L. Streit's Books

Poisson Point Processes

Imaging, Tracking, and Sensing

By: Roy L. Streit

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Poisson Point Processes

Imaging, Tracking, and Sensing

By: Roy L. Streit

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 computed tomography to multiple target tracking and distributed sensor detection, written from an engineering perspective. A valuable discussion of the basic properties of finite random sets is included. Maximum likelihood estimation techniques are discussed for several parametric forms of the intensity function, including Gaussian sums, together with their Cramer-Rao bounds. These methods are then used to investigate: -Several medical imaging techniques, including positron emission tomography (PET), single photon emission computed tomography (SPECT), and transmission tomography (CT scans) -Various multi-target and multi-sensor tracking applications, -Practical applications in areas like distributed sensing and detection, -Related finite point processes such as marked processes, hard core processes, cluster processes, and doubly stochastic processes, Perfect for researchers, engineers and graduate students working in electrical engineering and computer science, Poisson Point Processes will prove to be an extremely valuable volume for those seeking insight into the nature of these processes and their diverse applications.

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Page Count

274

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1441969233

ISBN 13

9781441969231

White Noise

An Infinite Dimensional Calculus

By: Takeyuki Hida,Hui-Hsiung Kuo,Jürgen Potthoff,L. Streit

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White Noise

An Infinite Dimensional Calculus

By: Takeyuki Hida,Hui-Hsiung Kuo,Jürgen Potthoff,L. Streit

Many areas of applied mathematics call for an efficient calculus in infinite dimensions. This is most apparent in quantum physics and in all disciplines of science which describe natural phenomena by equations involving stochasticity. With this monograph we intend to provide a framework for analysis in infinite dimensions which is flexible enough to be applicable in many areas, and which on the other hand is intuitive and efficient. Whether or not we achieved our aim must be left to the judgment of the reader. This book treats the theory and applications of analysis and functional analysis in infinite dimensions based on white noise. By white noise we mean the generalized Gaussian process which is (informally) given by the time derivative of the Wiener process, i.e., by the velocity of Brownian mdtion. Therefore, in essence we present analysis on a Gaussian space, and applications to various areas of sClence. Calculus, analysis, and functional analysis in infinite dimensions (or dimension-free formulations of these parts of classical mathematics) have a long history. Early examples can be found in the works of Dirichlet, Euler, Hamilton, Lagrange, and Riemann on variational problems. At the beginning of this century, Frechet, Gateaux and Volterra made essential contributions to the calculus of functions over infinite dimensional spaces. The important and inspiring work of Wiener and Levy followed during the first half of this century. Moreover, the articles and books of Wiener and Levy had a view towards probability theory.

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Page Count

528

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401736804

ISBN 13

9789401736800

Introduction to Bayesian Tracking and Particle Filters

By: Lawrence D. Stone,Roy L. Streit,Stephen L. Anderson

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Introduction to Bayesian Tracking and Particle Filters

By: Lawrence D. Stone,Roy L. Streit,Stephen L. Anderson

This book provides a quick but insightful introduction to Bayesian tracking and particle filtering for a person who has some background in probability and statistics and wishes to learn the basics of single-target tracking. It also introduces the reader to multiple target tracking by presenting useful approximate methods that are easy to implement compared to full-blown multiple target trackers. The book presents the basic concepts of Bayesian inference and demonstrates the power of the Bayesian method through numerous applications of particle filters to tracking and smoothing problems. It emphasizes target motion models that incorporate knowledge about the target’s behavior in a natural fashion rather than assumptions made for mathematical convenience. The background provided by this book allows a person to quickly become a productive member of a project team using Bayesian filtering and to develop new methods and techniques for problems the team may face.

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Page Count

124

Publisher

Springer Nature

Published Date

ISBN 10

3031322428

ISBN 13

9783031322426

Bayesian Multiple Target Tracking, Second Edition

By: Lawrence D. Stone,Roy L. Streit,Thomas L. Corwin,Kristine L. Bell

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Bayesian Multiple Target Tracking, Second Edition

By: Lawrence D. Stone,Roy L. Streit,Thomas L. Corwin,Kristine L. Bell

This second edition has undergone substantial revision from the 1999 first edition, recognizing that a lot has changed in the multiple target tracking field. One of the most dramatic changes is in the widespread use of particle filters to implement nonlinear, non-Gaussian Bayesian trackers. This book views multiple target tracking as a Bayesian inference problem. Within this framework it develops the theory of single target tracking, multiple target tracking, and likelihood ratio detection and tracking. In addition to providing a detailed description of a basic particle filter that implements the Bayesian single target recursion, this resource provides numerous examples that involve the use of particle filters. With these examples illustrating the developed concepts, algorithms, and approaches -- the book helps radar engineers develop tracking solutions when observations are non-linear functions of target state, when the target state distributions or measurement error distributions are not Gaussian, in low data rate and low signal to noise ratio situations, and when notions of contact and association are merged or unresolved among more than one target.

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Page Count

315

Publisher

Artech House

Published Date

ISBN 10

1608075532

ISBN 13

9781608075539

Book's by L. Streit

Poisson Point Processes

Poisson Point Processes

White Noise

White Noise

Introduction to Bayesian Tracking and Particle Filters

Introduction to Bayesian Tracking and Particle Filters

Bayesian Multiple Target Tracking, Second Edition

Bayesian Multiple Target Tracking, Second Edition

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