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Overview
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.
Synopsis
Introduction to Optimal Estimation is an introductory but comprehensive treatment of the important topics of Kalman and Wiener filtering. In addition, least-squares, maximum-likelihood and maximum a posteriori (based on discrete-time measurements) estimation are developed, covering a broad range of techniques in a single textbook. Emphasis is placed on showing how these different approaches can be fitted together to form a systematic rationale for optimal estimation. The different matters to be addressed in actually computing estimates and characterizing the properties of estimates viewed as random variables are explained and underlined throughout. The text also incorporates study of nonlinear filtering, focusing on the extended Kalman filter and on a recently-developed nonlinear estimator based on a block-form version of the Levenberg-Marquardt algorithm.
Introduction to Optimal Estimation is for use in a single course (or, with judicious pruning, a one-quarter course) on estimation by senior undergraduates or first-year graduate students. A number of the examples in this text were fashioned using MATLAB® and some of the homework problems require it. Students using this book will need to have completed a standard course on probability and random variables and at least one course in signals and systems including state-space theory for linear systems.