Adaptive linear prediction filters based on maximum a posteriori estimation

In this paper, we develop adaptive linear prediction filters in the framework of maximum a posteriori (MAP) estimation. It is shown how priors can be used to regularize the solution and references to known algorithms are made. The adaptive filters are suitable for implementation in real-time and by simulation with an adaptive line enhancer (ALE), it is shown how the parameters of the estimation problem affect the convergence of the adaptive filter. The adaptive line enhancer (ALE) is a widely used adaptive filter to separate periodic signals from additive background noise where it has traditionally been implemented using the least-mean-square (LMS) or recursive-least-square (RLS) filter. The derived algorithms can generally be used in any adaptive filter application with a desired target signal.