Statistical orbit determination:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Elsevier Academic Press
2004
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| Schlagworte: | |
| Online-Zugang: | Table of contents Publisher description Inhaltsverzeichnis |
| Beschreibung: | XV, 547 S. Ill. 24 cm |
| ISBN: | 0126836302 |
Internformat
MARC
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| 100 | 1 | |a Tapley, Byron D. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Statistical orbit determination |c Byron D. Tapley ; Bob E. Schutz ; George H. Born |
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier Academic Press |c 2004 | |
| 300 | |a XV, 547 S. |b Ill. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Mécanique orbitale | |
| 650 | 4 | |a Satellites artificiels - Orbites - Modèles mathématiques | |
| 650 | 4 | |a Trajectoires spatiales | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Orbital mechanics | |
| 650 | 4 | |a Artificial satellites |x Orbits |x Mathematical models | |
| 650 | 4 | |a Space trajectories | |
| 650 | 0 | 7 | |a Bahnelement |0 (DE-588)4326738-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Satellit |0 (DE-588)4136498-3 |2 gnd |9 rswk-swf |
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| 655 | 7 | |0 (DE-588)4056995-0 |a Statistik |2 gnd-content | |
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| 689 | 0 | 2 | |a Bahnelement |0 (DE-588)4326738-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Schutz, Bob E. |e Sonstige |4 oth | |
| 700 | 1 | |a Born, George H. |e Sonstige |4 oth | |
| 856 | 4 | |u http://www.loc.gov/catdir/toc/els051/2004043275.html |3 Table of contents | |
| 856 | 4 | |u http://www.loc.gov/catdir/description/els051/2004043275.html |3 Publisher description | |
| 856 | 4 | 2 | |m GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014661574&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804135159448993792 |
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| adam_text | STATISTICAL ORBIT DETERMINATION BYRON D. TAPLEY CENTER FOR SPACE
RESEARCH THE UNIVERSITY OF TEXAS AT AUSTIN BOB E. SCHUTZ CENTER FOR
SPACE RESEARCH THE UNIVERSITY OF TEXAS AT AUSTIN GEORGE H. BORN COLORADO
CENTER FOR ASTRODYNAMICS RESEARCH UNIVERSITY OF COLORADO, BOULDER
ELSEVIER ACADEMIC PRESS AMSTERDAM * BOSTON * HEIDELBERG * LONDON * NEW
YORK * OXFORD PARIS * SAN DIEGO * SAN FRANCISCO * SINGAPORE * SYDNEY *
TOKYO CONTENTS PREFACE XI 1 ORBIT DETERMINATION CONCEPTS 1 1.1
INTRODUCTION 1 1.2 UNIFORM GRAVITY FIELD MODEL 3 1.2.1 FORMULATION OF
THE PROBLEM 4 1.2.2 THE EQUATION OF THE ORBIT 5 1.2.3 THE ROLE OF THE
OBSERVATION 5 1.2.4 LINEARIZATION PROCEDURE 9 1.2.5 STATE TRANSITION
MATRIX 11 1.3 BACKGROUND AND OVERVIEW 13 1.4 SUMMARY 14 1.5 REFERENCES
15 1.6 EXERCISES 16 2 THE ORBIT PROBLEM 17 2.1 HISTORICAL BACKGROUND 17
