Résumé:
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 N
2
, is shown by simulations to
have performance close to that of the Kalman filter with true
model parameters. In this paper, we apply a component-wise
EM approach to further reduce the complexity to being linear in the number of adaptive filtering coefficients. The good
performance of the resulting algorithm is illustrated in simulations. The AR(1) state model can be further approximated
by a random walk, leading to further simplified adaptive filter that can be interpreted an LMS algorithm with a variable
step-size per filter tap
