Generalized Savitzky–Golay filters for identification of nonstationary systems

Abstract

The problem of identification of nonstationary systems using noncausal estimation schemes is considered and a new class of identification algorithms, combining the basis functions approach with local estimation technique, is described. Unlike the classical basis function estimation schemes, the proposed local basis function estimators are not used to obtain interval approximations of the parameter trajectory, but provide a sequence of point estimates corresponding to consecutive instants of time. Based on the results of theoretical analysis conducted for nonstationary finite impulse response systems the paper proposes two mechanisms for adaptive selection of the number of basis functions and the size of the local analysis window.