2.2 PROBLEM OF TWO BODIES: GENERAL PROPERTIES . 19 2.2.1 MOTION IN THE
PLANE 21 2.2.2 MOTION IN SPACE 28 2.2.3 BASIC COORDINATE SYSTEMS 29
2.2.4 ORBIT ELEMENTS AND POSITION/VELOCITY 32 2.2.5 POSITION/VELOCITY
PREDICTION 35 2.2.6 STATE TRANSITION MATRIX AND ERROR PROPAGATION 40 2.3
PERTURBED MOTION 44 2.3.1 CLASSICAL EXAMPLE: LUNAR PROBLEM 45 2.3.2
VARIATION OF PARAMETERS 48 2.3.3 GRAVITATIONAL PERTURBATIONS: MASS
DISTRIBUTION 50 2.3.4 GRAVITATIONAL PERTURBATIONS: OBLATENESS AND OTHER
EFFECTS 56 2.3.5 GRAVITATIONAL PERTURBATIONS: THIRD-BODY EFFECTS 61 IN
IV CONTENTS 2.3.6 GRAVITATIONAL PERTURBATIONS: TEMPORAL CHANGES IN
GRAVITY 64 2.3.7 GRAVITATIONAL PERTURBATIONS: GENERAL RELATIVITY 65
2.3.8 NONGRAVITATIONAL PERTURBATIONS: ATMOSPHERIC RESISTANCE . 66 2.3.9
NONGRAVITATIONAL PERTURBATIONS: RADIATION PRESSURE .... 68 2.3.10
NONGRAVITATIONAL PERTURBATIONS: OTHER 68 2.3.11 PERTURBED EQUATIONS OF
MOTION: SUMMARY 69 2.4 COORDINATE SYSTEMS AND TIME: INTRODUCTION 71
2.4.1 PRECESSION AND NUTATION 71 2.4.2 EARTH ROTATION AND TIME 74 2.4.3
EARTH-FIXED AND TOPOCENTRIC SYSTEMS 77 2.4.4 TRANSFORMATION BETWEEN ECF
AND ECI 82 2.5 ORBIT ACCURACY 82 2.6 REFERENCES 84 2.7 EXERCISES 87 3
OBSERVATIONS 93 3.1 INTRODUCTION 93 3.2 OBSERVATIONS 94 3.2.1 IDEAL
RANGE 94 3.2.2 IDEAL RANGE-RATE 95 3.2.3 IDEAL AZIMUTH AND ELEVATION
ANGLES 95 3.2.4 EXAMPLES: IDEAL OBSERVATIONS 95 3.3 CONCEPTUAL
MEASUREMENT SYSTEMS 99 3.3.1 RANGE 99 3.3.2 RANGE-RATE 107 3.4
REALIZATION OF MEASUREMENTS 110 3.4.1 CONSIDERATIONS 110 3.4.2
ATMOSPHERIC EFFECTS 110 3.4.3 GENERAL RELATIVITY 115 3.5 MEASUREMENT
SYSTEMS 116 3.5.1 ONE-WAY RANGE 116 3.5.2 TWO-WAY RANGE 125 3.5.3
DOPPLER SYSTEMS 132 3.5.4 EXAMPLES 134 3.6 DIFFERENCED MEASUREMENTS 139
3.6.1 DIFFERENCED GPS MEASUREMENTS 140 3.6.2 DIFFERENCED ALTIMETER DATA
145 3.7 SATELLITE POSITIONS 147 3.8 ANGLES 148 3.9 REFERENCES 149 3.10
EXERCISES 151 CONTENTS V 4 FUNDAMENTALS OF ORBIT DETERMINATION 159 4.1
INTRODUCTION 159 4.2 LINEARIZATION OF THE ORBIT DETERMINATION PROCESS
160 4.2.1 THE STATE TRANSITION MATRIX 164 4.2.2 SOLUTION FOR THE STATE
TRANSITION MATRIX 167 4.2.3 RELATING THE OBSERVATIONS TO AN EPOCH STATE
172 4.3 THE LEAST SQUARES SOLUTION 173 4.3.1 THE MINIMUM NORM SOLUTION
174 4.3.2 SHORTCOMINGS OF THE LEAST SQUARES SOLUTION 176 4.3.3 WEIGHTED
LEAST SQUARES SOLUTION 176 4.3.4 AN ALTERNATE LEAST SQUARES APPROACH 178
4.4 THE MINIMUM VARIANCE ESTIMATE 183 4.4.1 PROPAGATION OF THE ESTIMATE
AND COVARIANCE MATRIX .... 188 4.4.2 MINIMUM VARIANCE ESTIMATE WITH A
PRIORI INFORMATION . . 188 4.5 MAXIMUM LIKELIHOOD AND BAYESIAN
ESTIMATION 190 4.6 COMPUTATIONAL ALGORITHM FOR THE BATCH PROCESSOR 194
4.7 THE SEQUENTIAL ESTIMATION ALGORITHM 199 4.7.1 THE SEQUENTIAL
COMPUTATIONAL ALGORITHM 201 4.7.2 THE EXTENDED SEQUENTIAL ESTIMATION
ALGORITHM 209 4.7.3 THE EXTENDED SEQUENTIAL COMPUTATIONAL ALGORITHM ....
