A transient analysis for the convex combination of two adaptive filters with transfer of coefficients

Abstract

This paper proposes an improved model for the transient of convex combinations of adaptive filters. A previous model, based on a first-order Taylor series approximation of the nonlinear functions that appear in convex combinations, tended to overestimate the variance of the auxiliary variable used to estimate the mixing parameter. In this paper, we apply a second-order Taylor approximation that improves these estimates, and obtains better agreement with simulations. In addition, we also extend the model to include a simple mechanism for the transfer of coefficients between the constituent filters, a procedure that greatly improves the convergence of the overall filter, and provide an expression to select the free parameter used in such a scheme.