Introduction to Optimal Estimation

This book provides an introductory, yet comprehensive, treatment of both Wiener and Kalman filtering, along with a development of least-squares estimation, maximum likelihood estimation, and maximum a posteriori estimation based on discrete-time measurements. A good deal of emphasis is placed in the text on showing how these different approaches to estimation fit together to form a systematic development of optimal estimation. Included in the text is a chapter on nonlinear filtering, focusing on the extended Kalman filter (EKF) and a new measurement update that uses the Levenburg-Marquardt algorithm to obtain more accurate results in comparison to the EKF measurement update. Applications of nonlinear filtering are also considered, including the identification of nonlinear systems modeled by neural networks, FM demodulation, target tracking based on polar-coordinate measurements, and multiple target tracking.

This book, developed from a set of lecture notes by Professor Kamen, and since expanded and refined by both authors, is an introductory yet comprehensive study of its field. It contains examples that use MATLAB^® and many of the problems discussed require the use of MATLAB^®. The primary objective is to provide students with an extensive coverage of Wiener and Kalman filtering along with the development of least squares estimation, maximum likelihood estimation and a posteriori estimation, based on discrete-time measurements. In the study of these estimation techniques there is strong emphasis on how they interrelate and fit together to form a systematic development of optimal estimation. Also included in the text is a chapter on nonlinear filtering, focusing on the extended Kalman filter and a recently-developed nonlinear estimator based on a block-form version of the Levenberg-Marquadt Algorithm.