210 4.7.4 THE PREDICTION RESIDUAL 210 4.8 EXAMPLE PROBLEMS 211 4.8.1
LINEAR SYSTEM 211 4.8.2 SPRING-MASS PROBLEM 216 4.9 STATE NOISE
COMPENSATION ALGORITHM 220 4.9.1 THE GAUSS-MARKOV PROCESS 230 4.10
INFORMATION FILTER 233 4.11 BATCH AND SEQUENTIAL ESTIMATION 237 4.12
OBSERVABILITY 237 4.13 ERROR SOURCES 241 4.14 ORBIT ACCURACY 244 4.15
SMOOTHING 246 4.15.1 COMPUTATIONAL ALGORITHM FOR SMOOTHER 250 4.16 THE
PROBABILITY ELLIPSOID 251 4.16.1 TRANSFORMATION OF THE COVARIANCE MATRIX
BETWEEN COORDINATE SYSTEMS 257 4.17 COMBINING ESTIMATES 258 4.18
REFERENCES 261 4.19 EXERCISES 264 VI CONTENTS 5 SQUARE ROOT SOLUTION
METHODS 285 5.1 INTRODUCTION 285 5.2 CHOLESKY DECOMPOSITION 286 5.2.1
THE CHOLESKY ALGORITHM 287 5.2.2 THE SQUARE ROOT FREE CHOLESKY ALGORITHM
288 5.3 LEAST SQUARES SOLUTION VIA ORTHOGONAL TRANSFORMATION 290 5.4
GIVENS TRANSFORMATIONS 291 5.4.1 A PRIORI INFORMATION AND INITIALIZATION
294 5.4.2 GIVENS COMPUTATIONAL ALGORITHM 298 5.4.3 SQUARE ROOT FREE
GIVENS TRANSFORMATION 301 5.4.4 SQUARE ROOT FREE GIVENS COMPUTATIONAL
ALGORITHM . . . . 305 5.4.5 A SIMPLIFIED SQUARE ROOT FREE GIVENS
TRANSFORMATION . .307 5.4.6 IMPLEMENTATION CONSIDERATIONS 309 5.5 THE
HOUSEHOLDER TRANSFORMATION 310 5.5.1 APPLICATION TO THE SOLUTION OF THE
LEAST SQUARES PROBLEM . 315 5.5.2 HOUSEHOLDER COMPUTATIONAL ALGORITHM
316 5.6 NUMERICAL EXAMPLES 318 5.6.1 CHOLESKY DECOMPOSITION 318 5.6.2
GIVENS TRANSFORMATION 320 5.6.3 HOUSEHOLDER TRANSFORMATION 322 5.6.4 A
MORE ILLUSTRATIVE EXAMPLE 324 5.6.5 CHOLESKY DECOMPOSITION 325 5.6.6
SQUARE ROOT FREE GIVENS TRANSFORMATION 326 5.6.7 THE HOUSEHOLDER
TRANSFORMATION 329 5.7 SQUARE ROOT FILTER ALGORITHMS 330 5.7.1 THE
SQUARE ROOT MEASUREMENT UPDATE ALGORITHMS .... 332 5.7.2 SQUARE ROOT
FREE MEASUREMENT UPDATE ALGORITHMS .... 340 5.8 TIME UPDATE OF THE
ESTIMATION ERROR COVARIANCE MATRIX 343 5.9 CONTINUOUS STATE ERROR
COVARIANCE PROPAGATION 346 5.9.1 TRIANGULAR SQUARE ROOT ALGORITHM 349
5.10 THE SQUARE ROOT INFORMATION FILTER 351 5.10.1 THE SQUARE ROOT
INFORMATION FILTER WITH TIME-DEPENDENT EFFECTS 353 5.10.2 THE DYNAMIC
CASE WITH PROCESS NOISE 358 5.10.3 SRIF COMPUTATIONAL ALGORITHM 363
5.10.4 SMOOTHING WITH THE SRIF 364 5.11 PROCESS NOISE PARAMETER
FILTERING/SMOOTHING USING A SRIF . . . 369 5.11.1 EXPONENTIALLY
CORRELATED PROCESS NOISE SRIF 371 5.11.2 SMOOTHING WITH A SRIF 377 5.12
REFERENCES 380 5.13 EXERCISES 381 CONTENTS VII 6 CONSIDER COVARIANCE
ANALYSIS 387 6.1 INTRODUCTION 387 6.2 BIAS IN LINEAR ESTIMATION PROBLEMS
388 6.3 FORMULATION OF THE CONSIDER COVARIANCE MATRIX 389 6.4 THE
SENSITIVITY AND PERTURBATION MATRICES 397 6.4.1 EXAMPLE APPLICATION OF A
SENSITIVITY AND PERTURBATION MATRIX 398 6.5 INCLUSION OF TIME-DEPENDENT
EFFECTS 400 6.6 PROPAGATION OF THE ERROR COVARIANCE 405 6.7 SEQUENTIAL
CONSIDER COVARIANCE ANALYSIS 407 6.8 EXAMPLE: FREELY FALLING POINT MASS
410 6.8.1 PROPAGATION WITH TIME 415 6.8.2 THE SEQUENTIAL CONSIDER
ALGORITHM 416 6.8.3 PERTURBATION IN THE STATE ESTIMATE 419 6.9 EXAMPLE:
SPRING-MASS PROBLEM 420 6.10 ERRORS IN THE OBSERVATION NOISE AND A
PRIORI STATE COVARIANCES . . 425 6.11 ERRORS IN PROCESS NOISE,
