Holdings: Fundamentals of high accuracy inertial navigation

Fundamentals of high accuracy inertial navigation:

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Bibliographic Details
Main Author:	Chatfield, Averil B. (Author)
Format:	Book
Language:	English
Published:	Reston, Va. American Inst. of Aeronautics and Astronautics 1997
Edition:	2. printing
Series:	Progress in astronautics and aeronautics 174
Subjects:	Navigation par inertie - Mathématiques Inertial navigation Trägheitsnavigation
Online Access:	Inhaltsverzeichnis
Item Description:	Literaturangaben
Physical Description:	XIV, 339 S. graph. Darst.
ISBN:	1563472430

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adam_text	FUNDAMENTALS OF HIGH ACCURACY INERTIAL NAVIGATION AVERIL B. CHATFIELD VOLUME 174 PROGRESS IN ASTRONAUTICS AND AERONAUTICS PAUL ZARCHAN, EDITOR-IN-CHIEF CHARLES STARK DRAPER LABORATORY, INC. CAMBRIDGE, MASSACHUSETTS PUBLISHED BY THE AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS, INC. 1801 ALEXANDER BELL DRIVE, RESTON, VIRGINIA 20191-4344 TABLE OF CONTENTS PREFACE XIII CHAPTER 1. INTRODUCTION 1 I. FORCES PRODUCING MOTION 1 A. GRAVITATION 1 B. INERTIA 2 II. INERTIAL EQUIVALENCE OF EARTH-CENTERED FRAME 3 III. FUNDAMENTAL EQUATION OF INERTIAL NAVIGATION 4 IV. DESCRIPTION OF AN INERTIAL NAVIGATION SYSTEM 5 V. INERTIAL MEASUREMENTS 5 VI. FOUR PHASES OF INERTIAL NAVIGATION 6 VII. ROLE OF GEODESY 7 VIII. REFERENCE EARTH MODEL 7 PART I INERTIAL NAVIGATION CHAPTER 2. NOTATION, COORDINATE SYSTEMS, AND UNITS 15 I. NOTATION CONVENTIONS 15 II. COORDINATE SYSTEM DEFINITIONS 18 A. SOFTWARE IMPLEMENTED 18 B. HARDWARE IMPLEMENTED 22 III. COORDINATE TRANSFORMATION CHARACTERISTICS 23 A. ORTHOGONAL 23 B. NONORTHOGONAL 25 IV. COMMONLY USED COORDINATE ROTATIONS 30 A. EARTH-CENTERED INERTIAL TO EARTH-CENTERED EARTH-FIXED 30 B. EARTH-CENTERED INERTIAL TO LOCAL GEODETIC VERTICAL 31 C. EARTH-CENTERED INERTIAL TO LOCAL GEOCENTRIC VERTICAL 31 D. EARTH-CENTERED EARTH-FIXED TO LOCAL GEODETIC VERTICAL 31 E. EARTH-CENTERED EARTH-FIXED TO LOCARASTRONOMIC VERTICAL 31 F. STAR LINE-OF-SIGHT TO PLATFORM 31 G. STAR TO EARTH-CENTERED INERTIAL 32 V. UNITS 32 CHAPTER 3. EQUATIONS OF MOTION IN A CENTRAL FORCE GRAVITY FIELD .... 33 I. MOTION IN INERTIAL COORDINATES WITH ZERO-SPECIFIC FORCE . 33 A. ZERO-SPECIFIC FORCE /. 34 B. SCHULER FREQUENCY . . . 36 II. STATE-SPACE FORM 37 A. LAPLACE TRANSFORM FORM 38 B. FREQUENCY RESPONSE 39 VII III. MOTION IN INERTIAL COMPUTATION COORDINATES D .... 