Estimation, control, and the discrete Kalman filter / Donald E. Catlin

This book presents an introduction to a family of estimation, observation and filtering problems. The author starts with the definition of minimum variance estimation. Then he introduces the notion of entropy and, using the maximum entropy principle, solves minimum variance estimation with a prior covariance problem. Next the linear minimum variance estimation is considered. In a Bayesian approach the recursive linear estimator of random variables with linear additively corrupted observation is obtained. These results are applied to recursive estimation of discrete linear dynamical systems called Kalman filters. Special attention is devoted to the estimation of priors necessary to initialize the Bayesian estimation. The last two chapters concern an application of the Kalman filtering techniques to partially observed linear stochastic control with quadratic cost and fixed interval smoothing.
The book is specifically designed as a one-semester text for students in applied mathematics and engineering. For the convenience of the reader the author provides basic probability concepts and a series of appendices containing the essentials of measure and integration theory and Hilbert spaces. There are many comments and explanations, sometimes of a philosophical nature, which should allow the reader to realize that the mathematics presented is a useful tool for describing difficult practical problems. The text seems to be a valuable handbook in applied mathematical sciences. (MSN)