Estimation with Applications To Tracking and Navigation.pdf

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Estimation with Applications to Tracking & Navigation

Contents

Preface

Nomenclature

Ch1 Introduction

Ch2 Basic Concepts in Estimation

Ch3 Linear Estimation in Static Systems

Ch4 Linear Dynamic Systems with Random Inputs

Ch5 State Estimation in Discrete-Time Linear Dynamic Systems

Ch6 Estimation for Kinematic Models

Ch7 Computational Aspects of Estimation

Ch8 Extensions of Discrete-Time Linear Estimation

Ch9 Continuous-Time Linear State Estimation

Ch10 State Estimation for Nonlinear Dynamic Systems

Ch11 Adaptive Estimation & Maneuvering Targets

Ch12 Introduction to Navigation Applications

Bibliography

Index

Estimation with Applications To Tracking and Navigation

Estimation with Applications To Tracking and Navigation Yaakov Bar-Shalom X.-Rong Li Thiagalingam Kirubarajan A Wiley-Interscience JOHN WILEY New York l Chichester l Weinheim l Brisbane l Singapore l Toronto Publication & SONS, INC.

This text is printed on acid-free paper. @ Copyright 0 2001 by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada. the prior written No part of this publication may be reproduced, form or by any means, electronic, mechanical, except as permitted either appropriate 0 1923, addressed NY 10158-0012, under Section permission fax (978) 750-4744. fee to the Copyright to the Permissions (2 12) 850-6011, (978) 750-8400, per-copy stored photocopying, in a retrieval system or transmitted in any recording, scanning or otherwise, Act, without 107 or 108 of the 1976 United States Copyright of the Publisher, or authorization Clearance Center, through 222 Rosewood of the payment Drive, Danvers, MA should be Requests to the Publisher for permission Department, John Wiley & Sons, fax (2 12) 850-6008, E-Mail: Inc., 605 Third Avenue, New York, PERMREQ @ WILEY.COM. For ordering and customer service, call 1-800-CALL-WILEY. Library of Congress Cataloging-in-Publication Data Bar-Shalom, Yaakov. Estimation with applications to tracking and navigation / by Yaakov Bar-Shalom, X.-Rong Li, Thiagalingam Kirubarajan. p. cm. Includes bibliographical ISBN O-47 l-4 1655-X 1. Motion control devices. references and index. (cloth) Robots-Control Kirubarajan, systems. Thiagalingam. 2. Remote control. 3. Telecommunication systems. 4. 5. Process control. 6. Estimation theory. I. Li, X.-Rong. II. III. Title. .B37 2001 TJ214.5 68 1’.2-dc2 1 2001022366 Printed in the United States of America. 10987654321

To Eva, Tali, Yael and Michael To Peizhu, Helen and Linda To Appa, Amma, Ketha, Abi and Arun YBS XRL TK

Lemma 1. Make things as simple as possible but not simpler. A. Einstein Theorem 1. By making things absolutely clear, people will become confused. A Chinese fortune cookie Corollary 1. We wi 11 make things simple but not too simple, clear but not too c lear. Lemma 2. Uncertainty is everywhere. Theorem 2. Uncertainty cannot be conquered. Corollary 2. Embrace it! Paraphrased after Michael Moschen, professonal juggler.

1 INTRODUCTION 1.1 1.2 1.3 1.4 of State Estimation: Vehicle Collision Avoidance Prerequisites ALGEBRA AND LINEAR SYSTEMS Algebra the Determinant Operations of a Matrix and Projection of Vectors Jacobian Eigenvectors, Linear and Hessian and Quadratic Dynamic Systems Forms - Controllability and Observability Linear Dynamic Systems - Controllability and Observability Contents Areas PREFACE ACRONYMS MATHEMATICAL NOTATIONS and Related REVIEW OF LINEAR and Chapter and Notations Objectives Overview OF PROBABILITY and the Axioms of Estimation of Estimation/Filtering Estimation Applications Preview An Example Definitions Some Linear Inversion Orthogonal The Gradient, Eigenvalues, Continuous-Time Discrete-Time BACKGROUND 1.1.1 1.1.2 1.1.3 1.1.4 SCOPE OF THE TEXT 1.2.1 1.2.2 BRIEF 1.3.1 1.3.2 1.3.3 1.3.4 1.35 1.3.6 1.3.7 1.3.8 BRIEF 1.4.1 1.4.2 1.4.3 1.4.4 1.4.5 1.4.6 1.4.7 1.48 1.4.9 1.4.10 1.4.11 1.4.12 1.4.13 1.4.14 1.4.15 1.4.16 1.4.17 1.4.18 1.4.19 1.4.20 1.4.21 1.4.22 REVIEW Events Random Probability Mixed Expectations and Moments Joint PDF of Two Random Independent Vector-Valued Conditional The Total Probability Bayes’ Conditional Gaussian Joint Expected Mixture Chi-Square Weighted Random Random Walk Markov Random Processes Sequences, Random Probability Mass Function and Conditional Events and Formula Random Variables Value Probability of Quadratic Density Sum of Chi-Square Processes THEORY of Probability Variables and Probability Density Function Random Variable and Mixed Probability-PDF of a Scalar Random Variables Independent Variables and PDF Random and Their Moments Variable Variables Theorem Expectations and Their Smoothing Property Gaussian Random and Quartic Functions Variables Forms Variables Random Variables Process Distributed Random and the Wiener Markov Sequences and Markov Chains xvii xxi xxii 1 1 1 3 4 10 15 15 16 19 19 20 21 23 24 25 27 29 31 31 33 35 36 37 38 41 41 44 45 47 50 51 52 54 55 57 60 61 65 66 69 ix