OBSERVATION NOISE, AND STATE COVARIANCE 427 6.12 COVARIANCE ANALYSIS AND
ORTHOGONAL TRANSFORMATIONS 430 6.13 REFERENCES 434 6.14 EXERCISES 435 A
PROBABILITY AND STATISTICS 439 A.I INTRODUCTION 439 A.2 AXIOMS OF
PROBABILITY 440 A.3 CONDITIONAL PROBABILITY 443 A.4 PROBABILITY DENSITY
AND DISTRIBUTION FUNCTIONS 443 A.5 EXPECTED VALUES 445 A.6 EXAMPLES AND
DISCUSSION OF EXPECTATION 446 A.7 MOMENT GENERATING FUNCTIONS 448 A.8
SOME IMPORTANT CONTINUOUS DISTRIBUTIONS 449 A.8.1 UNIFORM OR RECTANGULAR
DISTRIBUTION 449 A.8.2 THE GAUSSIAN OR NORMAL DISTRIBUTION 450 A.9 TWO
RANDOM VARIABLES 452 A. 10 MARGINAL DISTRIBUTIONS 453 A. 11 INDEPENDENCE
OF RANDOM VARIABLES 454 A.12 CONDITIONAL PROBABILITY 454 A. 13 EXPECTED
VALUES OF BIVARIATE FUNCTIONS 455 A. 14 THE VARIANCE-COVARIANCE MATRIX
456 A.15 PROPERTIES OF THE CORRELATION COEFFICIENT 458 A. 16 PROPERTIES
OF COVARIANCE AND CORRELATION 460 A. 17 BIVARIATE NORMAL DISTRIBUTION
460 A.18 MARGINAL DISTRIBUTIONS 461 VIII CONTENTS A. 19 THE MULTIVANATE
NORMAL DISTRIBUTION 462 A. 19.1 THE CONDITIONAL DISTRIBUTION FOR
MULTIVARIATE NORMAL VARIABLES 464 A.20 THE CENTRAL LIMIT THEOREM 465
A.21 BAYES THEOREM 465 A.22 STOCHASTIC PROCESSES 467 A.22.1 DEFINITIONS
FOR STOCHASTIC PROCESSES 469 A.23 REFERENCES 471 B REVIEW OF MATRIX
CONCEPTS 473 B.I INTRODUCTION 473 B.2 RANK 475 B.3 QUADRATIC FORMS 475
B.4 DETERMINANTS 476 B.5 MATRIX TRACE 477 B.6 EIGENVALUES AND
EIGENVECTORS 478 B.7 THE DERIVATIVES OF MATRICES AND VECTORS 478 B.8
MAXIMA AND MINIMA 480 B.9 USEFUL MATRIX INVERSION THEOREMS 481 B.10
REFERENCE 483 C EQUATIONS OF MOTION 485 C.I LAGRANGE PLANETARY EQUATIONS
485 C.2 GAUSSIAN FORM 485 C.3 REFERENCES 486 D CONSTANTS 487 D.I
PHYSICAL CONSTANTS 487 D.2 EARTH CONSTANTS 487 D.3 LUNAR, SOLAR, AND
PLANETARY MASSES 488 D.4 REFERENCES 490 E ANALYTICAL THEORY FOR
NEAR-CIRCULAR ORBITS 493 E.I DESCRIPTION 493 E.2 EXAMPLE 497 E.3
REFERENCES 497 F EXAMPLE OF STATE NOISE AND DYNAMIC MODEL COMPENSATION
499 F.I INTRODUCTION 499 F.2 STATE NOISE COMPENSATION 501 F.3 DYNAMIC
MODEL COMPENSATION 505 F.4 REFERENCE 509 CONTENTS IX G SOLUTION OF THE
LINEARIZED EQUATIONS OF MOTION 511 G.I INTRODUCTION 511 G.2 THE STATE
TRANSITION MATRIX 513 H TRANSFORMATION BETWEEN ECI AND ECF COORDINATES
517 H.I INTRODUCTION 517 H.2 MATRIX P 518 H.3 MATRIX N 519 H.4 MATRIX S
519 H.5 MATRIX W 521 H.6 REFERENCES 521 BIBLIOGRAPHY ABBREVIATIONS 523
BIBLIOGRAPHY 525 AUTHOR INDEX 537 INDEX 541
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| adam_txt |
STATISTICAL ORBIT DETERMINATION BYRON D. TAPLEY CENTER FOR SPACE
RESEARCH THE UNIVERSITY OF TEXAS AT AUSTIN BOB E. SCHUTZ CENTER FOR
SPACE RESEARCH THE UNIVERSITY OF TEXAS AT AUSTIN GEORGE H. BORN COLORADO
CENTER FOR ASTRODYNAMICS RESEARCH UNIVERSITY OF COLORADO, BOULDER
ELSEVIER ACADEMIC PRESS AMSTERDAM * BOSTON * HEIDELBERG * LONDON * NEW
YORK * OXFORD PARIS * SAN DIEGO * SAN FRANCISCO * SINGAPORE * SYDNEY *
TOKYO CONTENTS PREFACE XI 1 ORBIT DETERMINATION CONCEPTS 1 1.1
INTRODUCTION 1 1.2 UNIFORM GRAVITY FIELD MODEL 3 1.2.1 FORMULATION OF
