Multisensor Decision And Estimation Fusion

247 Pages·2003·11.69 MB·English

by  Yunmin Zhu (auth.)

MULTISENSOR DECISION AND
ESTIMATION FUSION
The Kluwer International Series on
ASIAN STUDIES IN COMPUTER
AND INFORMATION SCIENCE
Series Editor
Kai-Yuan Cai
Beijing University ofA eronautics and Astronautics, Beijing, CHINA
Editorial Advisory Board
Han-Fu Chen, Institute of System Science, Chinese Academy of Sciences
Jun-Liang Chen, Beijing University of Post and Telecommunication
Lin Huang, Peking University
Wei Li, Beijing University of Aeronautics and Astronautics
Hui-Min Lin, Institute of Software Technology, Chinese Academy of Sciences
Zhi-Yong Liu, Institute of Computing Technology, Chinese Academyof Sciences
Ru-Qian Lu, Institute of Mathematics, Chinese Academy of Sciences
Shi-Tuan Shen, Beijing University of Aeronautics and Astronautics
Qing-Yun Shi, Peking University
You-Xian Sun, Zhejiang University
Lian-Hua Xiao, National Natural Science Foundation of China
Xiao-Hu You, Southeast University
Bo Zhang, Tsinghua University
Da-Zhong Zheng, Tsinghua University
Bing-Kun Zhou, Tsinghua University
Xing-Ming Zhou, Changsha University of Technology
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MULTISENSOR DECISION AND
ESTIMATION FUSION
YunminZbu
Sichuan University, P.R. China
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library of Congress Cataloging-in-Publication Data
Zhu, Yunmin, 1944-
Multisensor decision and estimation fusion / Yunmin Zhu.
p. cm.--(Kluwer international series on Asian studies in computer and information
science ; 14)
Includes bibliographical references and index.
ISBN 978-1-4613-5367-6 ISBN 978-1-4615-1045-1 (eBook)
DOI 10.1007/978-1-4615-1045-1
1. Multisensor data fusion. 2. Multicriteria decision making. 1. Title. II. Series.
TK7870 .z43 2002
006.3--dc21 2002034044
Copyright © 2003 by Springer Science+Business Media New York
Origina11y published by Kluwer Academic Publishers in 2003
Softcover reprint ofthe hardcover Ist edition 2003
AU rights reserved. No part of this work may be reproduced, stored in a retrieval system,
or transmitted in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording, or otherwise, without the written permission from the Publisher,
with the exception of any material supplied specifically for the purpose of being entered and
executed on a computer system, for exclusive use by the purchaser of the work.
Permission for books published in Europe: [e-mail]
Permissions for books published in the United States of America: [e-mail]
Printed on acid-free paper.
To My Parents,
Hong You & Guoding Zhu,
My Wife, Shengna Gu,
My Daughter, Ji Zhu,
My Son, Yu Zhu
SERIES EDITOR'S
ACKNOWLEDGMENTS
I am pleased to acknowledge the assistance to the editorial work by Beijing
University of Aeronautics and Astronautics and the National Natural Science
Foundation of China
Kai-Yuan Cai
Series Editor
Department ofA utomatic Control
Beijing University ofA eronautics and Astronautics
Beijing 100083
China
Contents
List of Figures xi
List of Tables xiii
Preface xv
Acknowledgments xix
Part I DECISION FUSION
1. INTRODUCTION 3
1.1 Conventional Statistical Decision 3
1.1.1 Basic model of statistical decision 3
1.1.2 Hypothesis testing 5
1.2 Multisensor Statistical Decision Fusion Summary 6
1.2.1 Brief introduction to multisensor data fusion 6
1.2.2 Some basic issues 7
1.2.3 The previous studies of decision fusion 9
1.3 Three Conventional Single Sensor Decisions 11
1.3.1 Bayes decision 11
1.3.2 Neyman-Pearson decision 13
1.3.3 Sequential decision 15
2. TWO SENSOR BINARY DECISIONS 37
2.1 Introduction 37
2.1.1 Problem formulation 37
2.1.2 The relationship of distributed and classical decisions 40
2.2 Optimal Sensor Rule of Bayes Decision 41
2.2.1 Fixed point type necessary condition 42
2.2.2 Existence of the optimal sensor rule 47
x MULT/SENSOR DECISION AND ESTIMATION FUSION
2.3 An Algorithm for Computing the Optimal Sensor Rule 48
