Söderström T. Discrete-time Stochastic Systems. Estimation and Control

Springer, 2002. — 387 p.This book has been written for graduate courses in stochastic dynamic systems. It has emerged from various lecture notes (in Swedish and in English) that I have compiled and used in different courses at Uppsala University since 1978.
The current text is a second edition of a book originally published by Prentice Hall International in 1994. All chapters have been revised. A number of typographical and other errors have been corrected. Various new material and results, including further problems, have been added.
The reader is assumed to be somewhat familiar with dynamic systems and stochastic processes. In particular, it is assumed that the reader has a working knowledge of the following areas (or is prepared to re-examine this background elsewhere, should it be necessary): fundamentals of linear discrete-time systems (such as state space models and their relationships with transfer function operators and weighting functions); fundamentals of probability theory (including Gaussian distributed random vectors and conditional probabilities); fundamentals of linear algebra and matrix calculations; fundamentals of stochastic processes (such as the concepts of covariance function and spectral density, particularly in discrete time).Some Probability Theory
Models
Analysis
Optimal Estimation
Optimal State Estimation for Linear Systems
Optimal Estimation for Linear Systems by Polynomial Methods
Illustration of Optimal Linear Estimation
Nonlinear Filtering
Introduction to Optimal Stochastic Control
Linear Quadratic Gaussian Control