THE PROBLEM 4 1.2.2 THE EQUATION OF THE ORBIT 5 1.2.3 THE ROLE OF THE
OBSERVATION 5 1.2.4 LINEARIZATION PROCEDURE 9 1.2.5 STATE TRANSITION
MATRIX 11 1.3 BACKGROUND AND OVERVIEW 13 1.4 SUMMARY 14 1.5 REFERENCES
15 1.6 EXERCISES 16 2 THE ORBIT PROBLEM 17 2.1 HISTORICAL BACKGROUND 17
2.2 PROBLEM OF TWO BODIES: GENERAL PROPERTIES . 19 2.2.1 MOTION IN THE
PLANE 21 2.2.2 MOTION IN SPACE 28 2.2.3 BASIC COORDINATE SYSTEMS 29
2.2.4 ORBIT ELEMENTS AND POSITION/VELOCITY 32 2.2.5 POSITION/VELOCITY
PREDICTION 35 2.2.6 STATE TRANSITION MATRIX AND ERROR PROPAGATION 40 2.3
PERTURBED MOTION 44 2.3.1 CLASSICAL EXAMPLE: LUNAR PROBLEM 45 2.3.2
VARIATION OF PARAMETERS 48 2.3.3 GRAVITATIONAL PERTURBATIONS: MASS
DISTRIBUTION 50 2.3.4 GRAVITATIONAL PERTURBATIONS: OBLATENESS AND OTHER
EFFECTS 56 2.3.5 GRAVITATIONAL PERTURBATIONS: THIRD-BODY EFFECTS 61 IN
IV CONTENTS 2.3.6 GRAVITATIONAL PERTURBATIONS: TEMPORAL CHANGES IN
GRAVITY 64 2.3.7 GRAVITATIONAL PERTURBATIONS: GENERAL RELATIVITY 65
2.3.8 NONGRAVITATIONAL PERTURBATIONS: ATMOSPHERIC RESISTANCE . 66 2.3.9
NONGRAVITATIONAL PERTURBATIONS: RADIATION PRESSURE . 68 2.3.10
NONGRAVITATIONAL PERTURBATIONS: OTHER 68 2.3.11 PERTURBED EQUATIONS OF
MOTION: SUMMARY 69 2.4 COORDINATE SYSTEMS AND TIME: INTRODUCTION 71
2.4.1 PRECESSION AND NUTATION 71 2.4.2 EARTH ROTATION AND TIME 74 2.4.3
EARTH-FIXED AND TOPOCENTRIC SYSTEMS 77 2.4.4 TRANSFORMATION BETWEEN ECF
AND ECI 82 2.5 ORBIT ACCURACY 82 2.6 REFERENCES 84 2.7 EXERCISES 87 3
OBSERVATIONS 93 3.1 INTRODUCTION 93 3.2 OBSERVATIONS 94 3.2.1 IDEAL
RANGE 94 3.2.2 IDEAL RANGE-RATE 95 3.2.3 IDEAL AZIMUTH AND ELEVATION
ANGLES 95 3.2.4 EXAMPLES: IDEAL OBSERVATIONS 95 3.3 CONCEPTUAL
MEASUREMENT SYSTEMS 99 3.3.1 RANGE 99 3.3.2 RANGE-RATE 107 3.4
REALIZATION OF MEASUREMENTS 110 3.4.1 CONSIDERATIONS 110 3.4.2
ATMOSPHERIC EFFECTS 110 3.4.3 GENERAL RELATIVITY 115 3.5 MEASUREMENT
SYSTEMS 116 3.5.1 ONE-WAY RANGE 116 3.5.2 TWO-WAY RANGE 125 3.5.3
DOPPLER SYSTEMS 132 3.5.4 EXAMPLES 134 3.6 DIFFERENCED MEASUREMENTS 139
3.6.1 DIFFERENCED GPS MEASUREMENTS 140 3.6.2 DIFFERENCED ALTIMETER DATA
145 3.7 SATELLITE POSITIONS 147 3.8 ANGLES 148 3.9 REFERENCES 149 3.10
EXERCISES 151 CONTENTS V 4 FUNDAMENTALS OF ORBIT DETERMINATION 159 4.1
INTRODUCTION 159 4.2 LINEARIZATION OF THE ORBIT DETERMINATION PROCESS
160 4.2.1 THE STATE TRANSITION MATRIX 164 4.2.2 SOLUTION FOR THE STATE
TRANSITION MATRIX 167 4.2.3 RELATING THE OBSERVATIONS TO AN EPOCH STATE
172 4.3 THE LEAST SQUARES SOLUTION 173 4.3.1 THE MINIMUM NORM SOLUTION
174 4.3.2 SHORTCOMINGS OF THE LEAST SQUARES SOLUTION 176 4.3.3 WEIGHTED
LEAST SQUARES SOLUTION 176 4.3.4 AN ALTERNATE LEAST SQUARES APPROACH 178
4.4 THE MINIMUM VARIANCE ESTIMATE 183 4.4.1 PROPAGATION OF THE ESTIMATE
AND COVARIANCE MATRIX . 188 4.4.2 MINIMUM VARIANCE ESTIMATE WITH A
PRIORI INFORMATION . . 188 4.5 MAXIMUM LIKELIHOOD AND BAYESIAN
ESTIMATION 190 4.6 COMPUTATIONAL ALGORITHM FOR THE BATCH PROCESSOR 194
4.7 THE SEQUENTIAL ESTIMATION ALGORITHM 199 4.7.1 THE SEQUENTIAL
COMPUTATIONAL ALGORITHM 201 4.7.2 THE EXTENDED SEQUENTIAL ESTIMATION
ALGORITHM 209 4.7.3 THE EXTENDED SEQUENTIAL COMPUTATIONAL ALGORITHM .
