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详细说明：book{ author = {Anderson, Brian DO and Moore, John B}, title = {Optimal filtering}, publisher = {Prentice-Hall, Inc.}, address = {New Jersey}, year = {1979}, type = {Book} }OPTIMAL FILTERING Brian D.O. Anderson John b. moore Professors of Electrical Engineering University of Newcastle New south wales. australia PRENTICE-HALL INC. Englewood Cliffs, New Jersey 07632 LIbrary of Congress Cataloging in Publication Data ANDEON, BRIAN D O Optimal filtering. (Information and system sciences series) Includes bibliographies and index 1. sigmal processing. 2. Electric fiters. I Moore, John Barratt, date joiat author. TK51025.A53 6213815’32 78-8938 ISN013-638122-7 C 1979 by Prentice-Hall, Inc Englewood Cliffs, N.J. 07632 All rights reserved. No part of this book may be reproduced in any form or by any means without permission in writing from the publisher. Printed in the United States of america 1098765432 PRENTICE-HALL INTERNATIONAL, INC. London PRENTICE-HALL OF AUSTRALIA PTY LIMITED, Sydney PRENTICE-HALL OF CANADA, LTD, Toronto PRENTICE-HALL OF INDIA PRIVATE LIMITED, New Delhi PRENTICE-HALL OF JAPAN, INC, Tokyo PRENTICE-HALL OF SOUTHEAST ASIA PTE LTD, Singapore WHITEHALL BOOKS LIMITED, Wellington, New Zealand CONTENTS PREFACE INTRODUCTION 1.1 Filtering 7 1.2 History of Signal Filtering 2 1.3 Subject Matter of this Book 4 1.4 Outline of the book 6 References 7 FILTERING, LINEAR SYSTEMS, AND ESTIMATION 2.1 Systems, Noise, Filtering, Smoothing, and Prediction 9 2.2 The Gauss-Markov Discrete-time Mode/ 12 2.3 Estimation Criteria 23 References 34 vi CONTENTS THE DISCRETE-TIME KALMAN FILTER 36 3.1 The Kalman fite 3.2 Best Linear Estimator Property of the Kaiman Filte 46 3.3 / dentification as a Kalman F∥ tering Problen50 3. 4 Application of Kaiman Fiiters 53 Refere 59 TIME-INVARANT FILTERS 62 4.1 Background to Time invariance of the F谁te 62 4.2 Stability Properties of Linear Discrete-time Systems 63 4.3 Stationary Beh of Linear Systems 6 4. 4 Time /variance and Asymptotic stability of the Filter 76 4.5 Frequency Domain Formulas 85 Refe s88 5 KALMAN FILTER PROPERTIES 90 5.1 Introduction 90 5.2 Minimum Variance and Linear Minimum stimation,; Orthogonality and projection 92 5.3 The Innovations Sequence 100 5. 4 The KaIman Kilter 105 5.5 True Filtered Estimates and the signal-to-Noise Ratio∥ Property 715 5.6 nverse Problems When is a Filter Optima/7 122 References 127 COMPUTATIONAL ASPECTS 129 6.1 Signal Mode/ Errors, Filter Divergence, and Data Saturation 129 6.2 Exponentia/ Data Weighting-- A Filter with Prescribed Degree of Stability 135 CONTENTS vii 6.3 The Matrix Inversion Lemma and the Information Filter 138 6.4 Sequential Processing 142 6.5 Square Root Filtering 147 6.6 The High Measurement Noise Case 153 6.7 Chandrasekhar-7ype, Doubling. and Nonrecursive Algorithms155 References 162 SMOOTHING OF DISCRETE-TIME SIGNALS 165 7.1 Introduction to Smoothing 165 7.2 Fixed-point Smoothing 170 7.3 Fixed-/ag Smoothing 776 7.4 Fixed-interval Smoothing 187 References 190 APPLICATIONS IN NONLINEAR FILTERING 193 8.1 Nonlinear filtering 8.2 The Extended Kalman Filter 795 8. 3 A Bound Optima/ Filter 205 8. 4 Gaussian Sum Estimators 211 References 221 INNOVATIONS REPRESENTATIONS 9 SPECTRAL FACTORIZATION WIENER AND LEVINSON FILTERING 223 9. 1 /ntroduction 223 9.2 Kalman Filter Design from Covariance Data 227 9.3 nnovations Representations with Finite /nitia/ Time 230 9.4 Stationary /nnovations Representations and spectral factorization 238 9.5 Wiener Filtering 254 9.6 Levinson Filters 258 References 264 0 PARAMETER DENTIFICATION AND ADAPTIVE ESTIMATION 267 10. 