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1、Aboelmagd NoureldinTashfeen B.KaramatJacques GeorgyFundamentals of InertialNavigation,Satellite-basedPositioning and theirIntegration123Dr.Aboelmagd NoureldinDepartment of Electrical and ComputerEngineeringRoyal Military College of Canada/Queens UniversityKingstonCanadaTashfeen B.KaramatDepartment o

2、f Electricaland Computer EngineeringQueens UniversityKingstonCanadaJacques GeorgyTrusted Positioning Inc.CalgaryCanadaISBN 978-3-642-30465-1ISBN 978-3-642-30466-8(eBook)DOI 10.1007/978-3-642-30466-8Springer Heidelberg New York Dordrecht LondonLibrary of Congress Control Number:2012945733?Springer-Ve

3、rlag Berlin Heidelberg 2013This work is subject to copyright.All rights are reserved by the Publisher,whether the whole or part ofthe material is concerned,specifically the rights of translation,reprinting,reuse of illustrations,recitation,broadcasting,reproduction on microfilms or in any other phys

4、ical way,and transmission orinformation storage and retrieval,electronic adaptation,computer software,or by similar or dissimilarmethodology now known or hereafter developed.Exempted from this legal reservation are briefexcerpts in connection with reviews or scholarly analysis or material supplied s

5、pecifically for thepurpose of being entered and executed on a computer system,for exclusive use by the purchaser of thework.Duplication of this publication or parts thereof is permitted only under the provisions ofthe Copyright Law of the Publishers location,in its current version,and permission for

6、 use must alwaysbe obtained from Springer.Permissions for use may be obtained through RightsLink at the CopyrightClearance Center.Violations are liable to prosecution under the respective Copyright Law.The use of general descriptive names,registered names,trademarks,service marks,etc.in thispublicat

7、ion does not imply,even in the absence of a specific statement,that such names are exemptfrom the relevant protective laws and regulations and therefore free for general use.While the advice and information in this book are believed to be true and accurate at the date ofpublication,neither the autho

8、rs nor the editors nor the publisher can accept any legal responsibility forany errors or omissions that may be made.The publisher makes no warranty,express or implied,withrespect to the material contained herein.Printed on acid-free paperSpringer is part of Springer Science+Business Media()I dedica

9、te this book to my mother and fatherfor their love and sacrifices and to my wifeand three sons,Abdelrahman,Yehia andTareq for their support,encouragement andpatienceAboelmagd NoureldinTo my parents,Karamat and Safeena fortheir love,my brother Khaver for his kindpatronage after the early demise of my

10、parents,my wife Shazia and my sons Fahaamand Saarim for their unwavering supportTashfeen KaramatTo my wife Sarah for her great love andvaluable support,to my parents,Ford andLucie,for all their great love and its acts,continuous encouragement and supportthroughout my life,and to my sister Basmafor h

11、er love and encouragementJacques GeorgyContents1Introduction.11.1General Classification of Positioning Techniques.21.1.1Techniques Using Relative Measurements(Known as DR).21.1.2Techniques Using Absolute Measurements(Known as Reference Based Systems).21.1.3Combined Systems.41.2GNSS-Based Positioning

12、 Techniques.51.2.1Global Positioning System.61.3Integration of GPS with Other Systems.81.3.1GPS Augmentation Systems.81.3.2Local Wireless-Based Positioning Systems.91.3.3Vehicle Motion Sensors.111.3.4Other Aiding Sensors.121.3.5Digital Maps.131.4Inertial Navigation.131.5Integrated INS/GPS Navigation

13、.141.6Types of INS/GPS Integration.151.6.1Loosely Coupled INS/GPS Integration.161.6.2Tightly Coupled INS/GPS Integration.161.6.3Ultra-Tightly or Deeply Coupled Integration.161.7INS/GPS Fusion Algorithm.181.8Summary of the Chapters.18References.192Basic Navigational Mathematics,Reference Framesand th

14、e Earths Geometry.212.1Basic Navigation Mathematical Techniques.212.1.1Vector Notation.212.1.2Vector Coordinate Transformation.22vii2.1.3Angular Velocity Vectors.232.1.4Skew-Symmetric Matrix.232.1.5Basic Operations with Skew-Symmetric Matrices.242.1.6Angular Velocity Coordinate Transformations.242.1

