Combined Parametric-Nonparametric Identification of Block-Oriented Systems

This book considers a problem of block-oriented nonlinear dynamic system identification in the presence of random disturbances. This class of systems includes various interconnections of linear dynamic blocks and static nonlinear elements, e.g., Hammerstein system, Wiener system, Wiener-Hammerstein ('sandwich') system and additive NARMAX systems with feedback. Interconnecting signals are not accessible for measurement. The combined parametric-nonparametric algorithms, proposed in the book, can be selected dependently on the prior knowledge of the system and signals. Most of them are based on the decomposition of the complex system identification task into simpler local sub-problems by using non-parametric (kernel or orthogonal) regression estimation. In the parametric stage, the generalized least squares or the instrumental variables technique is commonly applied to cope with correlated excitations. Limit properties of the algorithms have been shown analytically and illustrated in simple experiments.