210 4.7.4 THE PREDICTION RESIDUAL 210 4.8 EXAMPLE PROBLEMS 211 4.8.1
LINEAR SYSTEM 211 4.8.2 SPRING-MASS PROBLEM 216 4.9 STATE NOISE
COMPENSATION ALGORITHM 220 4.9.1 THE GAUSS-MARKOV PROCESS 230 4.10
INFORMATION FILTER 233 4.11 BATCH AND SEQUENTIAL ESTIMATION 237 4.12
OBSERVABILITY 237 4.13 ERROR SOURCES 241 4.14 ORBIT ACCURACY 244 4.15
SMOOTHING 246 4.15.1 COMPUTATIONAL ALGORITHM FOR SMOOTHER 250 4.16 THE
PROBABILITY ELLIPSOID 251 4.16.1 TRANSFORMATION OF THE COVARIANCE MATRIX
BETWEEN COORDINATE SYSTEMS 257 4.17 COMBINING ESTIMATES 258 4.18
REFERENCES 261 4.19 EXERCISES 264 VI CONTENTS 5 SQUARE ROOT SOLUTION
METHODS 285 5.1 INTRODUCTION 285 5.2 CHOLESKY DECOMPOSITION 286 5.2.1
THE CHOLESKY ALGORITHM 287 5.2.2 THE SQUARE ROOT FREE CHOLESKY ALGORITHM
288 5.3 LEAST SQUARES SOLUTION VIA ORTHOGONAL TRANSFORMATION 290 5.4
GIVENS TRANSFORMATIONS 291 5.4.1 A PRIORI INFORMATION AND INITIALIZATION
294 5.4.2 GIVENS COMPUTATIONAL ALGORITHM 298 5.4.3 SQUARE ROOT FREE
GIVENS TRANSFORMATION 301 5.4.4 SQUARE ROOT FREE GIVENS COMPUTATIONAL
ALGORITHM . . . . 305 5.4.5 A SIMPLIFIED SQUARE ROOT FREE GIVENS
TRANSFORMATION . .307 5.4.6 IMPLEMENTATION CONSIDERATIONS 309 5.5 THE
HOUSEHOLDER TRANSFORMATION 310 5.5.1 APPLICATION TO THE SOLUTION OF THE
LEAST SQUARES PROBLEM . 315 5.5.2 HOUSEHOLDER COMPUTATIONAL ALGORITHM
316 5.6 NUMERICAL EXAMPLES 318 5.6.1 CHOLESKY DECOMPOSITION 318 5.6.2
GIVENS TRANSFORMATION 320 5.6.3 HOUSEHOLDER TRANSFORMATION 322 5.6.4 A
MORE ILLUSTRATIVE EXAMPLE 324 5.6.5 CHOLESKY DECOMPOSITION 325 5.6.6
SQUARE ROOT FREE GIVENS TRANSFORMATION 326 5.6.7 THE HOUSEHOLDER
TRANSFORMATION 329 5.7 SQUARE ROOT FILTER ALGORITHMS 330 5.7.1 THE
SQUARE ROOT MEASUREMENT UPDATE ALGORITHMS . 332 5.7.2 SQUARE ROOT
FREE MEASUREMENT UPDATE ALGORITHMS . 340 5.8 TIME UPDATE OF THE
ESTIMATION ERROR COVARIANCE MATRIX 343 5.9 CONTINUOUS STATE ERROR
COVARIANCE PROPAGATION 346 5.9.1 TRIANGULAR SQUARE ROOT ALGORITHM 349
5.10 THE SQUARE ROOT INFORMATION FILTER 351 5.10.1 THE SQUARE ROOT
INFORMATION FILTER WITH TIME-DEPENDENT EFFECTS 353 5.10.2 THE DYNAMIC
CASE WITH PROCESS NOISE 358 5.10.3 SRIF COMPUTATIONAL ALGORITHM 363
5.10.4 SMOOTHING WITH THE SRIF 364 5.11 PROCESS NOISE PARAMETER
FILTERING/SMOOTHING USING A SRIF . . . 369 5.11.1 EXPONENTIALLY
CORRELATED PROCESS NOISE SRIF 371 5.11.2 SMOOTHING WITH A SRIF 377 5.12
REFERENCES 380 5.13 EXERCISES 381 CONTENTS VII 6 CONSIDER COVARIANCE
ANALYSIS 387 6.1 INTRODUCTION 387 6.2 BIAS IN LINEAR ESTIMATION PROBLEMS
388 6.3 FORMULATION OF THE CONSIDER COVARIANCE MATRIX 389 6.4 THE
SENSITIVITY AND PERTURBATION MATRICES 397 6.4.1 EXAMPLE APPLICATION OF A
SENSITIVITY AND PERTURBATION MATRIX 398 6.5 INCLUSION OF TIME-DEPENDENT
EFFECTS 400 6.6 PROPAGATION OF THE ERROR COVARIANCE 405 6.7 SEQUENTIAL
CONSIDER COVARIANCE ANALYSIS 407 6.8 EXAMPLE: FREELY FALLING POINT MASS
410 6.8.1 PROPAGATION WITH TIME 415 6.8.2 THE SEQUENTIAL CONSIDER
ALGORITHM 416 6.8.3 PERTURBATION IN THE STATE ESTIMATE 419 6.9 EXAMPLE:
SPRING-MASS PROBLEM 420 6.10 ERRORS IN THE OBSERVATION NOISE AND A
PRIORI STATE COVARIANCES . . 425 6.11 ERRORS IN PROCESS NOISE,
OBSERVATION NOISE, AND STATE COVARIANCE 427 6.12 COVARIANCE ANALYSIS AND
ORTHOGONAL TRANSFORMATIONS 430 6.13 REFERENCES 434 6.14 EXERCISES 435 A
PROBABILITY AND STATISTICS 439 A.I INTRODUCTION 439 A.2 AXIOMS OF
PROBABILITY 440 A.3 CONDITIONAL PROBABILITY 443 A.4 PROBABILITY DENSITY
