Maximum a Posteriori based Adaptive Algorithms

It is well known that most adaptive filtering algorithms are developed based on the methods of least mean squares or of least squares. The popular adaptive algorithms such like the LMS, the RLS and their variants have been developed for different applications. In this paper, we propose to use maximum a posteriori (MAP) probability approach to estimate the filter coefficients. We show that the RLS, LMS and their variants based on the MAP method are in fact particular cases where the models of the filtering errors and the filter coefficients are with different probability density functions. We can further explore new adaptive algorithms within MAP framework.