Recursive least squares estimation of nonlinear multiple-input systems using orthonormal function expansions

We present a computational scheme to obtain adaptive non-linear, multiple-input models of the Volterra-Wiener class, by utilizing function expansions of the Volterra kernels in a recursive least-squares formulation. Function expansions have been proven successful in linear and nonlinear systems identification as they result in a significant reduction of the required free parameters, which is a major limiting factor particularly for nonlinear systems, whereby this number depends exponentially on the nonlinear system order. We illustrate the performance of the proposed scheme by presenting results for a simulated linear two-input system with time-varying characteristics.