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Review of "Diakoptics and Networks" by Harvey H. Happ

The preface of this book states that "this text provides a comprehensive treatment of estimation theory with applications to communications and control." Further, the statement is made that "the text is written by engineers for engineers." The book achieves these stated goals and is quite adequate for a course in estimation theory or a text for the practicing research engineer. The first chapter briefly introduces estimation theory and outlines the material presented in succeeding chapters. Chapters 2, 3, and the first half of 4 provide a general review of probability theory, random variables, and stochastic processes with emphasis on Gaussian processes. They are well written (as are the remaining chapters) and are necessary background for the development of estimation theory. The basic concepts of probability are dealt with in Chapter 2, including algebraic operations on random variables and expectations. Chapter 3 extends the probability theory concepts into the study of stochastic processes. The format is that of a review with the exception of a very important and detailed section on linear system responses. The first part of Chapter 4 delineates some special concepts involving GaussMarkov processes. The central limit theorem is developed along with multivariate Gaussian processes. A person well grounded in probability theory can eliminate the reading of these chapters. Chapter 5 develops decision theory using both Bayes risk and Neyman-Pearson criterion. Two sections are devoted to sequential detection theory and point out the close relationship between estimation and decision theory. The most important material in the book is contained in Chapters 6-9. Bayesian estimation theory is developed along with maximum likelihood methods in Chapter 6. Sections on pseudo-Bayes estimators, error analysis, and least-squares curve fitting are given. This chapter provides an excellent introduction to the subject of estimation theory, and the relationships presented are fundamental to the understanding of modern estimation theory in the remainder of the text. Chapter 7 gives a clear and concise presentation of the basic development of the discrete and continuous Kalman filter. Its relationship to the Wiener filter is detailed and the asymptotic behavior discussed. Chapter 8 extends the optimum linear filter to include colored noise inputs, prediction algorithms, and fixed-point, fixed-lag, and fixed-interval smoothing algorithms. An error and sensitivity analysis is conducted in some detail and the divergence problem is discussed. Chapter 9 gives explicit consideration to problems in nonlinear estimation. The approach develops around a derived modified Fokker-Planck equation. Maximum a posteriori estimation algorithms for both the discrete and continuous cases are derived along with a linearized Kalman filter. Comparisons of the various algorithms are made, and as an extension nonlinear smoothing algorithms are developed. Overall the book represents an excellent contribution to the estimation theory area. Many example problems are given that provide varied applications in the communication and control fields. Some mathematical rigor is ignored, but the general presentation of the material is clear and concise, and the title adequately describes its contents.