Use of discrete laguerre expansions for noniterative identification of nonlinear wiener models

A noniterative least-squares method is presented to identify a discrete-time Wiener model, which consists of a linear dynamic element followed by a nonlinear static element. The identification algorithm represents the linear dynamics as a Laguerre FIR (finite impulse response) expansion with a time-scaling factor and approximates the static nonlinearity by an inverse polynomial function with a reference point. The incorporation of an adjustable reference point allows an arbitrary input design for the identification test and renders the algorithm robust with respect to noise. Furthermore, a proper selection of the time-scaling factor and the output reference value could facilitate accurate estimation of the linear and nonlinear elements, respectively. With the two arguments specified a priori, the regression equation becomes linear-in-parameters, involving the Laguerre and polynomial coefficients to be estimated. Two error criteria concerning the internal variable are then proposed to infer their proper values. When the process is highly nonlinear, a four-segment piecewise linear function is developed to replace the polynomial function for the approximation of static nonlinearity. Another error criterion concerning the output variable is employed to find the partition points for the four segments. Simulation study with four physical examples demonstrates that the proposed identification method is valid for a variety of test conditions and nonlinearities.