Bayesian methods are named for the great mathematician, Thomas Bayes. They have found application in almost all fields of applied statistics and signal processing. Among the various filtering methods available, Bayesian filtering and smoothing are popular methods for signal processing. Filtering and smoothing processes are relatively easy for time-invariant and linear systems. But many real-world systems are time variant and nonlinear in nature, making the filtering and smoothing processes challenging. This book discusses filtering methods for time-variant and nonlinear systems.

The author starts nicely with descriptions of Bayesian filtering and smoothing, and a list of possible applications and algorithms. Each and every concept is presented with graphs obtained by simulation. The book also includes very helpful MATLAB exercises, a comprehensive list of symbols and abbreviations at the beginning of the book, and a set of high-quality references at the end.

There are 13 chapters. The first two introduce the basics of Bayesian filtering and smoothing and clearly outline the flow of the book. I was quite impressed by the comprehensive list of all possible applications. The next five chapters, 3 to 7, are dedicated to filtering methods, such as linear regression, state space models, extended and unscented Kalman filters, and particle filters. All these filtering methods are illustrated with a pendulum example and the algorithms are well presented analytically. Chapters 8 to 11 focus on Bayesian, Gaussian, and particle smoothing methods. Here, too, the pendulum example is used to illustrate the methods, supported by strong analysis. Next is a chapter on parameter estimation, including various estimation methods for state space models. The last chapter addresses the interesting topic of “Which method should I choose?”

Readers with limited mathematical backgrounds would get more out of the book if the author had included more numerical illustrations and explanations. However, I believe advanced readers and electrical engineering graduate students with solid mathematical backgrounds will find it quite useful.

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