Steady-State Performance Comparison of Bayesian and Standard Adaptive Filtering

It has been known for a long time that for best tracking results adaptive filtering should be formulated as a Kalman filtering problem, leading to Bayesian Adaptive Filtering (BAF). BAF techniques with acceptable complexity can be obtained by focusing on a diagonal AR(1) model for the time-varying optimal filter settings. The hyper-parameters of the AR(1) model can be adapted by introducing EM techniques and one sample fixed-lag smoothing at little extra cost. Standard AF techniques such as the LMS and RLS algorithms are equipped with only one hyper-parameter (stepsize, forgetting factor) to optimize their tracking behavior. In this paper we compare the steady-state tracking performance of Bayesian and standard AF techniques.