15、.7Least Squares Method.252.1.8Linearization of Non-Linear Equations.262.2Coordinate Frames.272.2.1Earth-Centered Inertial Frame.272.2.2Earth-Centered Earth-Fixed Frame.282.2.3Local-Level Frame.282.2.4Wander Frame.292.2.5Computational Frame.312.2.6Body Frame.312.2.7Orbital Coordinate System.322.3Coor

16、dinate Transformations.332.3.1Euler Angles and Elementary Rotational Matrices.342.3.2Transformation Between ECI and ECEF.382.3.3Transformation Between LLF and ECEF.392.3.4Transformation Between LLF and Wander Frame.402.3.5Transformation Between ECEF and Wander Frame.412.3.6Transformation Between Bod

17、y Frame and LLF.422.3.7Transformation From Body Frame to ECEFand ECI Frame.432.3.8Time Derivative of the Transformation Matrix.432.3.9Time Derivative of the Position Vectorin the Inertial Frame.452.3.10 Time Derivative of the Velocity Vector in the InertialFrame.452.4The Geometry of the Earth.462.4.

18、1Important Definitions.472.4.2Normal and Meridian Radii.482.5Types of Coordinates in the ECEF Frame.492.5.1Rectangular Coordinates in the ECEF Frame.492.5.2Geodetic Coordinates in the ECEF Frame.492.5.3Conversion From Geodetic to Rectangular Coordinatesin the ECEF Frame.502.5.4Conversion From Rectan

19、gular to Geodetic Coordinatesin the ECEF Frame.502.6Earth Gravity.52References.63viiiContents3Global Positioning System.653.1GPS Observables.653.1.1Pseudo-Ranges Measurements.663.1.2Carrier Phase Measurements.673.1.3Doppler Measurements.683.2GPS Structure.693.2.1Space Segment.693.2.2Control Segment.

20、693.2.3User Segment.713.3GPS Signals.713.3.1Traditional GPS Signals.713.3.2GPS Modernization.733.4GPS Error Sources.733.4.1Satellite Clock Error.743.4.2Receiver Clock Error.743.4.3Ionosphere Delay.743.4.4Tropospheric Delay.763.4.5Multipath Errors.763.4.6Satellite Orbital Errors.763.4.7Receiver Noise

21、.773.4.8User Equivalent Range Error.773.5GPS Augmentation.773.5.1Differential GPS.793.5.2Local Area DGPS.793.5.3Wide Area DGPS.803.5.4Assisted GPS.813.6GPS Satellite Orbits.843.6.1Keplers Laws.843.6.2Keplerian Orbital Elements.853.6.3GPS Orbital Parameters.873.7Ephemeris Data Processing.883.7.1Calcu

22、lation of Satellite Clock Corrections.883.7.2Atmospheric Corrections.903.7.3Calculation of Satellite Position.943.7.4Calculation of Satellite Velocity.963.8Receiver Position and Velocity Estimation.973.8.1Pseudo-Range Measurements.973.8.2Position Estimation.983.8.3Satellite Geometry and Dilution of

23、Precision.1013.8.4Doppler Measurements.1053.8.5Velocity Estimation from Doppler.1063.8.6Position and Velocity Estimation.107Contentsix3.9Carrier Phase Positioning.1093.9.1Relative Positioning and Linear Combinationsof GPS Observables.1103.9.2Relative Positioning.1113.9.3Linear Combinations of GPS Me

24、asurements.1113.9.4Position Estimation from Carrier Phase Measurements.1173.10 Integer Ambiguity.1193.10.1 Integer Ambiguity Resolution.1203.10.2 Ambiguity Dilution of Precision.121References.1214Inertial Navigation System.1254.1Principle of Inertial Navigation.1254.2Physical Implementation of an IN

25、S.1264.3Inertial Measurement Unit.1274.4Inertial Sensors.1284.4.1Accelerometers.1294.4.2Gyroscopes.1314.5Basics of Inertial Navigation.1324.5.1Navigation in One Dimension.1334.5.2Navigation in Two Dimensions.1334.6Navigation in Three Dimensions.1364.7Overview of an Inertial Navigation System in 3D.1

26、374.8Theoretical Measurements of the Inertial Sensor.1374.8.1Theoretical Measurements of a StationaryAccelerometer Triad.1374.8.2Theoretical Measurements of a Stationary Gyro Triad.1394.8.3Theoretical Measurements of a Moving Gyro Triad.1414.9Notes on Inertial Sensor Measurements.1454.10 Inertial Se

