The book combines both rigor and intuition to derive most of the classical results of linear and nonlinear filtering and beyond. Many fundamental results recently discovered by the author are included. Furthermore, many results that have appeared in recent years in the literature are also presented. The most interesting feature of the book is that all the derivations of the linear filter equations given in Chapters 3-11, beginning from the classical Kalman filter presented in Chapters 3 and 5, are based on one basic principle which is fully rigorous but also very intuitive and easily understandable. The second most interesting feature is that the book provides a rigorous theoretical basis for the numerical solution of nonlinear filter equations illustrated by multidimensional examples. The book also provides a strong foundation for theoretical understanding of the subject based on the theory of stochastic differential equations.
Introduction to stochastic processes; stochastic differential equations; Kalman filtering for linear systems driven by Weiner process I; Kalman filtering for linear systems driven by Weiner process II; discrete Kalman filtering; linear filtering with correlated noise I; linear filtering with correlated noise II; linear filtering with correlated noise III; linear filtering of jump processes; linear filtering with constraints; filtering for linear systems driven by second order random processes; extended Kalman filtering I,II, and III; nonlinear filtering; numerical techniques for nonlinear filtering; partially observed control; system identification.