40 A. TRANSFER FUNCTIONS 40 B. PROPAGATION OF INITIAL STATE 41 C. FREQUENCY RESPONSE FUNCTIONS 41 IV. MOTION IN EARTH-FIXED COMPUTATION COORDINATES 43 A. SIGNIFICANCE OF TERMS IN EQUATION OF MOTION 44 B. TRANSFER FUNCTIONS 44 C. PROPAGATION OF INITIAL STATE 46 D. FREQUENCY RESPONSE FUNCTIONS 49 V. EFFECT OF VELOCITY DAMPING 53 A. PROPAGATION OF INITIAL STATE 53 B. FREQUENCY RESPONSE FUNCTIONS 55 CHAPTER 4. INERTIAL INSTRUMENTATION 59 I. GYROSCOPE 59 A. ROTATING WHEEL 60 B. OPTICAL 64 C. RECENTLY DEVELOPED INSTRUMENTS 67 II. ACCELEROMETER 68 A. PENDULOUS INTEGRATING GYRO 68 B. PROOF MASS 69 C. VIBRATING STRING 70 D. FIBER OPTIC 71 III. GRADIOMETER 71 A. GRAVITY GRADIENT TENSOR 71 B. OUTPUT EQUATIONS 72 C. OUTPUT EQUATION PROCESSING 74 IV. GIMBAL CONFIGURATIONS 75 A. MECHANICAL FRAME 75 B. FLOATING SPHERE 75 V. STRAPDOWN CONFIGURATION 76 CHAPTER 5. CALIBRATION 79 I. PHYSICAL REFERENCE VECTORS 79 A. SPECIFIC FORCE 79 B. ANGULAR RATE 81 II. CALIBRATION PROCEDURE 82 A. INERTIAL MEASUREMENT UNIT CONFIGURATION 82 B. PLATFORM ROTATION SCHEDULE 83 III. ACCELEROMETER CALIBRATION 87 A. OBSERVATION EQUATION 87 B. APPLICATION OF THE OBSERVATION EQUATION 90 IV. GYRO CALIBRATION 93 A. OBSERVATION EQUATIONMAGNITUDE FORM 93 B. OBSERVATION EQUATIONVECTOR FORM 99 CHAPTER 6. INITIAL ALIGNMENT AND ATTITUDE COMPUTATION 109 I. INITIAL ALIGNMENT 109 A. ANALYTICAL COARSE ALIGNMENT 110 B. ALIGNING AN IMU STABLE PLATFORM TO LGV COORDINATES 115 VIII C. ALIGNING A STRAPDOWN SYSTEM TO LGV COORDINATES 117 II. ATTITUDE 120 A. PLATFORM TO EARTH-CENTERED INTERTIAL 120 B. PLATFORM TO LOCAL ASTRONOMIC VERTICAL 123 C. ~BODY-TO-EARTH-CENTERED-INERTIAL USING QUATERNIONS 123 D. ROTATING A VECTOR USING QUATERNIONS 126 CHAPER 7. GEODETIC VARIABLES AND CONSTANTS 129 I. METHOD OF DERIVING VALUES FOR THE GEODETIC VARIABLES AND CONSTANTS .... 129 A. APPARENT GRAVITY MAGNITUDE 129 B. ASTRONOMIC COORDINATES 132 C. GEOCENTRIC GRAVITATIONAL CONSTANT 134 D. SEMIMAJOR AXIS, FLATTENING, AND SHCS 134 E. EARTH ROTATION RATE 134 F. POLE LOCATION 134 G. GEODETIC COORDINATES 135 H. GEOID HEIGHT 136 I. HEIGHT ABOVE MEAN SEA LEVEL 136 II. WORLD GEODETIC SYSTEM 1984 137 A. SPHERICAL HARMONIC COEFFICIENTS 137 B. EQUIPOTENTIAL SURFACES ASSOCIATED WITH SHCS 139 C. PHYSICAL MEANING OF THE LOW DEGREE AND ORDER SHCS 140 D. REGIONAL DATUM TRANSFORMATIONS 142 III. GRAVITY MODELS 143 A. SPHERICAL HARMONIC 143 B. POINT MASS 145 C. TWO-DIMENSIONAL FOURIER SERIES 148 D. TWO-DIMENSIONAL TABLE 148 E. OTHER TYPES OF MODELS 149 IV. USEFUL INCREMENTAL TERMS OF GEODESY 149 A. DEFLECTIONS OF THE VERTICAL 149 B. AZIMUTH DIFFERENCES 149 V. EXTENDING GRAVITY SURVEYS WITH INTERTIAL MEASUREMENTS 149 CHAPTER 8. EQUATIONS OF MOTION WITH GENERAL GRAVITY MODEL 153 I. STATE-SPACE FORM IN EARTH-CENTERED INERTIAL COORDINATES 153 II. STATE-SPACE FORM IN EARTH-CENTERED EARTH-FIXED COORDINATES 156 III. STATE-SPACE FORM IN EARTH-CENTERED EARTH-FIXED COORDINATES WITH POINT-MASS GRAVITY MODEL 156 IV. STATE-SPACE FORM IN LOCAL GEODETIC VERTICAL COORDINATES 158 A. STANDARD FORM 158 B. PSEUDO-VELOCITY FORM 162 V. PLATFORM CONTROL LAWS 163 A. EARTH-CENTERED INERTIAL 163 B. EARTH-CENTERED EARTH-FIXED 163 C. LOCAL GEODETIC VERTICALTORQUED AZIMUTH 163 D. LOCAL GEODETIC VERTICALFREE AZIMUTH 164 E. LOCAL GEODETIC VERTICALPLATFORM CAROUSEL 164 F. LOCAL GEODETIC VERTICALPLATFORM TUMBLE 164 VI. INTEGRATION OF THE EQUATIONS OF MOTION 165 IX VII. SUMMARY OF EQUATIONS FOR COMPUTING THE TRANSITION MATRIX 166 A. EARTH-CENTERED INERTIAL COORDINATESSTABILIZED PLATFORM 166 B. EARTH-CENTERED EARTH-FIXED COORDINATESSTABILIZED PLATFORM ..... 