.2 NonlinearDynamics, 39010.6.2.1 NonlinearDynamicswithControl, 39010.6.2.2 PropagatingEstimates, 39010.6.2.3 PropagatingCovariances, 390

CONTENTS xxi

10.6.3 NonlinearSensors, 39110.6.3.1 PredictedSensorOutputs, 39110.6.3.2 CalculatingKalmanGains, 391

10.6.4 LinearizedKalmanFilter, 39110.6.5 ExtendedKalmanFiltering(EFK), 39210.6.6 AdaptiveKalmanFiltering, 393

10.7 Kalman–BucyFilter, 39510.7.1 ImplementationEquations, 39510.7.2 Kalman–BucyFilterParameters, 396

10.8 HostVehicleTrackingFiltersforGNSS, 39710.8.1 VehicleTrackingFilters, 39710.8.2 DynamicDilutionofInformation, 397

10.8.2.1 EffectonPositionUncertainty, 39810.8.3 SpecializedHostVehicleTrackingFilters, 399

10.8.3.1 UnknownConstantTrackingModel, 40110.8.3.2 DampedHarmonicResonator, 40110.8.3.3 Type2TrackingModel, 40210.8.3.4 DAMP1TrackingModel:VelocityDamping, 40310.8.3.5 DAMP2TrackingModel:Velocityand

AccelerationDamping, 40310.8.3.6 DAMP3TrackingModel:Position,Velocity,and

AccelerationDamping, 40510.8.3.7 TrackingModelsforHighlyConstrained

Trajectories, 40810.8.3.8 FiltersforSpacecraft, 40910.8.3.9 OtherSpecializedVehicleFilterModels, 40910.8.3.10 FiltersforDifferentHostVehicleTypes, 40910.8.3.11 ParametersforVehicleDynamics, 40910.8.3.12 EmpiricalModelingofVehicleDynamics, 409

10.8.4 VehicleTrackingFilterComparison, 41110.8.4.1 SimulatedTrajectory, 41110.8.4.2 Results, 41210.8.4.3 ModelDimensionversus

ModelConstraints, 41210.8.4.4 RoleofModelFidelity, 413

10.9 AlternativeImplementations, 41310.9.1 Schmidt–KalmanSuboptimalFiltering, 413

10.9.1.1 StateVectorPartitioning, 41410.9.1.2 ImplementationEquations, 41410.9.1.3 SimulatedPerformanceinGNSS

PositionEstimation, 41510.9.2 SerialMeasurementProcessing, 416

10.9.2.1 MeasurementDecorrelation, 41610.9.2.2 SerialProcessingofDecorrelated

Measurements, 417

xxii CONTENTS

10.9.3 ImprovingNumericalStability, 41710.9.3.1 EffectsofFinitePrecision, 41710.9.3.2 AlternativeImplementations, 41810.9.3.3 ConditioningandScalingConsiderations, 419

10.9.4 KalmanFilterMonitoring, 42110.9.4.1 RejectingAnomalousSensorData, 42110.9.4.2 MonitoringFilterHealth, 423

10.10 Summary, 425Problems, 426References, 428

11 InertialNavigationErrorAnalysis, 430

11.1 ChapterFocus, 43011.2 ErrorsintheNavigationSolution, 432

11.2.1 TheNineCoreINSErrorVariables, 43211.2.2 CoordinatesUsedforINSErrorAnalysis, 43211.2.3 ModelVariablesandParameters, 432

11.2.3.1 INSOrientationVariablesandErrors, 43311.2.4 DynamicCouplingMechanisms, 439

11.2.4.1 DynamicCoupling, 43911.3 NavigationErrorDynamics, 442

11.3.1 ErrorDynamicsduetoVelocityIntegration, 44211.3.2 ErrorDynamicsduetoGravityCalculations, 443

11.3.2.1 INSGravityModeling, 44311.3.2.2 NavigationErrorModelfor

GravityCalculations, 44411.3.3 ErrorDynamicsduetoCoriolisAcceleration, 44511.3.4 ErrorDynamicsduetoCentrifugalAcceleration, 44611.3.5 ErrorDynamicsduetoEarthrateLeveling, 44711.3.6 ErrorDynamicsduetoVelocityLeveling, 44811.3.7 ErrorDynamicsduetoAcceleration

andMisalignments, 44911.3.8 CompositeModelfromAllEffects, 45011.3.9 VerticalNavigationInstability, 452