27、nsor Performance Characteristics.1464.11 Inertial Sensor Errors.1464.11.1 Systematic Errors.1464.11.2 Random Errors.1494.11.3 Notes on Random Errors.1514.11.4 Mathematical Models of Inertial Sensor Errors.1524.12 Classification of Inertial Sensors.1544.12.1 Gyroscope Technologies and their Applicati

28、ons.1554.12.2 Accelerometer Technologies and their Applications.1554.13 Calibration of Inertial Sensors.1554.13.1 Six-Position Static Test.1564.13.2 Angle Rate Tests.1584.14 Importance of Calibration of Inertial Sensors.1594.14.1 Case-I:Bias Error in an Accelerometer.1614.14.2 Case-II:Bias Error in

29、the Gyroscope.161xContents4.15 Initialization and Alignment of Inertial Sensors.1624.15.1 Position and Velocity Initialization.1624.15.2 Attitude Alignment.163References.1665Inertial Navigation System Modeling.1675.1Dynamic Modeling.1675.2Kinematic Modeling.1685.2.1Rigid Body Motion Modeling.1695.2.

30、2Observables.1695.3INS Mechanization.1705.3.1INS Mechanization in an Inertial Frame of Reference.1715.3.2INS Mechanization in ECEF Frame.1725.3.3INS Mechanization in the Local-Level Frame.1745.3.4INS Mechanization in Wander Frame.1805.4Parameterization of the Rotation Matrix.1835.4.1Solution to Tran

31、sformation Matrix.1845.4.2Quaternions.1865.4.3Solutions of the Quaternion Equation.1885.4.4Advantages of Quaternion.1895.5Step by Step Computation of Navigation Parametersin the l-Frame.1905.5.1Raw Measurement Data.1935.5.2Correction of the Measurement Data.1945.5.3Calculation and Updating of Rotati

32、on Matrix.1945.5.4Attitude Computation.1965.5.5Velocity Computation.1975.5.6Position Computation.198References.1996Modeling INS Errors by Linear State Equations.2016.1Local-Level Frame Error State Equations.2026.1.1Position Errors for Local-Level Frame.2036.1.2Velocity Errors for Local-Level Frame.2

33、056.1.3Attitude Errors for Local-Level Frame.2116.1.4Inertial Sensor Error States.2166.1.5Summary of Local-Level Frame Error State Equations.2176.2Schuler Effect.2196.2.1Error Model Along the East Channel.2196.2.2Error Model Along the North Channel.2216.2.3Understanding the Error Behavior of the Ine

34、rtialSystem.222References.223Contentsxi7Kalman Filter.2257.1Discrete-Time KF.2277.1.1KF Assumptions.2287.2KF Procedure.2297.2.1Time Update or Prediction.2307.2.2Measurement Update or Correction.2307.3KF Algorithm Steps.2337.4Non-Linear Kalman Filtering.2357.4.1Linearized KF.2357.4.2Extended KF.2367.

35、5KF Divergence Control.2367.5.1Addition of Fictitious Noise to the KF Process Model.2367.5.2Schmidt Epsilon Technique.2377.5.3Finite Memory Filtering.2377.5.4Fading Memory Filtering.2387.6Explanatory Examples.2387.6.1A Simple Navigation Example.2387.6.2Zero Velocity Update.2397.6.3Coordinate Update.

36、242References.2448INS/GPS Integration.2478.1Error Feedback Schemes.2488.1.1Open-Loop INS/GPS Architecture.2498.1.2Closed-Loop INS/GPS Architecture.2498.2Types of Integration.2498.2.1Loosely Coupled INS/GPS Integration.2508.2.2Tightly Coupled INS/GPS Integration.2518.2.3Ultra-Tight INS/GPS Integratio

37、n.2528.3Dynamic Error Model of INS Equations.2528.4Models for Loosely Coupled INS/GPS Integration.2558.4.1System Model.2558.4.2Measurement Model.2578.4.3The Overall Implementation Block Diagramof the Loosely Coupled INS/GPS Integration.2598.5Modeling Tightly Coupled INS/GPS Integration.2598.5.1Syste

38、m Model.2608.5.2Measurement Model.2628.5.3The Overall Measurements Model.269References.270 xiiContents9Three-Dimensional Reduced Inertial Sensor System/GPSIntegration for Land-Based Vehicles.2739.1Performance Analysis of 3D Positioning Utilizing a MEMSGrade Full IMU.2739.2The Proposed Techniques for

