Lessons in estimation theory for signal processing, communications, and control:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Englewood Cliffs, NJ
Prentice Hall
1995
|
| Schriftenreihe: | Prentice Hall signal processing series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Frühere Ausg. u.d.T.: Mendel, Jerry M.: Lessons in digital estimation theory |
| Beschreibung: | XIX, 561 S. graph. Darst. |
| ISBN: | 0131209817 |
Internformat
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Datensatz im Suchindex
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| adam_text | LESSONS IN ESTIMATION THEORY FOR SIGNAL PROCESSING, COMMUNICATIONS, AND
CONTROL JERRY M. MENDEL DEPARTMENT OF ELECTRICAL ENGINEERING UNIVERSITY
OF SOUTHERN CALIFORNIA LOS ANGELES, CALIFORNIA PRENTICE HALL PTR
ENGLEWOOD CLIFFS, NEW JERSEY 07632 CONTENTS PREFACE LESSON 1
INTRODUCTION, COVERAGE, PHILOSOPHY, AND COMPUTATION SUMMARY 1
INTRODUCTION 2 COVERAGE 3 PHILOSOPHY 6 COMPUTATION 7 SUMMARY QUESTIONS 8
LESSON 2 THE LINEAR MODEL SUMMARY 9 INTRODUCTION 9 EXAMPLES 10
NOTATIONAL PRELIMINARIES 18 COMPUTATION 20 SUPPLEMENTARY MATERIAL:
CONVOLUTIONAL MODEL IN REFLECTION SEISMOLOGY 21 SUMMARY QUESTIONS 23
PROBLEMS 24 XVII 1 VII LESSON 3 LEAST-SQUARES ESTIMATION: BATCH
PROCESSING SUMMARY 27 INTRODUCTION 27 NUMBER OF MEASUREMENTS 29
OBJECTIVE FUNCTION AND PROBLEM STATEMENT 29 DERIVATION OF ESTIMATOR 30
FIXED AND EXPANDING MEMORY ESTIMATORS 36 SCALE CHANGES AND NORMALIZATION
OF DATA 36 COMPUTATION 37 SUPPLEMENTARY MATERIAL: LEAST SQUARES, TOTAL
LEAST SQUARES, AND CONSTRAINED TOTAL LEAST SQUARES 38 SUMMARY QUESTIONS
39 PROBLEMS 40 LESSON 4 LEAST-SQUARES ESTIMATION: SINGULAR-VALUE
DECOMPOSITION SUMMARY 44 INTRODUCTION 44 SOME FACTS FROM LINEAR ALGEBRA
45 SINGULAR-VALUE DECOMPOSITION 45 USING SVD TO CALCULATE D LS (K) 49
COMPUTATION 51 SUPPLEMENTARY MATERIAL: PSEUDOINVERSE 51 SUMMARY
QUESTIONS 53 PROBLEMS 54 27 44 LESSON 5 LEAST-SQUARES ESTIMATION:
RECURSIVE PROCESSING SUMMARY 58 INTRODUCTION 58 RECURSIVE LEAST SQUARES:
INFORMATION FORM 59 MATRIX INVERSION LEMMA 62 RECURSIVE LEAST SQUARES:
COVARIANCE FORM 63 WHICH FORM TO USE 64 GENERALIZATION TO VECTOR
MEASUREMENTS 66 COMPUTATION 66 SUPPLEMENTARY MATERIAL: DERIVATION OF
START-UP CONDITIONS FOR RECURSIVE ALGORITHMS 67 SUMMARY QUESTIONS 69
PROBLEMS 70 LESSON 6 SMALL-SAMPLE PROPERTIES OF ESTIMATORS SUMMARY 74
INTRODUCTION 75 58 74 VIII CONTENTS UNBIASEDNESS 76 EFFICIENCY 77
SUPPLEMENTARY MATERIAL: PROOF OF THEOREM 6-4 86 SUMMARY QUESTIONS 87
PROBLEMS 88 LESSON 7 LARGE-SAMPLE PROPERTIES OF ESTIMATORS SUMMARY 91
INTRODUCTION 92 STOCHASTIC CONVERGENCE 92 ASYMPTOTIC UNBIASEDNESS 94
CONSISTENCY 95 ASYMPTOTIC DISTRIBUTIONS 99 ASYMPTOTIC NORMALITY 101
ASYMPTOTIC EFFICIENCY 103 SUMMARY QUESTIONS 104 PROBLEMS 105 LESSON 8
PROPERTIES OF LEAST-SQUARES ESTIMATORS SUMMARY 108 INTRODUCTION 109
