Stochastic Processes and Filtering Theory

Andrew H. Jazwinski (Eds.)0123815509, 9780123815507

This book presents a unified treatment of linear and nonlinear filtering theory for engineers, with sufficient emphasis on applications to enable the reader to use the theory. The need for this book is twofold. First, although linear estimation theory is relatively well known, it is largely scattered in the journal literature and has not been collected in a single source. Second, available literature on the continuous nonlinear theory is quite esoteric and controversial, and thus inaccessible to engineers uninitiated in measure theory and stochastic differential equations. Furthermore, it is not clear from the available literature whether the nonlinear theory can be applied to practical engineering problems. In attempting to fill the stated needs, the author has retained as much mathematical rigor as he felt was consistent with the prime objective-to explain the theory to engineers. Thus, the author has avoided measure theory in this book by using mean square convergence, on the premise that everyone knows how to average. As a result, the author only requires of the reader background in advanced calculus, theory of ordinary differential equations, and matrix analysis.

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Table of contents :
Content:
Edited by
Page iii

Copyright Page
Page iv

Dedication
Page v

Preface
Pages vii-viii
Andrew H. Jazwinski

Acknowledgments
Page ix

1 Introduction
Pages 1-7

2 Probability Theory and Random Variables
Pages 8-46

3 Stochastic Processes
Pages 47-92

4 Stochastic Differential Equations
Pages 93-141

5 Introduction to Filtering Theory
Pages 142-161

6 Nonlinear Filtering Theory
Pages 162-193

7 Linear Filtering Theory
Pages 194-265

8 Applications of Linear Theory
Pages 266-331

9 Approximate Nonlinear Filters
Pages 332-366

Author Index
Pages 367-370

Subject Index
Pages 371-376