This book motivates the use of Bayesian models for signal processing from a probabilistic perspective. The author shows the connection between classic model-based signal processing that relies on prior knowledge and the probabilistic Bayesian framework that can specify the distribution required to develop (particle) filters. This approach is coupled with showing the metamorphosis of sampling Monte Carlo methods. This methodology is a wonderful way to extract critical information from complex simulations of dynamic processes. All of this lays the groundwork and the foundations for solving signal processing problems presented in the later chapters of the text.

Signal processing has been utilized to obtain critical information in the presence of noise and uncertain data. Standard approaches rely on Gaussian (mostly linear) approaches to achieve solutions, but are not necessarily robust in the presence of noise. Because of this problem, the methods of choice are Bayesian, because they can incorporate nonlinear processes. Throughout the text, the author stresses the advantages of Bayesian methods with physics-based models, over strict model-based signal processing. To be current, the text includes a hierarchy of the latest particle filters, enabled by high-speed processor computers. The book provides algorithms, examples, applications, and case studies based on these approaches. The author does, however, pedagogically emphasize classical approaches--such as Kalman filters, Gaussian sums, and alternative filters--so that the reader can relate to standard approaches and then spring forward to the newer methodologies.

The text has ten chapters that cover a range of topics, from introductory material in chapter 1 to Bayesian processors for physics-based applications. Chapter 1 develops signal processing from a Bayesian perspective. Chapter 2 concentrates on the estimation aspects of Bayesian approaches, both from the maximum likelihood and the minimum variance standpoints. This leads to a sequential approach to Bayesian estimation. Chapter 3 simulates these methods and compares them to Monte Carlo methods. Chapter 4 models state spaces with sampled, discrete, Gauss-Markov, and nonlinear variations. Chapters 5 and 6 contrast classic state-space filters (linear, extended, and iterated Kalman filters) with modern Bayesian ones (sigma-point, quadrature, and Gaussian sums), and present two case studies: a resonant inductive circuit problem and two-dimensional tracking.

Chapters 7 to 10 present more advanced material. Chapter 7 introduces Bayesian state-space processors that are particle based. It discusses the importance of proposal distributions, as well as the practical aspects of particle filter design. The case study included in this chapter is a population growth problem. A hybrid approach of Bayesian and parametric processors is presented in chapter 8, with a case study on random target tracking, using a synthetic aperture towed array. Chapter 9 investigates hidden Markov models for Bayesian processors, and calculates the observation probability. The case study for this chapter is time reversal decoding. The last chapter brings it all together, with physics-based applications for Bayesian processors: optimal position estimation, broadband ocean acoustics, and detection of radioactive sources. An appendix provides an overview of probability and statistics concepts.

The text is highly advanced, but very relevant for the study of practical aspects of Bayesian signal processing. Candy, a former director of the Center for Advanced Signal and Image Sciences at the Lawrence Livermore National Laboratory, has produced a significant text for the field.