168 C. LOCAL GEODETIC VERTICAL COORDINATESSTANDARD FORMSTABILIZED PLATFORM 169 D. LOCAL GEODETIC VERTICAL COORDINATESPSEUDO-VELOCITY FORMSTABILIZED PLATFORM 171 E. EARTH-CENTERED INERTIAL COORDINATESSTRAPDOWN 172 F. EARTH-CENTERED EARTH-FIXED COORDINATESSTRAPDOWN 174 G. LOCAL GEODETIC VERTICAL COORDINATESSTANDARD FORMSTRAPDOWN.. 175 H. LOCAL GEODETIC VERTICAL COORDINATESPSEUDO-VELOCITY FORMSTRAPDOWN 177 PART II INERTIAL NAVIGATION WITH AIDS CHAPTER 9. INERTIAL NAVIGATION WITH EXTERNAL MEASUREMENTS 181 I. BASIS FOR USING EXTERNAL MEASUREMENTS 181 A. EQUATIONS OF RELATIVE MOTION 182 B. APPLICATION OF THE EQUATIONS OF RELATIVE MOTION 184 II. KALMAN FILTER STATE UPDATES 188 A. OVERVIEW OF NAVIGATION COMPUTATIONSEXTENDED KALMAN FILTER ... 189 B. GAIN EVALUATION AND COVARIANCE UPDATE 191 C. COVARIANCE PROPAGATION 192 D. SUMMARY OF NAVIGATION EQUATIONSEXTENDED KALMAN FILTER 194 E. SUMMARY OF NAVIGATION EQUATIONSLINEARIZED KALMAN FILTER 194 F. EXAMPLES OF EXTERNAL MEASUREMENT PREDICTIONS 196 G. EXAMPLES OF PARTIAL DERIVATIVE EVALUATIONS 201 H. EXAMPLE OF A SUBOPTIMAL FILTER 205 I. ALIASING 207 CHAPTER 10. ERROR EQUATIONS FOR THE KALMAN FILTER 211 I. ATTITUDE ERRORS 211 A. DEFINITIONS 211 B. ANGULAR EQUIVALENT OF THE POSITION ERROR 212 C. ACTUAL COORDINATE ROTATIONS IN TERMS OF ERRORS 214 D. ATTITUDE ERROR VECTOR DIFFERENTIAL EQUATIONS 214 II. SYSTEM DYNAMIC AND ERROR DISTRIBUTION MATRICES IN EARTH-CENTERED INERTIAL COORDINATES 215 A. ACCELERATIONEARTH-CENTERED INERTIAL COORDINATES 215 B. VELOCITYEARTH-CENTERED INERTIAL COORDINATES 218 C. STATE-SPACE FORM OF ERROR EQUATIONSEARTH-CENTERED INERTIAL COORDINATES 218 III. SYSTEM DYNAMIC AND ERROR DISTRIBUTION MATRICES IN EARTH-CENTERED EARTH-FIXED COORDINATES 219 A. ACCELERATION-R-EARTH-CENTERED EARTH-FIXED COORDINATES 219 B. VELOCITYEARTH-CENTERED EARTH-FIXED COORDINATES 220 C. STATE-SPACE FORM OF ERROR EQUATIONSEARTH-CENTERED EARTH-FIXED COORDINATES 220 IV. SYSTEM DYNAMIC AND ERROR DISTRIBUTION MATRICES IN LOCAL GEODETIC VERTICAL COORDINATES 221 A. SEMIPOSITION ERROR DEFINITION 221 B. SEMIVELOCITY ERROR DEFINITION 221 C. ACCELERATIONLOCAL GEODETIC VERTICAL COORDINATES 222 D. VELOCITYLOCAL GEODETIC VERTICAL COORDINATES 224 E. STATE-SPACE FORM OF ERROR EQUATIONSLOCAL GEODETIC VERTICAL COORDINATES 225 CHAPTER 11. STATE VARIABLE ERROR MODELS 227 I. INERTIAL AND EXTERNAL MEASUREMENT EQUIPMENT ERROR SHAPING FUNCTIONS . . 