Estimation of generalised Hammerstein-Wiener systems

Abstract

This paper examines the use of a so-called "generalised Hammerstein-Wiener" model structure that is formed as the concatenation of an arbitrary number of Hammerstein systems. The latter are taken here to be memoryless non-linearities followed by linear time invariant dynamics. Hammerstein, Wiener, Hammerstein-Wiener and Wiener-Hammerstein models are all special cases of this structure. The parameter estimation of this model is investigated by using a standard prediction error criterion coupled with a robust gradient based search algorithm. This approach is profiled using the Wiener-Hammerstein system benchmark data, which illustrates it to be effective and, via Monte-Carlo simulation, relatively robust against capture in local minima