Poisson Point Processes Imaging, Tracking, and Sensing
"Poisson Point Processes provides an overview of non-homogeneous and multidimensional Poisson point processes and their numerous applications. Readers will find constructive mathematical tools and applications ranging from emission and transmission comput
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Roy L. Streit
Poisson Point Processes Imaging, Tracking, and Sensing
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Roy L. Streit Metron Inc. 1818 Library St Reston Virginia 20190-6281, USA [email protected] www.roystreit.com
ISBN 978-1-4419-6922-4 e-ISBN 978-1-4419-6923-1 DOI 10.1007/978-1-4419-6923-1 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010932610 c Springer Science+Business Media, LLC 2010 All 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, 233 Spring Street, New York, NY 10013, USA), 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 in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To my wife, Nancy
Preface
A constructive approach to Poisson point processes (PPPs) is well suited to those who seek to learn quickly what they are, how they are used, and—above all— whether or not they can help the reader in whatever application they are working on. To help readers reach these goals, PPPs are defined via a two-step realization, or simulation, procedure. This procedure is subsequently used to obtain many wonderful properties of PPPs. The approach is pedagogically efficient because it uses a constructive definition of a PPP in place of the traditional PPP axioms that include, for example, independent scattering. The two approaches are in fact mathematically equivalent. The question of elegance is a matter of taste. Many readers will find the constructive definition easier to understand than an axiomatic one, especially on first encounter. In any event, the simulation approach is taken here because it provides an efficient entrée to PPPs and point processes generally. There are now several books on PPPs and related topics. Most seem to be written by mathematicians striving for mathematical rigor, and these are valuable books for that very reason. Many practitioners, however, do not have the background to read them without a serious commitment of time and effort. What I felt was lacking was a book that made PPPs accessible to many mathematically capable readers and that provided insight and technique without recourse to an axiomatic measure-theoretic approach. Therefore, while I was writing the book, the audience foremost in my mind was graduate students, especially beginning students in electrical engineering, computer science, and mathematics. The real audience for this book is, of course, anyone who wants to read it. PPPs came only slowly to my attention and from many sources, most of
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