227 A. RANDOM CONSTANT 228 B. RANDOM WALK 228 C. RANDOM RAMP 228 D. MARKOV 229 II. OMISSION GRAVITY MODEL ERROR SHAPING FUNCTIONS 229 A. GRAVITY DATABASE FORMAT 229 B. GRAVITY MODEL ERROR EQUATIONS OF MOTION 230 C. AUTOCORRELATION FUNCTION APPROXIMATION METHOD 232 D. INFLUENCE OF VEHICLE VELOCITY ON THE POWER SPECTRAL DENSITY 235 E. AUTOREGRESSIVE MOVING AVERAGE METHOD 237 PART III ACCURACY ANALYSIS CHAPTER 12. ACCURACY CRITERIA AND ANALYSIS TECHNIQUES 253 I. CENTRAL LIMIT THEOREM 253 II. STANDARD ERROR 254 A. UNCORRELATED STANDARD ERRORS FOR CIRCULAR-ERROR-PROBABLE CALCULATION 254 B. UNCORRELATED STANDARD ERRORS FOR SPHERICAL-ERROR-PROBABLE CALCULATION 255 III. GAUSSIAN DISTRIBUTION FUNCTION FOR NAVIGATION POSITION ERRORS 257 -IV. CIRCULAR ERROR PROBABLE AND SPHERICAL ERROR PROBABLE 257 A. CEP FOR EQUAL STANDARD ERRORS AND ZERO MEANS 257 B. SEP FOR EQUAL STANDARD ERRORS AND ZERO MEANS 259 C. CEP AND SEP FOR UNEQUAL STANDARD ERRORS AND NONZERO MEANS .... 260 D. VERIFICATION OF THE CEP AND SEP FORMULAS 264 V. ACCURACY ANALYSIS TECHNIQUES ..... 267 A. TYPES OF ERROR 267 B. ERROR ANALYSIS USING SENSITIVITY COEFFICIENTS 271 CHAPTER 13. ERROR EQUATIONS FOR CALIBRATION, ALIGNMENT, AND INITIALIZATION 273 I. INERTIAL INSTRUMENT CALIBRATION 273 A. APPARENT GRAVITY MAGNITUDE 274 B. REFERENCE ROTATION RATE 277 C. POLE LOCATION 278 II. ANALYTICAL ALIGNMENT 279 A. ASTRONOMIC COORDINATES 283 XI B. GEODETIC COORDINATES 284 C. SPECIFIC FORCE AND POLE POSITION 285 III. INITIALIZATION 286 A. INITIAL VELOCITY 286 B. INITIAL POSITION 287 C. CONVERSION TO EARTH-CENTERED INERTIAL AND LOCAL GEODETIC VERTICAL COORDINATES 288 IV. KALMAN FILTER COVARIANCE INITIALIZATION 288 CHAPTER 14. EVALUATION OF GRAVITY MODEL ERROR EFFECTS 291 I. SPHERICAL HARMONIC GRAVITY MODEL ERRORS 292 II. POINT-MASS MODEL GENERATION 293 III. SOURCES OF ERROR FOR POINT-MASS MODEL . . : 294 A. REPRESENTATION 295 B. REDUCTION 295 C. OMISSION 303 APPENDIX A. MATRIX INVERSE FORMULAS 305 APPENDIX B. LAPLACE TRANSFORMS 307 APPENDIX C. QUATERNIONS 311 APPENDIX D. ASSOCIATED LEGENDRE FUNCTIONS 313 APPENDIX E. ASSOCIATED LEGENDRE FUNCTION DERIVATIVES 315 APPENDIX F. PROCEDURE FOR GENERATING GRAVITY DISTURBANCE REALIZATIONS 317 APPENDIX G. PROCEDURE FOR GENERATING SPECIFIC FORCE PROFILE 321 INDEX 325 XII
adam_txt	FUNDAMENTALS OF HIGH ACCURACY INERTIAL NAVIGATION AVERIL B. CHATFIELD VOLUME 174 PROGRESS IN ASTRONAUTICS AND AERONAUTICS PAUL ZARCHAN, EDITOR-IN-CHIEF CHARLES STARK DRAPER LABORATORY, INC. CAMBRIDGE, MASSACHUSETTS PUBLISHED BY THE AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS, INC. 1801 ALEXANDER BELL DRIVE, RESTON, VIRGINIA 20191-4344 TABLE OF CONTENTS PREFACE XIII CHAPTER 1. INTRODUCTION 1 I. FORCES PRODUCING MOTION 1 A. GRAVITATION 1 B. INERTIA 2 II. INERTIAL EQUIVALENCE OF EARTH-CENTERED FRAME 3 III. FUNDAMENTAL EQUATION OF INERTIAL