Distributed Detection and Data Fusion

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1 Distributed Detection and Data Fusion Springer Science+ Business Media, LLC

2 Signal Processing and Data Fusion Synthetic Aperture Radar J.P. Fitch Multiplicative Complexity, Convolution and the DFT MT. Heideman Array Signal Processing S.u. Pillai Maximum Likelihood Deconvolution J.M Mendel Algorithms for Discrete Fourier Transform and Convolution T. Tolimieri, M. An. and C. Lu Algebraic Methods for Signal Processing and Communications Coding R.E. Blahut Electromagnetic Devices for Motion Control and Signal Processing Y.M Pulyer Mathematics of Multidimensional Fourier Transform Algorithms R. Tolimieri, M An, and C. Lu Lectures on Discrete Time Filtering R.S. Bucy Distributed Detection and Data Fusion P.K. Varshney

3 Pramod K. Varshney Distributed Detection and Data Fusion C.S. Burrus Consulting Editor With 62 Illustrations. ~. ~ Springer

4 Pramod K. Varshney Department of Electrical and Computer Engineering Syracuse University Syracuse, NY USA Consulting Editor Signal Processing and Digital Filtering C.S. Burrus Professor and Chairman Department of Electrical and Computer Engineering Rice University Houston, TX USA Library of Congress Cataloging-in-Publication Data Varshney, Pramod K. Distributed detection and data fusion/pramod K. Varshney. p. cm. - (Signal processing and digital filtering) Includes bibliographical references and index. ISBN ISBN (ebook) DOI / Signal processing. 2. Multisensor data fusion. 3. Signal detection. I. TitIe. II. Series. TK V '2-dc Printed on acid-free paper Springer Science+Business Media New York Origina1ly published by Springer-Verlag New York. lnc. in 1997 Softcover reprint ofthe hardcover Ist edition 1997 AII rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even it the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely byanyone. Production managed by Francine McNeilI; manufacturing supervised by Jacqui Ashri. Photocomposed copy prepared using the author's WordPerfect files ISBN

5 To My Parents, Raj Kumar & Narvada Devi Varshney, who celebrated their Golden Anniversary in 1996

6 tit 6 f i q o ~ c U f q 6 f i I q (: ~ ; 0 ~ 0 f i C \ 1 ~ I~ 6 f i q q : ; ~ d~ 1 { q~ ts ~ O f i qii f O r tit Your right is to action alone, never to the fruits thereof. Fruits of action should not be your motive, nor should you avoid action. - Sri Krishna 2.47 Bhagvad Gita

7 Preface This book provides an introductory treatment of the fundamentals of decision-making in a distributed framework. Classical detection theory assumes that complete observations are available at a central processor for decision-making. More recently, many applications have been identified in which observations are processed in a distributed manner and decisions are made at the distributed processors, or processed data (compressed observations) are conveyed to a fusion center that makes the global decision. Conventional detection theory has been extended so that it can deal with such distributed detection problems. A unified treatment of recent advances in this new branch of statistical decision theory is presented. Distributed detection under different formulations and for a variety of detection network topologies is discussed. This material is not available in any other book and has appeared relatively recently in technical journals. The level of presentation is such that the hook can be used as a graduate-level textbook. Numerous examples are presented throughout the book. It is assumed that the reader has been exposed to detection theory. The book will also serve as a useful reference for practicing engineers and researchers. I have actively pursued research on distributed detection and data fusion over the last decade, which ultimately interested me in writing this book. Many individuals have played a key role in the completion of this book. I would like to thank Vince Vannicola for his continued interest in my research and for his helpful suggestions throughout this period. It is a pleasure to acknowledge the stimulating discussions that ix

8 x Preface I have had wiih my numerous doctoral students. Their contribution to this research was invaluable. Dehbie Tysco started typing this manuscript. Cynthia Bromka-Skafidas gave it its final form. I am indehted to Cynthia for cheerfully going through many cycles of revisions and corrections. Chao-Tang Yu, Vajira Samarasooriya, and Miicahit Dner prepared the figures included in this hook. I greatly value their help. Thanks to Maureen Marano and Vajira Samarasooriya for their help during a critical phase of this project. I am grateful to Rome Laboratory and the Air Force Office of Scientific Research (AFOSR) for sponsoring my research. Special thanks go to Vince Vannicola and Jon Sjogren in this regard. Finally, I am at a loss to finel suitable words that express my deep appreciation for the significant contributions of my wife, Anju, and my sons, Lav and Kush. They have been extremely supportive throughout this project. Completion has been made possible hy their constant encouragement, patience, and understanding. Syracuse. New York Pramod K. Varshney

9 Contents Preface ix Introduction 1.1 Distributed Detection Systems I 1.2 Outline of the Book 4 2 Elements of Detection Theory Introduction Bayesian Detection Theory Minimax Detection Neyman-Pearson Test Sequential Detection Constant False Alarm Rate (CFAR) Detection Locally Optimum Detection 32 3 Distributed Bayesian Detection: Parallel Fusion Network Introduction Distributed Detection Without Fusion Design of Fusion Rules Detection with Parallel Fusion Network 72 4 Distributed Bayesian Detection: Other Network Topologies Introduction The Serial Network Tree Networks 137 xi

10 xii Contents 4.4 Detection Networks with Feedback Generalized Formulation for Detection Networks Distributed Detection with False Alarm Rate Constraints Introduction Distributed Neyman-Pearson Detection Distributed CFAR Detection Distributed Detection of Weak Signals Distributed Sequential Detection Introduction Sequential Test Performed at the Sensors Sequential Test Performed at the Fusion Center Information Theory and Distributed Hypothesis Testing Introduction Distributed Detection Based on Information Theoretic Criterion Multiterminal Detection with Data Compression 245 Selected Bibliography Index