39、 Overcoming MEMSGrade IMU Shortcomings for Land-Based Vehicles.2749.3Three-Dimensional Reduced Inertial Sensor System.2769.3.1Overview of 3D RISS.2769.3.2Advantages of 3D RISS for Wheel-Based LandVehicles.2779.3.3Derivation of the 3D RISS Motion Equations.2809.3.4Overview of 3D RISS Motion Model.285

40、9.4KF for Loosely Coupled 3D RISS/GPS Integration.2869.4.1The Linearized Error Model for 3D RISS.2879.4.2Measurement Model for Updating 3D RISS.2899.5KF for Tightly Coupled 3D RISS/GPS Integration.2909.5.1Augmenting the System Model.2909.5.2Raw GPS Measurement Model for Updating 3D RISS.290Reference

41、s.29610 Two Case Studies:Full IMU/GPS and 3D RISS/GPSIntegration.29710.1 Navigation Equipment Used for the Experiments.29710.1.1 Partial GPS Outage Criterion.29910.2 Performance of Tightly Coupled Algorithm withFull IMU/GPS.30010.2.1 Analysis of Selected GPS Outages.30310.3 Performance of Tightly Co

42、upled Algorithmfor 3D RISS/GPS.30710.3.1 Analysis of Selected GPS Outages.309References.313ContentsxiiiAbbreviations1DOne dimension2DTwo dimension3DThree dimensionADOPAmbiguity DOPAFMAmbiguity function methodA-GPSAssisted GPSAIArtificial intelligenceAOAAngle of arrivalARAmbiguity resolutionARAutoreg

43、ressiveARNSAeronautical radio navigation servicesARWAngle random walkBD-1Beidou-1BD-2Beidou-2BOCBinary offset carrierBPSKBinary phase shifted keyCASCChina aerospace science and technologyCASTChina academy of space technologyCDMACode division multiple accessCNSSCompass navigation satellite systemCORS

44、Continuously operating reference stationCTPConventional terrestrial poleCUPTCoordinate updateCWAASCanadian wide area augmentation systemDCMDirection cosine matricesDDDouble differenceDGPSDifferential GPSDLLDelay-lock loopsDOPDilution of precisionDRDead-reckoningxvDTGDynamically tuned gyroscopesDVB-T

45、Digital video broadcasting-terrestrialECEFEarth-centered earth-fixedECIEarth-centered inertialEGNOSEuropean geostationary navigation overlay serviceEKFExtended Kalman filterENUEast North UpEOTDEnhanced observed time differenceESAEuropean space agencyFAAFederal aviation administrationFASFFast ambigui

46、ty search filterFOCFull operational capabilityFOGFiber optic gyroscopesGAGANGeo-augmented navigation systemGBASGround-based augmentation systemsGDOPGeometric dilution of precisionGDPSGlobal differential GPSGLONASSGlobal navigation satellite systemGMGauss-MarkovGNSSGlobal navigation satellite systems

47、GPSGlobal positioning systemGRASGround-based regional augmentation systemGRSGeographic reference systemGSMGlobal system of mobileHDOPHorizontal dilution of precisionHOTHigher order termsHRGHemispherical resonant gyroscopesIAInteger ambiguityIFOGInterferometric fiber-optic gyroscopesIGSInternational

48、GNSS serviceIMUInertial measurement unitINSInertial navigation systemIOCInitial operational capabilityIRNSSIndian regional navigational satellite systemISAInertial sensor assemblyISDBIntegrated services digital broadcastingKFKalman filterLAASLocal area augmentation systemLADGPSLocal area DGPSLAMBDAL

49、east-squares ambiguity decorrelation adjustmentLIDARLight detection and rangingLKFLinearized Kalman filterLLFLocal-level framexviAbbreviationsLOSLine of sightLSASTLeast-squares ambiguity search techniqueMBOCMultiplexed binary offset carrierMCSMaster control stationMEMSMicro-electro-mechanical system

50、MSASMultifunction transport satellite(MTSAT)satellite augmentationsystemMTSATMultifunction transport satelliteNEDNorth East DownNGANational geospatial-intelligence agencyNGDGPSNationwide differential GPS systemNTSCNational television system committeeOTDOAObserved time difference of arrivalPDOPPositi