NAVIGATION 4 IV. DESCRIPTION OF AN INERTIAL NAVIGATION SYSTEM 5 V. INERTIAL MEASUREMENTS 5 VI. FOUR PHASES OF INERTIAL NAVIGATION 6 VII. ROLE OF GEODESY 7 VIII. REFERENCE EARTH MODEL 7 PART I INERTIAL NAVIGATION CHAPTER 2. NOTATION, COORDINATE SYSTEMS, AND UNITS 15 I. NOTATION CONVENTIONS 15 II. COORDINATE SYSTEM DEFINITIONS 18 A. SOFTWARE IMPLEMENTED 18 B. HARDWARE IMPLEMENTED 22 III. COORDINATE TRANSFORMATION CHARACTERISTICS 23 A. ORTHOGONAL 23 B. NONORTHOGONAL 25 IV. COMMONLY USED COORDINATE ROTATIONS 30 A. EARTH-CENTERED INERTIAL TO EARTH-CENTERED EARTH-FIXED 30 B. EARTH-CENTERED INERTIAL TO LOCAL GEODETIC VERTICAL 31 C. EARTH-CENTERED INERTIAL TO LOCAL GEOCENTRIC VERTICAL 31 D. EARTH-CENTERED EARTH-FIXED TO LOCAL GEODETIC VERTICAL 31 E. EARTH-CENTERED EARTH-FIXED TO LOCARASTRONOMIC VERTICAL 31 F. STAR LINE-OF-SIGHT TO PLATFORM 31 G. STAR TO EARTH-CENTERED INERTIAL 32 V. UNITS 32 CHAPTER 3. EQUATIONS OF MOTION IN A CENTRAL FORCE GRAVITY FIELD . 33 I. MOTION IN INERTIAL COORDINATES WITH ZERO-SPECIFIC FORCE . 33 A. ZERO-SPECIFIC FORCE /. 34 B. SCHULER FREQUENCY . . . 36 II. STATE-SPACE FORM 37 A. LAPLACE TRANSFORM FORM 38 B. FREQUENCY RESPONSE 39 VII III. MOTION IN INERTIAL COMPUTATION COORDINATES D . 40 A. TRANSFER FUNCTIONS 40 B. PROPAGATION OF INITIAL STATE 41 C. FREQUENCY RESPONSE FUNCTIONS 41 IV. MOTION IN EARTH-FIXED COMPUTATION COORDINATES 43 A. SIGNIFICANCE OF TERMS IN EQUATION OF MOTION 44 B. TRANSFER FUNCTIONS 44 C. PROPAGATION OF INITIAL STATE 46 D. FREQUENCY RESPONSE FUNCTIONS 49 V. EFFECT OF VELOCITY DAMPING 53 A. PROPAGATION OF INITIAL STATE 53 B. FREQUENCY RESPONSE FUNCTIONS 55 CHAPTER 4. INERTIAL INSTRUMENTATION 59 I. GYROSCOPE 59 A. ROTATING WHEEL 60 B. OPTICAL 64 C. RECENTLY DEVELOPED INSTRUMENTS 67 II. ACCELEROMETER 68 A. PENDULOUS INTEGRATING GYRO 68 B. PROOF MASS 69 C. VIBRATING STRING 70 D. FIBER OPTIC 71 III. GRADIOMETER 71 A. GRAVITY GRADIENT TENSOR 71 B. OUTPUT EQUATIONS 72 C. OUTPUT EQUATION PROCESSING 74 IV. GIMBAL CONFIGURATIONS 75 A. MECHANICAL FRAME 75 B. FLOATING SPHERE 75 V. STRAPDOWN CONFIGURATION 76 CHAPTER 5. CALIBRATION 79 I. PHYSICAL REFERENCE VECTORS 79 A. SPECIFIC FORCE 79 B. ANGULAR RATE 81 II. CALIBRATION PROCEDURE 82 A. INERTIAL MEASUREMENT UNIT CONFIGURATION 82 B. PLATFORM ROTATION SCHEDULE 83 III. ACCELEROMETER CALIBRATION 87 A. OBSERVATION EQUATION 87 B. APPLICATION OF THE OBSERVATION EQUATION 90 IV. GYRO CALIBRATION 93 A. OBSERVATION EQUATIONMAGNITUDE FORM 93 B. OBSERVATION EQUATIONVECTOR FORM 99 CHAPTER 6. INITIAL ALIGNMENT AND ATTITUDE COMPUTATION 109 I. INITIAL ALIGNMENT 109 A. ANALYTICAL COARSE ALIGNMENT 110 B. ALIGNING AN IMU STABLE PLATFORM TO LGV COORDINATES 115 VIII C. ALIGNING A STRAPDOWN SYSTEM TO LGV COORDINATES 117 II. ATTITUDE 120 A. PLATFORM TO EARTH-CENTERED INTERTIAL 120 B. PLATFORM TO LOCAL ASTRONOMIC VERTICAL 123 C. ~BODY-TO-EARTH-CENTERED-INERTIAL USING QUATERNIONS 123 D. ROTATING A VECTOR USING QUATERNIONS 126 CHAPER 7. GEODETIC VARIABLES AND CONSTANTS 129 I. METHOD OF DERIVING VALUES FOR THE GEODETIC VARIABLES AND CONSTANTS . 