Low complexity bayesian adaptive filtering with independent AR(1) filter coefficient models

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 non-stationary 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. The resulting algorithm, of complexity O(N2), is shown by simulations to have performance close to that of the Kalman filter with true model parameters.