SMALL-SAMPLE PROPERTIES OF LEAST-SQUARES ESTIMATORS 109 LARGE-SAMPLE
PROPERTIES OF LEAST-SQUARES ESTIMATORS 115 SUPPLEMENTARY MATERIAL:
EXPANSION OF TOTAL EXPECTATION 117 SUMMARY QUESTIONS 117 PROBLEMS 118
LESSON 9 BEST LINEAR UNBIASED ESTIMATION SUMMARY 121 INTRODUCTION 122
PROBLEM STATEMENT AND OBJECTIVE FUNCTION 122 DERIVATION OF ESTIMATOR 124
COMPARISON OF 9BLU(^) AND 0WLS(&) 125 SOME PROPERTIES OF 0BLU() 126
RECURSIVE BLUES 130 COMPUTATION 131 SUPPLEMENTARY MATERIAL: LAGRANGE S
METHOD 131 SUMMARY QUESTIONS 132 PROBLEMS 133 LESSON 10 LIKELIHOOD
SUMMARY 137 LIKELIHOOD DEFINED 137 91 108 121 137 CONTENTS IX LIKELIHOOD
RATIO 140 RESULTS DESCRIBED BY CONTINUOUS DISTRIBUTIONS 141 MULTIPLE
HYPOTHESES 141 DECISION MAKING USING LIKELIHOOD RATIO 142 SUPPLEMENTARY
MATERIAL: TRANSFORMATION OF VARIABLES AND PROBABILITY 144 SUMMARY
QUESTIONS 145 PROBLEMS 145 LESSON 11 MAXIMUM-LIKELIHOOD ESTIMATION
SUMMARY 147 LIKELIHOOD 148 MAXIMUM-LIKELIHOOD METHOD AND ESTIMATES 148
PROPERTIES OF MAXIMUM-LIKELIHOOD ESTIMATES 151 THE LINEAR MODEL [H(&)
DETERMINISTIC] 152 A LOG-LIKELIHOOD FUNCTION FOR AN IMPORTANT DYNAMICAL
SYSTEM COMPUTATION 156 SUMMARY QUESTIONS 157 PROBLEMS 158 LESSON 12
MULTIVARIATE GAUSSIAN RANDOM VARIABLES SUMMARY 164 INTRODUCTION 164
UNIVARIATE GAUSSIAN DENSITY FUNCTION 165 MULTIVARIATE GAUSSIAN DENSITY
FUNCTION 165 JOINTLY GAUSSIAN RANDOM VECTORS 165 THE CONDITIONAL DENSITY
FUNCTION 166 PROPERTIES OF MULTIVARIATE GAUSSIAN RANDOM VARIABLES 168
PROPERTIES OF CONDITIONAL MEAN 169 SUMMARY QUESTIONS 171 PROBLEMS 171
LESSON 13 MEAN-SQUARED ESTIMATION OF RANDOM PARAMETERS SUMMARY 173
INTRODUCTION 174 OBJECTIVE FUNCTION AND PROBLEM STATEMENT 174 DERIVATION
OF ESTIMATOR 175 PROPERTIES OF MEAN-SQUARED ESTIMATORS WHEN 0 AND Z(K)
ARE JOINTLY GAUSSIAN 178 GENERALIZATIONS 179 MEAN-SQUARED ESTIMATOR FOR
THE GENERIC LINEAR AND GAUSSIAN MODEL 179 BEST LINEAR UNBIASED
ESTIMATION, REVISITED 181 COMPUTATION 184 147 154 164 173 CONTENTS
SUPPLEMENTARY MATERIAL: THE CONDITIONAL MEAN ESTIMATOR A NONLINEAR
ESTIMATOR 185 SUMMARY QUESTIONS 188 PROBLEMS 189 184 LESSON 14 MAXIMUM A
POSTERIORI ESTIMATION OF RANDOM PARAMETERS 192 SUMMARY 192 INTRODUCTION
192 GENERAL RESULTS 193 THE GENERIC LINEAR AND GAUSSIAN MODEL 195
COMPUTATION 199 SUPPLEMENTARY MATERIAL: ELEMENTS OF BINARY DETECTION
THEORY 200 SUMMARY QUESTIONS 204 PROBLEMS 205 LESSON 15 ELEMENTS OF
DISCRETE-TIME GAUSS-MARKOV RANDOM SEQUENCES 211 SUMMARY 211 INTRODUCTION
212 DEFINITION AND PROPERTIES OF DISCRETE-TIME GAUSS-MARKOV RANDOM
SEQUENCES 212 THE BASIC STATE-VARIABLE MODEL 215 PROPERTIES OF THE BASIC
STATE-VARIABLE MODEL 216 SIGNAL-TO-NOISE RATIO 220 COMPUTATION 222
SUMMARY QUESTIONS 223 PROBLEMS 224 LESSON 16 STATE ESTIMATION:
PREDICTION 227 SUMMARY 227 INTRODUCTION 228 SINGLE-STAGE PREDICTOR 228 A
