Non-Iterative Identification of IIR Wiener Systems Using Orthogonal Polynomial

In this work, a non-iterative identification approach is presented for estimating a single-input single-output Wiener model, comprising an infinite impulse response discrete transfer function followed by static non-linearity. Global orthogonal basis functions and orthogonal Hermite polynomials are used as expansion bases for the linear subsystem and the non-linearity, respectively. A multi-index based method is used to transform the non-convex optimization over the parameter values into an over-parametrized linear regression. A singular value decomposition based method is then used to project the result of the over-parametrized linear regression onto the class of Wiener models, each comprising a linear element followed by a memoryless non-linearity. The advantages obtained by using orthogonal polynomials are illustrated using a series of simulation examples.