Nonlinear system identification using optimally selected Laguerre filter banks

A system's Volterra kernels may be estimated by identifying a Wiener-Bose model consisting of a bank of discrete Laguerre filters followed by a multiple input polynomial. This projects the kernels onto a reduced-order basis formed by the impulse responses of the Laguerre filters, dramatically reducing the number of estimated parameters, but requiring the a priori selection of two tuning parameters: a decay parameter that defines the Laguerre filters, and the number of filters in the bank. In applications to linear system identification, these tuning parameters can be selected automatically, using either an iterative optimization or an analytical solution. In this paper, both the iterative and analytical techniques are derived for the nonlinear case, and applied to the identification of Wiener-Bose models. A simulation study is used to evaluate the performance of the proposed algorithms