GENERAL STATE PREDICTOR 229 THE INNOVATIONS PROCESS 233 COMPUTATION 235
SUPPLEMENTARY MATERIAL: LINEAR PREDICTION 235 SUMMARY QUESTIONS 238
PROBLEMS 239 LESSON 17 STATE ESTIMATION: FILTERING (THE KALMAN FILTER)
242 SUMMARY 242 INTRODUCTION 243 CONTENTS XI A PRELIMINARY RESULT 245
THE KALMAN FILTER 246 OBSERVATIONS ABOUT THE KALMAN FILTER 248
COMPUTATION 253 SUPPLEMENTARY MATERIAL: MAP DERIVATION OF THE KALMAN
FILTER SUMMARY QUESTIONS 255 PROBLEMS 256 253 LESSON 18 STATE
ESTIMATION: FILTERING EXAMPLES SUMMARY 259 INTRODUCTION 260 EXAMPLES 260
SUPPLEMENTARY MATERIAL: APPLICATIONS OF KALMAN FILTERING SUMMARY
QUESTIONS 276 PROBLEMS 277 259 271 LESSON 19 STATE ESTIMATION:
STEADY-STATE KALMAN FILTER AND ITS RELATIONSHIP TO A DIGITAL WIENER
FILTER SUMMARY 279 INTRODUCTION 280 STEADY-STATE KALMAN FILTER 280
SINGLE-CHANNEL STEADY-STATE KALMAN FILTER 282 RELATIONSHIPS BETWEEN THE
STEADY-STATE KALMAN FILTER AND A FINITE IMPULSE RESPONSE DIGITAL WIENER
FILTER 286 COMPARISONS OF KALMAN AND WIENER FILTERS 293 COMPUTATION 294
SUPPLEMENTARY MATERIAL: SOME LINEAR SYSTEM CONCEPTS 294 THE LEVINSON
ALGORITHM 295 SUMMARY QUESTIONS 300 PROBLEMS 301 279 LESSON 20 STATE
ESTIMATION: SMOOTHING SUMMARY 304 THREE TYPES OF SMOOTHERS 305
APPROACHES FOR DERIVING SMOOTHERS 306 A SUMMARY OF IMPORTANT FORMULAS
306 SINGLE-STAGE SMOOTHER 306 DOUBLE-STAGE SMOOTHER 309 SINGLE- AND
DOUBLE-STAGE SMOOTHERS AS GENERAL SMOOTHERS COMPUTATION 314 SUMMARY
QUESTIONS 314 PROBLEMS 315 304 312 XII CONTENTS LESSON 21 STATE
ESTIMATION: SMOOTHING (GENERAL RESULTS) SUMMARY 317 INTRODUCTION 318
FIXED-INTERVAL SMOOTHING 318 FIXED-POINT SMOOTHING 323 FIXED-LAG
SMOOTHING 325 COMPUTATION 328 SUPPLEMENTARY MATERIAL: SECOND-ORDER
GAUSS-MARKOV RANDOM SEQUENCES MINIMUM-VARIANCE DECONVOLUTION (MVD) 329
STEADY-STATE MVD FILTER 332 RELATIONSHIP BETWEEN STEADY-STATE MVD FILTER
AND AN INFINITE IMPULSE RESPONSE DIGITAL WIENER DECONVOLUTION FILTER 338
MAXIMUM-LIKELIHOOD DECONVOLUTION 340 SUMMARY QUESTIONS 341 PROBLEMS 342
317 328 LESSON 22 STATE ESTIMATION FOR THE NOT-SO-BASIC STATE-VARIABLE
MODEL SUMMARY 345 INTRODUCTION 346 BIASES 346 CORRELATED NOISES 347
COLORED NOISES 350 PERFECT MEASUREMENTS: REDUCED-ORDER ESTIMATORS 354
FINAL REMARK 357 COMPUTATION 357 SUPPLEMENTARY MATERIAL: DERIVATION OF
EQUATION (22-14) SUMMARY QUESTIONS 360 PROBLEMS 361 345 359 LESSON 23
LINEARIZATION AND DISCRETIZATION OF NONLINEAR SYSTEMS SUMMARY 364
INTRODUCTION 365 A DYNAMICAL MODEL 365 LINEAR PERTURBATION EQUATIONS 367
DISCRETIZATION OF A LINEAR TIME-VARYING STATE-VARIABLE MODEL 371
DISCRETIZED PERTURBATION STATE-VARIABLE MODEL 374 COMPUTATION 374
SUPPLEMENTARY MATERIAL: PROOF OF THEOREM 23-1 375 SUMMARY QUESTIONS 376
PROBLEMS 377 364 CONTENTS XIII LESSON 24 ITERATED LEAST SQUARES AND
EXTENDED KALMAN FILTERING 384 SUMMARY 384 INTRODUCTION 385 ITERATED