129 A. APPARENT GRAVITY MAGNITUDE 129 B. ASTRONOMIC COORDINATES 132 C. GEOCENTRIC GRAVITATIONAL CONSTANT 134 D. SEMIMAJOR AXIS, FLATTENING, AND SHCS 134 E. EARTH ROTATION RATE 134 F. POLE LOCATION 134 G. GEODETIC COORDINATES 135 H. GEOID HEIGHT 136 I. HEIGHT ABOVE MEAN SEA LEVEL 136 II. WORLD GEODETIC SYSTEM 1984 137 A. SPHERICAL HARMONIC COEFFICIENTS 137 B. EQUIPOTENTIAL SURFACES ASSOCIATED WITH SHCS 139 C. PHYSICAL MEANING OF THE LOW DEGREE AND ORDER SHCS 140 D. REGIONAL DATUM TRANSFORMATIONS 142 III. GRAVITY MODELS 143 A. SPHERICAL HARMONIC 143 B. POINT MASS 145 C. TWO-DIMENSIONAL FOURIER SERIES 148 D. TWO-DIMENSIONAL TABLE 148 E. OTHER TYPES OF MODELS 149 IV. USEFUL INCREMENTAL TERMS OF GEODESY 149 A. DEFLECTIONS OF THE VERTICAL 149 B. AZIMUTH DIFFERENCES 149 V. EXTENDING GRAVITY SURVEYS WITH INTERTIAL MEASUREMENTS 149 CHAPTER 8. EQUATIONS OF MOTION WITH GENERAL GRAVITY MODEL 153 I. STATE-SPACE FORM IN EARTH-CENTERED INERTIAL COORDINATES 153 II. STATE-SPACE FORM IN EARTH-CENTERED EARTH-FIXED COORDINATES 156 III. STATE-SPACE FORM IN EARTH-CENTERED EARTH-FIXED COORDINATES WITH POINT-MASS GRAVITY MODEL 156 IV. STATE-SPACE FORM IN LOCAL GEODETIC VERTICAL COORDINATES 158 A. STANDARD FORM 158 B. PSEUDO-VELOCITY FORM 162 V. PLATFORM CONTROL LAWS 163 A. EARTH-CENTERED INERTIAL 163 B. EARTH-CENTERED EARTH-FIXED 163 C. LOCAL GEODETIC VERTICALTORQUED AZIMUTH 163 D. LOCAL GEODETIC VERTICALFREE AZIMUTH 164 E. LOCAL GEODETIC VERTICALPLATFORM CAROUSEL 164 F. LOCAL GEODETIC VERTICALPLATFORM TUMBLE 164 VI. INTEGRATION OF THE EQUATIONS OF MOTION 165 IX VII. SUMMARY OF EQUATIONS FOR COMPUTING THE TRANSITION MATRIX 166 A. EARTH-CENTERED INERTIAL COORDINATESSTABILIZED PLATFORM 166 B. EARTH-CENTERED EARTH-FIXED COORDINATESSTABILIZED PLATFORM . 168 C. LOCAL GEODETIC VERTICAL COORDINATESSTANDARD FORMSTABILIZED PLATFORM 169 D. LOCAL GEODETIC VERTICAL COORDINATESPSEUDO-VELOCITY FORMSTABILIZED PLATFORM 171 E. EARTH-CENTERED INERTIAL COORDINATESSTRAPDOWN 172 F. EARTH-CENTERED EARTH-FIXED COORDINATESSTRAPDOWN 174 G. LOCAL GEODETIC VERTICAL COORDINATESSTANDARD FORMSTRAPDOWN. 175 H. LOCAL GEODETIC VERTICAL COORDINATESPSEUDO-VELOCITY FORMSTRAPDOWN 177 PART II INERTIAL NAVIGATION WITH AIDS CHAPTER 9. INERTIAL NAVIGATION WITH EXTERNAL MEASUREMENTS 181 I. BASIS FOR USING EXTERNAL MEASUREMENTS 181 A. EQUATIONS OF RELATIVE MOTION 182 B. APPLICATION OF THE EQUATIONS OF RELATIVE MOTION 184 II. KALMAN FILTER STATE UPDATES 188 A. OVERVIEW OF NAVIGATION COMPUTATIONSEXTENDED KALMAN FILTER . 