AND DISTRIBUTION FUNCTIONS 443 A.5 EXPECTED VALUES 445 A.6 EXAMPLES AND
DISCUSSION OF EXPECTATION 446 A.7 MOMENT GENERATING FUNCTIONS 448 A.8
SOME IMPORTANT CONTINUOUS DISTRIBUTIONS 449 A.8.1 UNIFORM OR RECTANGULAR
DISTRIBUTION 449 A.8.2 THE GAUSSIAN OR NORMAL DISTRIBUTION 450 A.9 TWO
RANDOM VARIABLES 452 A. 10 MARGINAL DISTRIBUTIONS 453 A. 11 INDEPENDENCE
OF RANDOM VARIABLES 454 A.12 CONDITIONAL PROBABILITY 454 A. 13 EXPECTED
VALUES OF BIVARIATE FUNCTIONS 455 A. 14 THE VARIANCE-COVARIANCE MATRIX
456 A.15 PROPERTIES OF THE CORRELATION COEFFICIENT 458 A. 16 PROPERTIES
OF COVARIANCE AND CORRELATION 460 A. 17 BIVARIATE NORMAL DISTRIBUTION
460 A.18 MARGINAL DISTRIBUTIONS 461 VIII CONTENTS A. 19 THE MULTIVANATE
NORMAL DISTRIBUTION 462 A. 19.1 THE CONDITIONAL DISTRIBUTION FOR
MULTIVARIATE NORMAL VARIABLES 464 A.20 THE CENTRAL LIMIT THEOREM 465
A.21 BAYES THEOREM 465 A.22 STOCHASTIC PROCESSES 467 A.22.1 DEFINITIONS
FOR STOCHASTIC PROCESSES 469 A.23 REFERENCES 471 B REVIEW OF MATRIX
CONCEPTS 473 B.I INTRODUCTION 473 B.2 RANK 475 B.3 QUADRATIC FORMS 475
B.4 DETERMINANTS 476 B.5 MATRIX TRACE 477 B.6 EIGENVALUES AND
EIGENVECTORS 478 B.7 THE DERIVATIVES OF MATRICES AND VECTORS 478 B.8
MAXIMA AND MINIMA 480 B.9 USEFUL MATRIX INVERSION THEOREMS 481 B.10
REFERENCE 483 C EQUATIONS OF MOTION 485 C.I LAGRANGE PLANETARY EQUATIONS
485 C.2 GAUSSIAN FORM 485 C.3 REFERENCES 486 D CONSTANTS 487 D.I
PHYSICAL CONSTANTS 487 D.2 EARTH CONSTANTS 487 D.3 LUNAR, SOLAR, AND
PLANETARY MASSES 488 D.4 REFERENCES 490 E ANALYTICAL THEORY FOR
NEAR-CIRCULAR ORBITS 493 E.I DESCRIPTION 493 E.2 EXAMPLE 497 E.3
REFERENCES 497 F EXAMPLE OF STATE NOISE AND DYNAMIC MODEL COMPENSATION
499 F.I INTRODUCTION 499 F.2 STATE NOISE COMPENSATION 501 F.3 DYNAMIC
MODEL COMPENSATION 505 F.4 REFERENCE 509 CONTENTS IX G SOLUTION OF THE
LINEARIZED EQUATIONS OF MOTION 511 G.I INTRODUCTION 511 G.2 THE STATE
TRANSITION MATRIX 513 H TRANSFORMATION BETWEEN ECI AND ECF COORDINATES
517 H.I INTRODUCTION 517 H.2 MATRIX P 518 H.3 MATRIX N 519 H.4 MATRIX S'
519 H.5 MATRIX W 521 H.6 REFERENCES 521 BIBLIOGRAPHY ABBREVIATIONS 523
BIBLIOGRAPHY 525 AUTHOR INDEX 537 INDEX 541 |
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| author | Tapley, Byron D. |
| author_facet | Tapley, Byron D. |
| author_role | aut |
| author_sort | Tapley, Byron D. |
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| building | Verbundindex |
| bvnumber | BV021444574 |
| callnumber-first | T - Technology |
| callnumber-label | TL1050 |
| callnumber-raw | TL1050 |
| callnumber-search | TL1050 |
| callnumber-sort | TL 41050 |
| callnumber-subject | TL - Motor Vehicles and Aeronautics |
| classification_rvk | US 1250 |
| classification_tum | VER 843f |
| ctrlnum | (OCoLC)54529775 (DE-599)BVBBV021444574 |
| dewey-full | 629.4/113 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 629 - Other branches of engineering |
| dewey-raw | 629.4/113 |
| dewey-search | 629.4/113 |
| dewey-sort | 3629.4 3113 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik Verkehrstechnik Verkehr / Transport |
| discipline_str_mv | Physik Verkehrstechnik Verkehr / Transport |
| format | Book |
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| genre | (DE-588)4056995-0 Statistik gnd-content |
| genre_facet | Statistik |
| id | DE-604.BV021444574 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:04:08Z |
| indexdate | 2024-07-09T20:36:04Z |
| institution | BVB |
| isbn | 0126836302 |
