Building an accurate mathematical model of a complex system in the presence of noisy data is a difficult task. An experiment must be designed, a model must be constructed from physical laws, and the model parameters must be estimated from the experimental measurements. Several books address system identification, including those containing theory and applications to discrete time models. This book attempts to fill a “gap in the literature…on the accurate modeling of linear dynamic systems from noisy measurements leading to physical interpretation.”

The first two chapters provide a general introduction to the theory and methods of parameter estimation. The authors outline the identification process and provide concrete examples. They discuss several parameter estimation methods based on least squares and include numerical considerations. These chapters provide the background for the rest of the book.

The heart of the book is chapters 3 through 5. The authors present a frequency domain maximum likelihood estimator that is appropriate for linear time invariant systems with independent Gaussian noise on both the input and output Fourier coefficients. A good perspective is provided on where this work fits in with other approaches. A chapter on the design of optimal excitation signals follows. The core chapters conclude with some advice on selecting the right model and, in particular, some techniques for evaluating the appropriateness of a given model.

The remaining chapters extend the proposed estimation technique and provide many detailed applications. General advice is given for constructing a transfer function model.

This book is well written. It is aimed at the practicing engineer or the researcher interested in modeling linear dynamic systems. Each chapter begins with a preview and ends with a summary, providing a clear sense of where the authors are headed. No exercises appear in the book, but the authors have developed a Matlab toolbox that could be used in the classroom. An extensive list of references is included.