189 B. GAIN EVALUATION AND COVARIANCE UPDATE 191 C. COVARIANCE PROPAGATION 192 D. SUMMARY OF NAVIGATION EQUATIONSEXTENDED KALMAN FILTER 194 E. SUMMARY OF NAVIGATION EQUATIONSLINEARIZED KALMAN FILTER 194 F. EXAMPLES OF EXTERNAL MEASUREMENT PREDICTIONS 196 G. EXAMPLES OF PARTIAL DERIVATIVE EVALUATIONS 201 H. EXAMPLE OF A SUBOPTIMAL FILTER 205 I. ALIASING 207 CHAPTER 10. ERROR EQUATIONS FOR THE KALMAN FILTER 211 I. ATTITUDE ERRORS 211 A. DEFINITIONS 211 B. ANGULAR EQUIVALENT OF THE POSITION ERROR 212 C. ACTUAL COORDINATE ROTATIONS IN TERMS OF ERRORS 214 D. ATTITUDE ERROR VECTOR DIFFERENTIAL EQUATIONS 214 II. SYSTEM DYNAMIC AND ERROR DISTRIBUTION MATRICES IN EARTH-CENTERED INERTIAL COORDINATES 215 A. ACCELERATIONEARTH-CENTERED INERTIAL COORDINATES 215 B. VELOCITYEARTH-CENTERED INERTIAL COORDINATES 218 C. STATE-SPACE FORM OF ERROR EQUATIONSEARTH-CENTERED INERTIAL COORDINATES 218 III. SYSTEM DYNAMIC AND ERROR DISTRIBUTION MATRICES IN EARTH-CENTERED EARTH-FIXED COORDINATES 219 A. ACCELERATION-R-EARTH-CENTERED EARTH-FIXED COORDINATES 219 B. VELOCITYEARTH-CENTERED EARTH-FIXED COORDINATES 220 C. STATE-SPACE FORM OF ERROR EQUATIONSEARTH-CENTERED EARTH-FIXED COORDINATES ' 220 IV. SYSTEM DYNAMIC AND ERROR DISTRIBUTION MATRICES IN LOCAL GEODETIC VERTICAL COORDINATES 221 A. SEMIPOSITION ERROR DEFINITION 221 B. SEMIVELOCITY ERROR DEFINITION 221 C. ACCELERATIONLOCAL GEODETIC VERTICAL COORDINATES 222 D. VELOCITYLOCAL GEODETIC VERTICAL COORDINATES 224 E. STATE-SPACE FORM OF ERROR EQUATIONSLOCAL GEODETIC VERTICAL COORDINATES 225 CHAPTER 11. STATE VARIABLE ERROR MODELS 227 I. INERTIAL AND EXTERNAL MEASUREMENT EQUIPMENT ERROR SHAPING FUNCTIONS . . 227 A. RANDOM CONSTANT 228 B. RANDOM WALK 228 C. RANDOM RAMP 228 D. MARKOV 229 II. OMISSION GRAVITY MODEL ERROR SHAPING FUNCTIONS 229 A. GRAVITY DATABASE FORMAT 229 B. GRAVITY MODEL ERROR EQUATIONS OF MOTION 230 C. AUTOCORRELATION FUNCTION APPROXIMATION METHOD 232 D. INFLUENCE OF VEHICLE VELOCITY ON THE POWER SPECTRAL DENSITY 235 E. AUTOREGRESSIVE MOVING AVERAGE METHOD 237 PART III ACCURACY ANALYSIS CHAPTER 12. ACCURACY CRITERIA AND ANALYSIS TECHNIQUES 253 I. CENTRAL LIMIT THEOREM 253 II. STANDARD ERROR 254 A. UNCORRELATED STANDARD ERRORS FOR CIRCULAR-ERROR-PROBABLE CALCULATION 254 B. UNCORRELATED STANDARD ERRORS FOR SPHERICAL-ERROR-PROBABLE CALCULATION 255 III. GAUSSIAN DISTRIBUTION FUNCTION FOR NAVIGATION POSITION ERRORS 257 -IV. CIRCULAR ERROR PROBABLE AND SPHERICAL ERROR PROBABLE 257 A. CEP FOR EQUAL STANDARD ERRORS AND ZERO MEANS 257 B. SEP FOR EQUAL STANDARD ERRORS AND ZERO MEANS 259 C. CEP AND SEP FOR UNEQUAL STANDARD ERRORS AND NONZERO MEANS . 260 D. VERIFICATION OF THE CEP AND SEP FORMULAS 264 V. ACCURACY ANALYSIS TECHNIQUES ." 