Adaptive Filtering and Change Detection Fredrik Gustafsson Copyright © 2000 John Wiley & Sons, Ltd Isbns: 0-471-49287-6 (Hardback); 0-470-84161-3 (Electronic)
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Adaptive Filtering and Change Detection Fredrik Gustafsson Copyright © 2000 John Wiley & Sons, Ltd ISBNs: 0-471-49287-6 (Hardback); 0-470-84161-3 (Electronic) Adaptive Filtering and Change Detection Adaptive Filtering and Change Detection Fredrik Gustafsson Linkoping University, Linkoping, Sweden JOHN WILEY & SONS, LTD Chichester Weinheim NewYork Brisbane Singapore Toronto Copyright 0 2000 by John Wiley & Sons Ltd Baffins Lane, Chichester, West Sussex, PO 19lUD, England National 01243 779777 International (+44) 1243 779777 e-mail (for orders and customer service enquiries): [email protected] Visit our Home Page on http://www.wiley.co.uk or http://www.wiley.com All Rights Reserved.No part of this publication may be reproduced, storedin a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the termsof the Copyright Designs and PatentsAct 1988 or under the termsof a licence issuedby the Copyright Licensing Agency,90 Tottenham Court Road, London, W1P 9HE,UK, without the permissionin writing of the Publisher, with the exceptionof any material supplied specifically for the purposeof being entered and executed on a computer system, for exclusive use by the ofpurchaser the publication. 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Other Wiley Editorial Ofices John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, USA Wiley-VCH Verlag GmbH Pappelallee 3, D-69469 Weinheim, Germany Jacaranda Wiley Ltd,33 Park Road, Milton, Queensland 4064, Australia John Wiley & Sons (Canada) Ltd, 22 Worcester Road Rexdale, Ontario, M9W 1L1, Canada John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 British Library Cataloguing in Publication Data A catalogue record for this bookis available from the British Library ISBN 0 471 49287 6 Produced from PostScript files supplied by the authors Printed and boundin Great Britainby Antony Rowe, Chippenham, Wilts This book is printed on acid-free paper responsibly manufactured from sustainable forestry, in which at least two trees are planted for each one used for paper production. Contents Preface ix Part I: Introduction 1 Extend ed summary1. Extended 3 1.1. About the book .......................... 3 1.2. Adaptivelinear filtering ..................... 8 1.3. Changedetection ......................... 17 1.4. Evaluation and formal design .................. 26 2 . Applications 31 2.1. Change in the meanmodel ................... 32 2.2. Change in the variance model .................. 35 2.3. FIR model ............................. 37 2.4. AR model ............................. 39 2.5. ARX model ............................ 42 2.6. Regression model ......................... 46 2.7. State space model ........................ 49 2.8. Multiple models .......................... 49 2.9. Parameterized non-linear models ................ 51 S ignal estimationPart II: Signal 55 On -line approaches3 . On-line 57 3.1. Introduction ............................ 57 3.2. Filteringapproaches ....................... 59 3.3. Summary of leastsquares approaches .............. 59 3.4. Stopping rules andthe CUSUM test .............. 63 vi Contents 3.5. Likelihood based changedetection ............... 70 3.6. Applications ............................ 81 3.A. Derivations ............................ 84 4 . Off-line approaches 89 4.1. Basics ............................... 89 4.2. Segmentationcriteria ....................... 91 4.3. On-line local search for optimum ................ 94 4.4.Off-line global search for optimum ............... 98 4.5. Changepoint estimation ..................... 102 4.6. Applications ............................ 106 Partestimation 111: Parameter 111 Ad aptive filtering 113 filtering 5 . Adaptive 5.1. Basics ............................... 114 5.2. Signal models ........................... 115 5.3. Systemidentification ....................... 121 5.4. Adaptivealgorithms ....................... 133 5.5. Performanceanalysis ....................... 144 5.6. Whitenessbased change detection ............... 148 5.7. Asimulation example ...................... 149 5.8. Adaptive filters incommunication ............... 153 5.9.Noise cancelation ......................... 167 5.10. Applications ............................ 173 5.11. Speech coding in GSM ...................... 185 5.A. Squareroot implementation ................... 189 5.B. Derivations ............................ 190 6 . Changedetection based slidingon windows 205 6.1. Basics ............................... 205 6.2. Distancemeasures ........................ 211 6.3. Likelihood based detection and isolation ............ 218 6.4. Design optimization ....................... 225 6.5. Applications ............................ 227 7 . Changedetection based banksfilter231 on 7.1. Basics ............................... 231 7.2. Problemsetup .......................... 233 Contents vii 7.3. Statistical criteria ........................ 234 7.4. Information based criteria .................... 240 7.5. On-line local search for optimum ................ 242 7.6.Off-line global search for optimum ............... 245 7.7. Applications ............................ 246 7.A. Two inequalities for likelihoods ................. 252 7.B. The posterior probabilities of a jump sequence ........ 256 S tate estimationPart W: State 261 Kalm an filtering 263 filtering 8 . Kalman 8.1. Basics ............................... 264 8.2. State space modeling ....................... 267 8.3. TheKalman filter ........................ 278 8.4. Time-invariant signal model ................... 286 8.5. Smoothing ............................. 290 8.6. Computationalaspects ...................... 295 8.7. Squareroot implementation ................... 300 8.8. Sensor fusion ........................... 306 8.9. Theextended Kalman filter ................... 313 8.10. Whiteness based change detection using the Kalman filter . 324 8.11. Estimation of covariances in state space models ........ 326 8.12. Applications ............................ 327 9 . Changedetection basedlikelihood on ratios 343 9.1. Basics ............................... 343 9.2. The likelihood approach ..................... 346 9.3. The GLR test ........................... 349 9.4. The MLR test ........................... 353 9.5. Simulationstudy ......................... 365 9.A. Derivation of the GLR test ................... 370 9.B. LS-based derivation of the MLR test .............. 372 I0. Changedetection based multipleon models 377 10.1. Basics ............................... 377 10.2. Examples of applications ..................... 378 10.3. On-line algorithms ........................ 385 10.4. Off-line algorithms ........................ 391 10.5. Local pruning in blind equalization ............... 395 viii Contents 10.A.Posterior distribution ....................... 397 11. Change detection based on algebraical consistencytests 403 11.1. Basics ............................... 403 11.2. Parity space change detection .................. 407 11.3. An observer approach ...................... 413 11.4. An input-output approach .................... 414 11.5. Applications ............................ 415 Part V: Theory 425 Evaluation theory12 . Evaluation 427 12.1. Filterevaluation ......................... 427 12.2. Evaluation of change detectors ................. 439 12.3. Performanceoptimization .................... 444 estimation 45113 . linear estimation 13.1. Projections ............................ 451 13.2. Conditional expectations ..................... 456 13.3. Wiener filters ........................... 460 Signal modelsA . Signal and471 notation B . Faultterminology detection 475 Bibliography 477 Index 493 Preface This book is rather broad in that it covers many disciplines regarding both mathematical tools (algebra, calculus, statistics) and application areas (air- borne, automotive, communication and standard signal processing and auto- matic control applications). The book covers all the theory an applied en- gineer or researcher can ask for: from algorithms with complete derivations, their properties to implementation aspects. Special emphasis has been placed on examples, applications with real data and case studies for illustrating the ideas and what can be achieved. There are more than 130 examples, of which at least ten are case studies that are reused at several occasions in the book. The practitioner who wants to get a quick solution to his problem may try the ‘student approach’ to learning, by studying standard examples and using pattern recognition to match them to the problem at hand. There is a strong connection to MATLABTMThere is an accompanying toolbox, where