LEAST SQUARES 385 EXTENDED KALMAN FILTER 386 APPLICATION TO PARAMETER
ESTIMATION 391 COMPUTATION 392 SUPPLEMENTARY MATERIAL: EKF FOR A
NONLINEAR DISCRETE-TIME SYSTEM 393 SUMMARY QUESTIONS 394 PROBLEMS 394
LESSON 25 MAXIMUM-LIKELIHOOD STATE AND PARAMETER ESTIMATION 397 SUMMARY
397 INTRODUCTION 398 A LOG-LIKELIHOOD FUNCTION FOR THE BASIC
STATE-VARIABLE MODEL ON COMPUTING 0 M L 400 A STEADY-STATE APPROXIMATION
404 COMPUTATION 408 SUMMARY QUESTIONS 409 PROBLEMS 410 398 LESSON 26
KALMAN-BUCY FILTERING 413 LESSON A SUMMARY 413 INTRODUCTION 413 SYSTEM
DESCRIPTION 414 STATISTICS OF THE STATE VECTOR 415 NOTATION AND PROBLEM
STATEMENT 416 THE KALMAN-BUCY FILTER 417 DERIVATION OF KBF USING A
FORMAL LIMITING PROCEDURE 418 STEADY-STATE KBF 421 AN IMPORTANT
APPLICATION FOR THE KBF 423 COMPUTATION 426 SUPPLEMENTARY MATERIAL:
PROOF OF THEOREM 26-1 427 DERIVATION OF THE KBF WHEN THE STRUCTURE OF
THE FILTER IS PRESPECIFIED 428 SUMMARY QUESTIONS 431 PROBLEMS 432
SUFFICIENT STATISTICS AND STATISTICAL ESTIMATION OF PARAMETERS SUMMARY
436 INTRODUCTION 437 436 XIV CONTENTS CONCEPT OF SUFFICIENT STATISTICS
437 EXPONENTIAL FAMILIES OF DISTRIBUTIONS 439 EXPONENTIAL FAMILIES AND
MAXIMUM-LIKELIHOOD ESTIMATION 441 SUFFICIENT STATISTICS AND UNIFORMLY
MINIMUM-VARIANCE UNBIASED ESTIMATION 444 SUMMARY QUESTIONS 448 PROBLEMS
449 LESSON B INTRODUCTION TO HIGHER-ORDER STATISTICS 450 SUMMARY 450
INTRODUCTION 451 DEFINITIONS OF HIGHER-ORDER STATISTICS 452 PROPERTIES
OF CUMULANTS 464 SUPPLEMENTARY MATERIAL: RELATIONSHIPS BETWEEN CUMULANTS
AND MOMENTS 466 PROOF OF THEOREM B-3 466 SUMMARY QUESTIONS 469 PROBLEMS
469 LESSON C ESTIMATION AND APPLICATIONS OF HIGHER-ORDER STATISTICS 473
SUMMARY 473 ESTIMATION OF CUMULANTS 474 ESTIMATION OF BISPECTRUM 476
APPLICATIONS OF HIGHER-ORDER STATISTICS TO LINEAR SYSTEMS 478
COMPUTATION 490 SUMMARY QUESTIONS 491 PROBLEMS 492 LESSON D INTRODUCTION
TO STATE-VARIABLE MODELS AND METHODS 499 SUMMARY 499 NOTIONS OF STATE,
STATE VARIABLES, AND STATE SPACE 500 CONSTRUCTING STATE-VARIABLE
REPRESENTATIONS 503 SOLUTIONS OF STATE EQUATIONS FOR TIME-INVARIANT
SYSTEMS 509 MISCELLANEOUS PROPERTIES 512 COMPUTATION 514 SUMMARY
QUESTIONS 514 PROBLEMS 515 APPENDIX A GLOSSARY OF MAJOR RESULTS 518
APPENDIX B ESTIMATION ALGORITHM M-FILES 524 INTRODUCTION 524 RECURSIVE
WEIGHTED LEAST-SQUARES ESTIMATOR 525 CONTENTS XV KALMAN FILTER 526
KALMAN PREDICTOR 529 SUBOPTIMAL FILTER 532 SUBOPTIMAL PREDICTOR 534
FIXED-INTERVAL SMOOTHER 536 APPENDIX C ANSWERS TO SUMMARY QUESTIONS 539
REFERENCES 542 INDEX 553 CONTENTS XVI
|
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| id | DE-604.BV010538367 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:54:43Z |
| institution | BVB |
| isbn | 0131209817 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007025151 |
