Adaptive Second-Order Volterra Filtering Based on an H∞ Criterion

Abstract

This paper presents an adaptive Volterra filter implementation based on an exponentially-weighted a posteriori H∞ filtering algorithm. Its fast array form is immediately obtained by following the derivation of the fast multichannel RLS filter. Also the steady-state performance of the H∞ Volterra filter is analyzed by using an approximate expression for its excess mean-square errors. Several numerical examples show that the H∞ Volterra filter could achieve a balance between convergence and tracking capability when its attenuation parameter is chosen adequately.