A two-stage approach to Bayesian adaptive filtering

The purpose of this paper is to introduce Bayesian Adaptive Filtering (BAF) techniques that are not immensely more complex than the LMS algorithm. The proposed two-stage approach consists of a first stage employing a basic fast tracking adaptive filter, followed by lowpass filtering and downsampling of the time-varying filter coefficients. The second stage then applies Kalman filtering at the reduced rate on a simplified state-space model, with an additive white noise measurement equation. The parameters in the state equation can be conveniently identified with an adaptiveEM algorithm. The first stage would typically employ a (Normalized) LMS algorithm with a large stepsize. The main assumption underlying the proposed two-stage approach is that even in fast tracking applications, the bandwidth of the optimal filter variation is typically small compared to the signal bandwitdh, motivating the downsampling operation. The first stage attempts to provide a bias-free filter estimate whereas the second stage optimizes the estimation variance. The performance of the proposed scheme is evaluated by simulations.