Optimal State Estimation Kalman, H,, and Nonlinear Approaches.pdf

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

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Optimal State Estimation

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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 US. at (800) 762-2974, outside the US. 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 integration Stability xiii xv xvii xxi 3 4 6 11 14 17 18 22 26 27 29 29 31 33 V

vi CONTENTS 2 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 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

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