ADVANCED ENGINEERING applications need useful mathematical models. System identification (SI) deals with the problem of obtaining models of dynamical systems from measured data. Software packages have made SI an everyday tool for many engineers and virtually a myriad of successful applications have been reported in the literature. As indicated by Ljung (1991), although system identification has developed into a mature, practical tool, it is not dead as a research area. The reason is that progress and new application areas require increasingly advanced modeling concepts.
System identification is often divided into non-parameteric and parameteric methods. As the reviewer was brought up in the Swedish school of SI, starting with the classical work of AstrGm and Bohlin (1965), he may tend to show a bias in favor of time domain parameteric SI methods; this should be taken into account when reading the review. The standard references Ljung and S/SderstrGm (1983( ), Ljung (1987) ) and SGderstr~im and Stoica (1989) thus act as the bible when reviewing new books in the area of SI. This is not completely fair when judging work that is motivated by application areas slightly outside the mainstream. It should be noted that the authors of the book are active in the area of instrumentation and measurements. The aim is to obtain dynamical models from noisy measurements, leading to physical interpretation. Con~quently, a frequency domain parametric approach is a natural choice.
In order to relate the book to the current status of SI, ~me relevant research issues will first be discussed.
The recent progress in robust control design has triggered frantic research activity around modeling of uncertainty in control systems; see e.g. the IEEE Trart~. Aut. Control Special Issue on System Identification for Robust Control Design, July 1992. A result of this effort is a renewed interest in frequency domain SI methods. Most of the frequency domain methods give non-parametric estimates. In Ljung and Glover (1981) frequency domain versus time domain methods in system identification are discussed. The idea of fitting parametric models to estimated frequency responses is classical. Recently, there has been extensive interest in such methods. For more details and relevant references see e.g. Parker and Bitmead (1987), LaMarie et al. (1991), Sidman et al. (1991) and Hemicki et al. (1991). The Empirical Transfer Function Estimate studied in Ljung (1985) gives insight into the connection between time domain and frequency domain SI methods. The same idea was used by Peter Whittle at the beginning of the 50s to derive the so-called Whittle estimator for time series analysis, see e.g. Chapter 6.2 in Hannan and Deistler (1988). The Whittle estimator can be derived by the maximum likelihood principle using statistical properties of Fourier coefficients. This is also the starting point for the main method of the book under review. The input and output signals are transformed into the frequency domain. A parameteric model of the system is then fitted to the corresponding spectral lines using a cost-function motivated by the maximum likelihood principle.
The first two chapters of the book introduce system identification in general and the maximum likelihood