Output-error adaptive bilinear filters

The authors present 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. The results of several computer experiments show that at least one of the O(N ²) complexity algorithms works almost as well as the more complex algorithms