1 Adaptive Estimation via Paralle/ Processing 267 10.2 Adaptive Estimation via Extended Least squares 279 References 286 dI CONTENTS COLORED NOISE AND SUBOPTIMAL REDUCED ORDER FILTERS 288 11.1 Genera/ Approaches to Dealing with Colored Noise 288 11.2 Filter Design with Markov Output Noise 290 11.3 Filter Design with Singular or Near-singular Output Noise 292 11.4 Suboptimal Design Given Colored Input or Measurement Noise 296 11.5 Suboptima/ Filter Design by Mode/ Order Reduction 301 References 30. APPENDIXES A BRIEF REVIEW OF RESULTS OF PROBABILITY THEORY 307 A 1 Pure Probability Theory 308 A 2 Stochastic Processes 316 A 3 Gaussian Random Variables Vectors, and Processes 320 References 323 BRIEF REVIEW OF SOME RESULTS OF MATRIX THEORY 324 References 339 BRIEF REVIEW OF SEVERAL MAJOR RESULTS OF LINEAR SYSTEM THEORY 340 R eferences 346 D LYAPUNOV STABILITY 347 References 349 AUTHOR INDEX 351 SUBJECT INDEX 354 PREFACE This book is a graduate level text which goes beyond and augments the undergraduate exposure engineering students might have to signal processing; particularly, communication systems and digital filtering theory The material covered in this book is vital for students in the fields of control and communications and relevant to students in such diverse areas as sta tistics, economics, bioengineering and operations research. The subject matter requires the student to work with linear system theory results and elemen- tary concepts in stochastic processes which are generally assumed at graduate level. However, this book is appropriate at the senior year undergraduate level for students with background in these areas. Certainly the book contains more material than is usually taught in one semester, so that for a one semester or quarter length course, the first three chapters(dealing with the rudiments of Kalman filtering) can be covered first, followed by a selection from later chapters. The chapters following Chapter 3 build in the main on the ideas in Chapters l, 2 and 3, rather than on all preceding chapters. They cover a miscellany of topics; for example time-invariant filters, smoothing, and nonlinear filters. Although there is a significant benefit in proceeding through the chapters in sequence this is not essential, as has been shown by the authors'experience in teaching this course. The pedagogical feature of the book most likely to startle the reader x PREFACE is the concentration on discrete-time filtering. Recent technological develop ments as well as the easier path offered students and instructors are the two reasons for this course of action Much of the material of the book has been with us in one form or another for ten to fifteen years, although again, much is relatively recent. This recent work has given new perspectives on the earlier material; for example, the notion of the innovations process provides helpful insights in deriving the Kalman filter. We acknowledge the research support funding of the Australian Research Grants Committee and the Australian Radio Research board We are indebted also for specific suggestions from colleagues, Dr. G. Goodwin and Dr. A. Cantoni; joint research activities with former Ph. D. students Peter Tam and Surapong Chirarattananon and to the typing expertise of Dianne Pief ke. We have appreciated discussions in the area of optimal filtering with many scholars including Professors K. Astrom, T. Kailath, D. Mayne, J Meditch and J Me B. D.O. ANDeRsON New South Wales, australia J B. moore

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