2.3.1 Gauss-Seidel iterative algorithm 48
2.3.2 The finite convergence of the discretized algorithm 49
2.4 Relationships with Likelihood Ratio Sensor Rules 53
2.5 Numerical Examples 55
2.6 Randomized Fusion Rules 60
3. MULTISENSOR BINARY DECISIONS 63
3.1 The Formulation for Bayes Binary Decision Problem 64
3.2 Formulation of Fusion Rules via Polynomials of Sensor Rules 65
3.3 Fixed Point Type Necessary Condition for the Optimal Sensor
Rules Given a Fusion Rule 67
3.4 The Finite Convergence of the Discretized Algorithm 71
3.5 The Optimal Fusion Rule and Some Interesting Properties 78
3.6 Numerical Examples of the Above Results 83
3.7 Optimal Sensor Rule of Neyman-Pearson Decision 88
3.7.1 Necessary condition 89
3.7.2 The algorithm to search for optimal sensor rules 92
3.7.3 Numerical examples 93
3.8 Sequential Decision Fusion Given Fusion Rule 94
3.8.1 Algorithm 94
3.8.2 Numerical example 97
4. MULTISENSOR MULTI-HYPOTHESIS NETWORK DECISION 101
4.1 Elementary Network Structures 101
4.1.1 Parallel network 101
4.1.2 Tandem network and tree network 103
4.1.3 Hybrid (tree) network 106
4.2 Formulation of Fusion Rule via Polynomial of Sensor rules 106
4.3 Fixed Point Type Necessary Condition for Optimal Sensor
Rules Given a Fusion Rule 110
4.4 Iterative Algorithm and Convergence 112
5. OPTIMAL FUSION RULE AND DESIGN OF NETWORK
COMMUNICATION STRUCTURES 117
5.1 Optimal Fusion Rule Given Sensor Rules 117
5.1.1 Problem formulation 118
5.1.2 Computation of likelihood ratios 122
5.1.3 Locally optimal sensor rules with communications 123
Contents Xl
5.1.4 Extensions to more general systems 126
5.1.5 Numerical examples 128
5.2 The Equivalent Classes of Fusion Rules 134
5.2.1 Preliminary definitions 136
5.2.2 Propositions 137
5.2.3 Applications of propositions 138
5.3 Unified Fusion Rule for Parallel Network 140
5.4 Unified Fusion Rule for Tandem and Tree Networks 145
5.5 Performance Comparison of Parallel and Tandem Networks 146
5.6 Numerical Examples 148
5.6.1 Three sensor system 148
5.6.2 Four sensor system 151
5.7 Optimization Design of Network Decision Systems 153
5.7.1 Selection of a network structure category 153
5.7.2 Allocation of sensors' positions and communication
amounts 153
Part II ESTIMATION FUSION
6. MULTISENSOR POINT ESTIMATION FUSION 159
6.1 Previous Main Results 160
6.2 Linear Minimum Variance Estimation Fusion 162
6.2.1 Formulation of the LMV fusion as an optimization
problem 163
6.2.2 Optimal fusion weights 165
6.2.3 Efficiency of the LMV fusion 168
6.2.4 Extension to a more general model 171
6.2.5 Previous fusion formulae as special cases 172
6.2.6 Discussion 173
6.2.7 Recursive computation of error covariance 175
6.3 The Optimality of Kalman Filtering Fusion with Feedback 177
6.3.1 Problem formulation 178
6.3.2 Global optimality of the feedback filtering fusion 181
6.3.3 Local estimate errors 182
6.3.4 The advantage of the feedback 182
6.3.5 Extension to a hybrid filtering fusion 183
6.4 Fusion of the Forgetting Factor RLS Algorithm 184
6.4.1 Forgetting factor RLS algorithm 185
xii MULTISENSOR DECISION AND ESTIMATION FUSION
6.4.2 Two types of distributed EFRLS fusion methods 186
6.4.3 Simulations 192
7. MULTISENSOR INTERVAL ESTIMATION FUSION 197
7.1 Statistical Interval Estimation Fusion Using Sensor Statistics 198
7.1.1 Problem formulation 198
7.1.2 Optimal convex linear fusion 200
7.1.3 Computation of the optimal weights 203
7.1.4 Nearly optimal linear fusion 204
7.1.5 Numerical examples 206
7.1.6 Inverting a hypothesis testing 211
7.2 Interval Estimation Fusion Using Sensor Estimates 212
7.2.1 Outputs of sensors 212
7.2.2 Combination rule of sensor outputs 213
7.2.3 Optimization criteria 218
7.3 Fault-Tolerant Interval Estimation Fusion 219
7.3.1 Without knowledge of confidence degrees 220
7.3.2 With knowledge of confidence degrees 221
7.3.3 Extension to sensors outputting mUltiple intervals 224
7.3.4 Conclusion 225
Index
235