Analysis of gradient-based adaptation algorithms for linear and nonlinear recursive filters

The problem of adapting linear and nonlinear recursive filters through a gradient-based optimization procedure is considered. The rigorous application of this technique implies a time-growing computation load. Recently, a method for estimating the weight updates was introduced, leading to a new class of algorithms. The convergence properties of these algorithms, when applied to a linear and then a nonlinear recursive filter, are exhibited through a dynamical analysis of the adaptation process. Since the general analysis is very difficult, the case of a first-order filter with a constant input is considered. Significant results are obtained in this particular application