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| owner_facet | DE-703 DE-92 DE-29T DE-1050 |
| physical | XIX, 561 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Prentice Hall |
| record_format | marc |
| series2 | Prentice Hall signal processing series |
| spelling | Mendel, Jerry M. 1938- Verfasser (DE-588)134275918 aut Lessons in estimation theory for signal processing, communications, and control Jerry M. Mendel Englewood Cliffs, NJ Prentice Hall 1995 XIX, 561 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Prentice Hall signal processing series Frühere Ausg. u.d.T.: Mendel, Jerry M.: Lessons in digital estimation theory Estimation, Théorie de l' ram Traitement du signal - Méthodes statistiques ram Télécommunications - Méthodes statistiques ram estimation statistique inriac modele lineaire inriac theorie estimation inriac Estimation theory Schätztheorie (DE-588)4121608-8 gnd rswk-swf Schätztheorie (DE-588)4121608-8 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007025151&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mendel, Jerry M. 1938- Lessons in estimation theory for signal processing, communications, and control Estimation, Théorie de l' ram Traitement du signal - Méthodes statistiques ram Télécommunications - Méthodes statistiques ram estimation statistique inriac modele lineaire inriac theorie estimation inriac Estimation theory Schätztheorie (DE-588)4121608-8 gnd |
| subject_GND | (DE-588)4121608-8 |
| title | Lessons in estimation theory for signal processing, communications, and control |
| title_auth | Lessons in estimation theory for signal processing, communications, and control |
| title_exact_search | Lessons in estimation theory for signal processing, communications, and control |
| title_full | Lessons in estimation theory for signal processing, communications, and control Jerry M. Mendel |
| title_fullStr | Lessons in estimation theory for signal processing, communications, and control Jerry M. Mendel |
| title_full_unstemmed | Lessons in estimation theory for signal processing, communications, and control Jerry M. Mendel |
| title_short | Lessons in estimation theory for signal processing, communications, and control |
| title_sort | lessons in estimation theory for signal processing communications and control |
| topic | Estimation, Théorie de l' ram Traitement du signal - Méthodes statistiques ram Télécommunications - Méthodes statistiques ram estimation statistique inriac modele lineaire inriac theorie estimation inriac Estimation theory Schätztheorie (DE-588)4121608-8 gnd |
| topic_facet | Estimation, Théorie de l' Traitement du signal - Méthodes statistiques Télécommunications - Méthodes statistiques estimation statistique modele lineaire theorie estimation Estimation theory Schätztheorie |
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