267 A. TYPES OF ERROR 267 B. ERROR ANALYSIS USING SENSITIVITY COEFFICIENTS 271 CHAPTER 13. ERROR EQUATIONS FOR CALIBRATION, ALIGNMENT, AND INITIALIZATION 273 I. INERTIAL INSTRUMENT CALIBRATION 273 A. APPARENT GRAVITY MAGNITUDE 274 B. REFERENCE ROTATION RATE 277 C. POLE LOCATION 278 II. ANALYTICAL ALIGNMENT 279 A. ASTRONOMIC COORDINATES 283 XI B. GEODETIC COORDINATES 284 C. SPECIFIC FORCE AND POLE POSITION 285 III. INITIALIZATION 286 A. INITIAL VELOCITY 286 B. INITIAL POSITION 287 C. CONVERSION TO EARTH-CENTERED INERTIAL AND LOCAL GEODETIC VERTICAL COORDINATES 288 IV. KALMAN FILTER COVARIANCE INITIALIZATION 288 CHAPTER 14. EVALUATION OF GRAVITY MODEL ERROR EFFECTS 291 I. SPHERICAL HARMONIC GRAVITY MODEL ERRORS 292 II. POINT-MASS MODEL GENERATION 293 III. SOURCES OF ERROR FOR POINT-MASS MODEL . . : 294 A. REPRESENTATION 295 B. REDUCTION 295 C. OMISSION 303 APPENDIX A. MATRIX INVERSE FORMULAS 305 APPENDIX B. LAPLACE TRANSFORMS 307 APPENDIX C. QUATERNIONS 311 APPENDIX D. ASSOCIATED LEGENDRE FUNCTIONS 313 APPENDIX E. ASSOCIATED LEGENDRE FUNCTION DERIVATIVES 315 APPENDIX F. PROCEDURE FOR GENERATING GRAVITY DISTURBANCE REALIZATIONS 317 APPENDIX G. PROCEDURE FOR GENERATING SPECIFIC FORCE PROFILE 321 INDEX 325 XII
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spelling	Chatfield, Averil B. Verfasser aut Fundamentals of high accuracy inertial navigation Averil B. Chatfield 2. printing Reston, Va. American Inst. of Aeronautics and Astronautics 1997 XIV, 339 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in astronautics and aeronautics 174 Literaturangaben Navigation par inertie - Mathématiques Inertial navigation Trägheitsnavigation (DE-588)4185821-9 gnd rswk-swf Trägheitsnavigation (DE-588)4185821-9 s DE-604 Progress in astronautics and aeronautics 174 (DE-604)BV001890233 174 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015385299&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Chatfield, Averil B. Fundamentals of high accuracy inertial navigation Progress in astronautics and aeronautics Navigation par inertie - Mathématiques Inertial navigation Trägheitsnavigation (DE-588)4185821-9 gnd
subject_GND	(DE-588)4185821-9
title	Fundamentals of high accuracy inertial navigation
title_auth	Fundamentals of high accuracy inertial navigation
title_exact_search	Fundamentals of high accuracy inertial navigation
title_exact_search_txtP	Fundamentals of high accuracy inertial navigation
title_full	Fundamentals of high accuracy inertial navigation Averil B. Chatfield
title_fullStr	Fundamentals of high accuracy inertial navigation Averil B. Chatfield
title_full_unstemmed	Fundamentals of high accuracy inertial navigation Averil B. Chatfield
title_short	Fundamentals of high accuracy inertial navigation
title_sort	fundamentals of high accuracy inertial navigation
topic	Navigation par inertie - Mathématiques Inertial navigation Trägheitsnavigation (DE-588)4185821-9 gnd
topic_facet	Navigation par inertie - Mathématiques Inertial navigation Trägheitsnavigation
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