| language | English |
| lccn | 2004043275 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014661574 |
| oclc_num | 54529775 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-83 |
| owner_facet | DE-91G DE-BY-TUM DE-83 |
| physical | XV, 547 S. Ill. 24 cm |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Elsevier Academic Press |
| record_format | marc |
| spelling | Tapley, Byron D. Verfasser aut Statistical orbit determination Byron D. Tapley ; Bob E. Schutz ; George H. Born Amsterdam [u.a.] Elsevier Academic Press 2004 XV, 547 S. Ill. 24 cm txt rdacontent n rdamedia nc rdacarrier Mécanique orbitale Satellites artificiels - Orbites - Modèles mathématiques Trajectoires spatiales Mathematisches Modell Orbital mechanics Artificial satellites Orbits Mathematical models Space trajectories Bahnelement (DE-588)4326738-5 gnd rswk-swf Satellit (DE-588)4136498-3 gnd rswk-swf Umlaufbahn (DE-588)4238276-2 gnd rswk-swf (DE-588)4056995-0 Statistik gnd-content Satellit (DE-588)4136498-3 s Umlaufbahn (DE-588)4238276-2 s Bahnelement (DE-588)4326738-5 s DE-604 Schutz, Bob E. Sonstige oth Born, George H. Sonstige oth http://www.loc.gov/catdir/toc/els051/2004043275.html Table of contents http://www.loc.gov/catdir/description/els051/2004043275.html Publisher description GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014661574&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tapley, Byron D. Statistical orbit determination Mécanique orbitale Satellites artificiels - Orbites - Modèles mathématiques Trajectoires spatiales Mathematisches Modell Orbital mechanics Artificial satellites Orbits Mathematical models Space trajectories Bahnelement (DE-588)4326738-5 gnd Satellit (DE-588)4136498-3 gnd Umlaufbahn (DE-588)4238276-2 gnd |
| subject_GND | (DE-588)4326738-5 (DE-588)4136498-3 (DE-588)4238276-2 (DE-588)4056995-0 |
| title | Statistical orbit determination |
| title_auth | Statistical orbit determination |
| title_exact_search | Statistical orbit determination |
| title_exact_search_txtP | Statistical orbit determination |
| title_full | Statistical orbit determination Byron D. Tapley ; Bob E. Schutz ; George H. Born |
| title_fullStr | Statistical orbit determination Byron D. Tapley ; Bob E. Schutz ; George H. Born |
| title_full_unstemmed | Statistical orbit determination Byron D. Tapley ; Bob E. Schutz ; George H. Born |
| title_short | Statistical orbit determination |
| title_sort | statistical orbit determination |
| topic | Mécanique orbitale Satellites artificiels - Orbites - Modèles mathématiques Trajectoires spatiales Mathematisches Modell Orbital mechanics Artificial satellites Orbits Mathematical models Space trajectories Bahnelement (DE-588)4326738-5 gnd Satellit (DE-588)4136498-3 gnd Umlaufbahn (DE-588)4238276-2 gnd |
| topic_facet | Mécanique orbitale Satellites artificiels - Orbites - Modèles mathématiques Trajectoires spatiales Mathematisches Modell Orbital mechanics Artificial satellites Orbits Mathematical models Space trajectories Bahnelement Satellit Umlaufbahn Statistik |
| url | http://www.loc.gov/catdir/toc/els051/2004043275.html http://www.loc.gov/catdir/description/els051/2004043275.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014661574&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT tapleybyrond statisticalorbitdetermination AT schutzbobe statisticalorbitdetermination AT borngeorgeh statisticalorbitdetermination |