11.3.9.1 AltimeterAiding, 45411.3.10 SchulerOscillations, 45711.3.11 CoreModelValidationandTuning, 459

11.3.11.1 HorizontalInertialNavigationModel, 45911.4 InertialSensorNoise, 459

11.4.1 CEPRateversusSensorNoise, 46111.5 SensorCompensationErrors, 461

11.5.1 SensorCompensationErrorModels, 46211.5.1.1 ExponentiallyCorrelatedParameter

DriftModel, 463

CONTENTS xxiii

11.5.1.2 DynamicCouplingintoNavigationErrors, 46511.5.1.3 AugmentedDynamicCoefficientMatrix, 465

11.6 SoftwareSources, 46711.7 Summary, 468Problems, 470References, 471

12 GNSS/INSIntegration, 472

12.1 ChapterFocus, 47212.1.1 Objective, 47212.1.2 OrderofPresentation, 473

12.2 GNSS/INSIntegrationOverview, 47312.2.1 HistoricalBackground, 47312.2.2 TheLoose/TightRanking, 475

12.2.2.1 LooselyCoupledImplementations, 47612.2.2.2 MoreTightlyCoupledImplementations, 47612.2.2.3 UltratightlyCoupledIntegration, 47712.2.2.4 Limitations, 477

12.2.3 UnifiedNavigationModel, 47712.3 UnifiedModelforGNSS/INSIntegration, 479

12.3.1 GNSSErrorModels, 47912.3.1.1 ReceiverClockErrorModel, 47912.3.1.2 AtmosphericPropagationDelayModel, 48012.3.1.3 PseudorangeMeasurementNoise, 481

12.3.2 INSErrorModels, 48112.3.2.1 NavigationErrorModel, 48112.3.2.2 SensorCompensationErrors, 481

12.3.3 GNSS/INSErrorModel, 48212.3.3.1 StateVariables, 48212.3.3.2 NumbersofStateVariables, 48212.3.3.3 DynamicCoefficientMatrix, 48312.3.3.4 ProcessNoiseCovariance, 48412.3.3.5 MeasurementSensitivities, 484

12.4 PerformanceAnalysis, 48512.4.1 DynamicSimulationModel, 485

12.4.1.1 StateTransitionMatrices(STMs), 48512.4.1.2 DynamicSimulation, 486

12.4.2 Results, 48612.4.2.1 Stand-AloneGNSSPerformance, 48612.4.2.2 Stand-AloneINSPerformance, 48812.4.2.3 IntegratedGNSS/INSPerformance, 488

12.5 OtherIntegrationIssues, 49012.5.1 Antenna/ISAOffsetCorrection, 49012.5.2 InfluenceofTrajectoriesonPerformance, 491

xxiv CONTENTS

12.6 Summary, 492Problem, 493References, 494

AppendixA Software, 495

A.1 SoftwareSources, 495A.2 SoftwareforChapter3, 496A.3 SoftwareforChapter4, 496A.4 SoftwareforChapter7, 496A.5 SoftwareforChapter10, 497A.6 SoftwareforChapter11, 498A.7 SoftwareforChapter12, 498A.8 Almanac/EphemerisDataSources, 499

AppendixB CoordinateSystemsandTransformations, 500

B.1 CoordinateTransformationMatrices, 500B.1.1 Notation, 500B.1.2 Definitions, 501B.1.3 UnitCoordinateVectors, 501B.1.4 DirectionCosines, 502B.1.5 CompositionofCoordinateTransformations, 503

B.2 InertialReferenceDirections, 503B.3 Application-DependentCoordinateSystems, 504

B.3.1 CartesianandPolarCoordinates, 504B.3.2 CelestialCoordinates, 505B.3.3 SatelliteOrbitCoordinates, 505B.3.4 ECICoordinates, 507B.3.5 Earth-Centered,Earth-Fixed(ECEF)Coordinates, 508

B.3.5.1 LongitudesinECEFCoordinates, 508B.3.5.2 LatitudesinECEFCoordinates, 508B.3.5.3 LatitudeonanEllipsoidalEarth, 509B.3.5.4 ParametricLatitude, 509B.3.5.5 GeodeticLatitude, 510B.3.5.6 WGS84ReferenceGeoidParameters, 513B.3.5.7 GeocentricLatitude, 513B.3.5.8 GeocentricRadius, 514

B.3.6 EllipsoidalRadiusofCurvature, 515B.3.7 LocalTangentPlane(LTP)Coordinates, 515

B.3.7.1 AlphaWanderCoordinates, 516B.3.7.2 ENU/NEDCoordinates, 516B.3.7.3 ENU/ECEFCoordinates, 516B.3.7.4 NED/ECEFCoordinates, 517

