This book presents a complete development of Bayesian estimation filters from first principles. We consider both linear and nonlinear dynamic systems driven by Gaussian or non-Gaussian noises. It is assumed that the dynamic systems are continuous because the observations related to those systems occur at discrete times only discrete filters are discussed. The primary goal is to present a comprehensive overview of most of the Bayesian estimation methods developed over the past 60 years in a unified approach that shows how each arises from the basic ideas underlying the Bayesian paradigms related to conditional densities.
The prerequisites for understanding the material presented in this book include a basic understanding of linear algebra, Bayesian probability theory, and numerical methods for finite differences and interpolation. Chapter 2 includes a review of all of these topics and is needed for an understanding of the remaining material in the book.
Many of the topics covered in this book grew out of a one semester course taught in the graduate mathematics department at the University of Maryland, College Park. The main goal of that course was to have the students develop their own Matlab® toolbox of target tracking methods. Several very specific tracking problems were presented to the students, and all homework problems consisted of coding each specific tracking (estimation) method into one or more Matlab® subroutines. In general, the subroutines the students developed ...