Hammerstein system identification by the Haar multiresolution approximation

The paper deals with recovering non-linearities in the Hammerstein systems using the multiresolution approximation-a basic concept of wavelet theory. The systems are driven by random signals and are disturbed by additive, whi te or coloured, random noise. The a priori information about system compone nts is non-parametric and a delay in the dynamical part of systems is admit ted. A non-parametric identification algorithm for estimating non-linear ch aracteristics of static parts is proposed and investigated. The algorithm i s based on the Haar multiresolution approximation. The pointwise convergenc e and the pointwise asymptotic rate of convergence of the algorithm are est ablished. It is shown that neither the form nor the convergence conditions of the algorithm need any modification if the noise is not white but correl ated. Also the asymptotic rate of convergence is the same for white and col oured noise, The theoretical results are confirmed by computer simulations. Copyright (C) 1999 John Wiley & Sons, Ltd.