Identification and prediction of nonlinear systems using orthonormal functions

In a recent paper Mulgrew [1] proposed a nonlinear filtering structure which utilises a set of orthonormal expansions to model nonlinear dynamical systems. Provisional results were presented for a simple 1-dimensional system. In this paper we extend the analysis of this structure to multi-dimensional filtering, and examine the application of the orthonormal structure for nonlinear system identification and communications channel equalisation. The link between the choice of Fourier basis functions and popular kernel probability density estimation techniques is examined.