Output-error adaptive bilinear filters

This paper presents an overview of several gradient type recursive algorithms for adaptive nonlinear filters equipped with bilinear system models. Bilinear models are attractive because they can approximate a large class of nonlinear systems with great parsimony in the use of coefficients. Two algorithms of complexity O(N3) (N is the memory span of the bilinear system model used in the adaptive filter) multiplications per sample and two other algorithms of complexity O(N2) multiplications per sample are presented in this paper. The results of several computer experiments show that at least one of the O(N2) complexity algorithms works almost as well as the more complex algorithms.