Optimal State Estimation Kalman, H-infinity, and Nonlinear Appro....pdf

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Cover Page

Title Page

ISBN 0471708585

CONTENTS (with page links)

PART I INTRODUCTORY MATERIAL

1 Linear systems theory

2 Probability theory

3 Least squares estimation

4 Propagation of states and covariances

PART II THE KALMAN FILTER

5 The discretetime Kalman filter

6 Alternate Kalman filter formulations

7 Kalman filter generalizations

8 The continuous-time Kalrnan filter

9 Optimal smoothing

10 Additional topics in Kalman filtering

PART III THE H∞ FILTER

11 The H∞ filter

12 Additional topics in H∞ filtering

PART IV NONLINEAR FILTERS

13 Nonlinear Kalman filtering

14 The unscented Kalman filter

15 The particle filter

Appendixes, References, Index

Acknowledgments

Acronyms

List of algorithms (with page links)

Introduction

PART I INTRODUCTORY MATERIAL

1 Linear systems theory

2 Probability theory

3 Least squares estimation

4 Propagation of states and covariances

PART II THE KALMAN FILTER

5 The discretetime Kalman filter

6 Alternate Kalman filter formulations

7 Kalman filter generalizations

8 The continuous-time Kalrnan filter

9 Optimal smoothing

10 Additional topics in Kalman filtering

PART III THE H∞ FILTER

11 The H∞ filter

12 Additional topics in H∞ filtering

PART IV NONLINEAR FILTERS

13 Nonlinear Kalman filtering

14 The unscented Kalman filter

15 The particle filter

Appendix A: Historical perspectives

Appendix B: Other books on Kalman filtering

Appendix C: State estimation and the meaning of life

References

INDEX (with page links)

A,B,C

D,E,F,G,H,I,J,K

L,M

N,O,P

Q,R,S

T,U,V,W,Y

Back Page

Optimal State Estimation

Optimal State Estimation Kalman, H,, and Nonlinear Approaches Dan Simon Cleveland State University A JOHN WILEY & SONS, INC., PUBLICATION

Copyright 6 2006 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 11 1 River Street, Hoboken, NJ 07030, (201) 748-601 1, fax (201) 748-6008 or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the U S . at (800) 762-2974, outside the U S . at (317) 572- 3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic format. For information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication is available. ISBN-13 978-0-471-70858-2 ISBN- 10 0-47 1-7085 8-5 Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1

CONTENTS Acknowledgments Acronyms List of algorithms Introduction PART I INTRODUCTORY MATERIAL 1 Linear systems theory 1.1 1.2 1.3 1.4 1.5 1.6 Matrix algebra and matrix calculus 1.1.1 Matrix algebra 1.1.2 The matrix inversion lemma 1.1.3 Matrix calculus 1.1.4 The history of matrices Linear systems Nonlinear systems Discretization Simulation 1.5.1 Rectangular integration 1.5.2 Trapezoidal integration 1.5.3 Rung-Kutta Stability integration xiii xv xvii xxi 3 4 6 11 14 17 18 22 26 27 29 29 31 33 V

vi CONTENTS 1.6.1 Continuous-time systems 1.6.2 Discret6time systems 1.7 Controllability and observability 1.7.1 Controllability 1.7.2 Observability 1.7.3 Stabilizability and detectability 1.8 Summary Problems 2 Probability theory 2.1 Probability 2.2 Random variables 2.3 Transformations of random variables 2.4 Multiple random variables 2.4.1 Statistical independence 2.4.2 Multivariate statistics White noise and colored noise 2.5 Stochastic Processes 2.6 2.7 Simulating correlated noise 2.8 Summary Problems 3 Least squares estimation 3.1 3.2 3.3 3.4 3.5 Estimation of a constant Weighted least squares estimation Recursive least squares estimation 3.3.1 Alternate estimator forms 3.3.2 Curve fitting Wiener filtering 3.4.1 Parametric filter optimization 3.4.2 General filter optimization 3.4.3 Noncausal filter optimization 3.4.4 Causal filter optimization 3.4.5 Comparison Summary Problems 4 Propagation of states and covariances 4.1 Discretetime systems 4.2 Sampled-data systems 4.3 Continuous-time systems 33 37 38 38 40 43 45 45 49 50 53 59 61 62 65 68 71 73 74 75 79 80 82 84 86 92 94 96 97 98 100 101 102 102 107 107 111 114

CONTENTS vii 4.4 Summary Problems PART II T H E KALMAN FILTER 5 The discretetime Kalman filter Derivation of the discretetime Kalman filter 5.1 5.2 Kalman filter properties 5.3 One-step Kalman filter equations 5.4 Alternate propagation of covariance 5.4.1 Multiple state systems 5.4.2 Scalar systems 5.5 Divergence issues 5.6 Summary Problems 6 Alternate Kalman filter formulations 6.1 Sequential Kalman filtering 6.2 Information filtering 6.3 Square root filtering 6.3.1 Condition number 6.3.2 6.3.3 6.3.4 6.3.5 Algorithms for orthogonal transformations The square root time-update equation Potter’s square root measurement-update equation Square root measurement update via triangularization 6.4 U-D filtering 6.4.1 6.4.2 U-D filtering: The measurement-update equation U-D filtering: The timeupdate equation 6.5 Summary Problems 7 Kalman filter generalizations 7.1 7.2 Correlated process and measurement noise Colored process and measurement noise 7.2.1 Colored process noise 7.2.2 7.2.3 Colored measurement noise: State augmentation Colored measurement noise: Measurement differencing 7.3 Steady-state filtering 7.3.1 a-/I filtering 7.3.2 a-p-y filtering 7.3.3 Kalman filtering with fading memory A Hamiltonian approach to steady-state filtering 7.4 117 117 123 124 129 131 135 135 137 139 144 145 149 150 156 158 159 162 165 169 171 174 174 176 178 179 183 184 188 188 189 190 193 199 202 203 208

viii CONTENTS 7.5 Constrained Kalman filtering 7.5.1 Model reduction 7.5.2 Perfect measurements 7.5.3 Projection approaches 7.5.4 A pdf truncation approach 7.6 Summary Problems 8 The continuous-time Kalrnan filter 8.1 Discretetime and continuous-time white noise Discretized simulation of noisy continuous-time systems 8.2 8.3 8.4 8.5 8.1.1 Process noise 8.1.2 Measurement noise 8.1.3 Derivation of the continuous-time Kalman filter Alternate solutions to the Riccati equation 8.3.1 The transition matrix approach 8.3.2 The Chandrasekhar algorithm 8.3.3 The square root filter Generalizations of the continuous-time filter 8.4.1 8.4.2 Colored measurement noise The steady-state continuous-time Kalman filter 8.5.1 The algebraic Riccati equation 8.5.2 8.5.3 Duality The Wiener filter is a Kalman filter Correlated process and measurement noise 8.6 Summary Problems 9 Optimal smoothing An alternate form for the Kalman filter 9.1 9.2 Fixed-point smoothing Estimation improvement due to smoothing 9.2.1 9.2.2 Smoothing constant states 9.3 Fixed-lag smoothing 9.4 Fixed-interval smoothing 9.4.1 Forward-backward smoothing 9.4.2 RTS smoothing 9.5 Summary Problems 212 212 213 214 218 223 225 229 230 230 232 232 233 238 238 242 246 247 248 249 252 253 257 258 259 260 263 265 267 270 274 274 279 280 286 294 294

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