Further results in multistage adaptive filtering

In this paper, we investigate some of the stochastic properties of two recently introduced multistage adaptive filtering algorithms, namely the LMS-Bayesian and the RLS-Bayesian algorithms. We study probability-1 convergence of these algorithms and derive their final mean squared error for stationary Gaussian time series. We will show that under some general independence assumptions, both algorithms are convergent in a probability-1 sense and achieve the performance of the best algorithm used in the mixture.