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Reviewer: Vladimir Botchev

Although this book is meant for an introductory course on the basic theory of signal detection and estimation, this text, like the topic, is highly complicated. As stated in the preface, a mastery of applied probability is required, and the text does not contain tutorial appendices to make it more self-contained. Therefore, this textbook will be profitable only to those with a solid graduate-level background in probability and statistics, and systems and signals theory. The book has seven chapters. The first chapter is an introduction with a brief overview of the contents and some remarks about the notation. Each of the remaining chapters deals with a major topic in the theory of signal detection and estimation. Chapter 2 introduces hypothesis testing; the classical Bayesian, minimax, and Neyman-Pearson formulations are considered. Worked examples illustrate the theory, and several end-of-chapter exercises are provided here and in all the later chapters. Chapter 3 discusses signal detection or, in other words, procedures for detecting signals embedded in noise. Only the discrete time case is considered. The author uses numerous examples to analyze all major topics, including observation models and detector structures; performance evaluation of detection procedures; and robust detection. Estimation theory is the theme of the next two chapters. Static parameter estimation is covered in chapter 4, and time-varying (or dynamic) parameter estimation, more widely known as signal estimation, is addressed in chapter 5. Bayesian and maximum-likelihood estimation form the core of chapter 4, while Kalman and Wiener filtering are central to chapter 5. The last two chapters discuss signal detection and estimation from the more classical point of view of observations modeled as a continuous time random process. Here the author acknowledges the mathematical complexity of the material and has included some pages discussing some of the essential definitions and theorems needed to gain a deeper understanding of subsequent material. The classical pathway is then followed, covering coherent detection and Wiener processes in chapter 6. Chapter 7, on estimation, presents continuous-time Kalman filtering and the advanced topic of nonlinear filtering. This text can be recommended as a good—although complex—introductory treatment of essential background theory for the detection and estimation of signals, for both the discrete-time and the continuous-time models.