B.3.8 RPYCoordinates, 518

CONTENTS xxv

B.3.9 VehicleAttitudeEulerAngles, 518B.3.9.1 RPY/ENUCoordinates, 519

B.3.10 GNSSNavigationCoordinates, 521B.4 CoordinateTransformationModels, 523

B.4.1 EulerAngles, 523B.4.2 RotationVectors, 524

B.4.2.1 RotationVectortoMatrix, 525B.4.2.2 MatrixtoRotationVector, 527B.4.2.3 SpecialCasesforsin(θ)≈0, 528B.4.2.4 TimeDerivativesofRotationVectors, 529B.4.2.5 TimeDerivativesofMatrixExpressions, 534B.4.2.6 PartialDerivativeswithRespecttoRotation

Vectors, 537B.4.3 DirectionCosineMatrix, 539

B.4.3.1 RotatingCoordinates, 540B.4.4 Quaternions, 543

B.4.4.1 QuaternionMatrices, 543B.4.4.2 AdditionandMultiplication, 544B.4.4.3 Conjugation, 545B.4.4.4 RepresentingRotations, 545

B.5 NewtonianMechanicsinRotatingCoordinates, 548B.5.1 RotatingCoordinates, 548B.5.2 TimeDerivativesofMatrixProducts, 549B.5.3 SolvingforCentrifugalandCoriolisAccelerations, 549

Index 551

xxvii

PREFACE

This book is intended for people who need a working knowledge of global navigation satellite systems (GNSSs), inertial navigation systems (INSs), and the Kalman filtering models and methods used in their integration. The book is designed to provide a usable, working familiarity with both the theoretical and practical aspects of these subjects. For that purpose, we include “real-world” problems from practice as illustrative examples. We also cover the more practical aspects of implementation: how to represent problems in a mathematical model, analyze performance as a function of model parameters, implement the mechanization equations in numerically stable algorithms, assess the computational requirements, test the validity of results, and monitor performance in operation with sensor data from Global Positioning System (GPS) and INS. These important attributes, often overlooked in theoretical treatments, are essential for effective application of theory to real-world problems.

The accompanying companion website (www.wiley.com/go/globalnavigation) contains MATLAB® m-files to demonstrate the workings of the navigation solutions involved. It includes Kalman filter algorithms with GNSS and INS data sets so that the reader can better discover how the Kalman filter works by observing it in action with GNSS and INS. The implementation of GNSS, INS, and Kalman filtering on computers also illuminates some of the practical considerations of finite-word-length arithmetic and the need for alternative algorithms to preserve the accuracy of the results. If the student wishes to apply what she or he learns, then it is essential that she or he experience its workings and failings—and learn to recognize the difference.

The book is organized for use as a text for an introductory course in GNSS technology at the senior level or as a first-year graduate-level course

xxviii PREFACE

in GNSS, INS, and Kalman filtering theory and applications. It could also be used for self-instruction or review by practicing engineers and scientists in these fields.

This third edition includes advances in GNSS/INS technology since the second edition in 2007, as well as many improvements suggested by reviewers and readers of the second edition. Changes in this third edition include the following:

1. Updates on the upgrades in existing GNSS systems and on other systems currently under development

2. Expanded coverage of basic principles of antenna design and practical antenna design solutions

3. Expanded coverage of basic principles of receiver design, and an update of the foundations for code and carrier acquisition and tracking within a GNSS receiver

4. Expanded coverage of inertial navigation, its history, its technology, and the mathematical models and methods used in its implementation

5. Derivations of dynamic models for the propagation of inertial navigation errors, including the effects of drifting sensor compensation parameters

6. Greatly expanded coverage of GNSS/INS integration, including deriva-tion of a unified GNSS/INS integration model, its MATLAB imple-mentations, and performance evaluation under simulated dynamic conditions

The accompanying website has also been augmented to include updated background material and additional MATLAB scripts for simulating GNSS-only and integrated GNSS/INS navigation. The CD-ROM includes satellite position determination, calculation of ionospheric delays, and dilution of precision.

Chapter 1 provides an overview of navigation, in general, and GNSS and inertial navigation, in particular. These overviews include fairly detailed descriptions of their respective histories, technologies, different implementa-tion strategies, and applications.

Chapter 2 covers the fundamental attributes of satellite navigation systems, in general, and the technologies involved, how the navigation solution is imple-mented, and how satellite geometries influence errors in the solution.

Chapter 3 covers the fundamentals of inertial navigation, starting with its nomenclature and continuing through to practical implementation methods, error sources, performance attributes, and development strategies.

Chapters 4–9 cover basic theory of GNSS for a senior-level class in geomat-ics, electrical engineering, systems engineering, and computer science. Subjects covered in detail include basic GNSS satellite signal structures, practical receiver antenna designs, receiver implementation structures, error sources, signal processing methods for eliminating or reducing recognized error sources,