On the convergence of Bayesian Adaptive Filtering

Standard adaptive filtering algorithms, including the popular LMS and RLS algorithms, possess only one parameter (step-size, forgetting factor) to adjust the tracking speed in a nonstationary environment. Furthermore, existing techniques for the automatic adjustment of this parameter are not totally satisfactory and are rarely used. In this paper we pursue the concept of Bayesian Adaptive Filtering (BAF) that we introduced earlier, based on modeling the optimal adptive filter coefficients as a stationary vector process, in particular a diagonal AR(1) model. Optimal adaptive filtering with such a state model becomes Kalman filtering. The AR(1) model parameters are determined with an adaptive version of the EM algorithm, which leads to linear prediction on reconstructed optimal filter correlations, and hence a meaningful approximation/estimation compromise. In this paper we will introduce the convergence behavior of the adaptive part.