X CONTENTS 1.5 1.6 1.4.23 BRIEF 1.5.1 1.5.2 1.5.3 1.5.4 NOTES 1.6.1 1.6.2 The Law of Large Numbers and the Central Limit Theorem REVIEW OF STATISTICS Testing Regions Runs Carlo of the Chi-Square Hypothesis Confidence Monte Tables AND PROBLEMS Bibliographical Problems Notes and Significance and Comparison and Gaussian of Algorithms Distributions IN ESTIMATION Outline Basic Concepts - Summary of Objectives ESTIMATION OF PARAMETER for Estimation of a Parameter LIKELIHOOD Definitions MLE MAP MAP The Sufficient vs. MAP Estimator Estimator of ML and MAP Estimators with Gaussian Prior Estimator with One-Sided with Diffuse Statistic and Exponential Prior Prior the Likelihood MEAN SQUARE Equation of LS and MMSE Estimators AND MINIMUM SQUARES Definitions Some LS Estimators MMSE vs. MAP ESTIMATORS Estimator in Gaussian Noise and a MAP of an ML the ML Estimation AND MSE OF AN ESTIMATOR Estimator of Two Parameters of Estimator of Variances Variances of an ML and a MAP and Sample the Sample Mean of the Probability EFFICIENCY of an Event OF ESTIMATORS Definitions Comparison The Variances Estimation of AND Consistency The Cramer-Rao Proof An Example Large Sample Lower the Cramer-Rao of Efficient Properties of Bound Lower Estimator of the Fisher and Bound the ML Estimator of Estimators of Estimator Properties PROBLEMS Notes Definitions Models CONCEPTS INTRODUCTION 2.1.1 2.1.2 THE PROBLEM 2.2.1 2.2.2 MAXIMUM 2.3.1 2.3.2 2.3.3 2.3.4 2.3.5 LEAST 2.4.1 2.4.2 2.4.3 UNBIASED Definition 2.5.1 Unbiasedness 2.5.2 Bias 2.5.3 THE VARIANCE 2.6.1 2.6.2 2.6.3 2.6.4 CONSISTENCY 2.7.1 2.7.2 2.7.3 2.7.4 2.7.5 SUMMARY 2.8.1 2.8.2 NOTES 2.9.1 2.9.2 Summary Summary AND in Bibliographical Problems 2 BASIC 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 LINEAR 3.1 3.2 3.3 AND MAXIMUM A POSTERIOR1 ESTIMATORS ERROR ESTIMATION Estimator Variance Information Matrix Outline Linear ESTIMATION INTRODUCTION 3.1.1 3.1.2 ESTIMATION 3.2.1 3.2.2 LINEAR 3.3.1 IN STATIC SYSTEMS Estimation in Static Systems - Summary of Objectives OF GAUSSIAN The Conditional Estimation MINIMUM The Principle Mean of Gaussian MEAN SQUARE of Orthogonality VECTORS RANDOM and Covariance Random Vectors for Gaussian Random Vectors - Summary ERROR ESTIMATION 70 72 72 74 79 82 85 85 85 89 89 89 89 90 90 91 92 92 92 94 95 96 98 98 100 100 101 101 102 102 104 104 105 106 107 108 108 109 110 112 113 114 114 115 115 115 116 121 121 121 121 122 122 123 123 123

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