On the Tracking Performance of Adaptive Filters and Their Combinations

Combinations of adaptive filters have attracted attention as a simple solution to improve filter performance, including tracking properties. In this paper, we consider combinations of LMS and RLS filters, and study their performance for tracking time-varying solutions. Modeling the variation of the parameter vector to be estimated as a first order autoregressive (AR) model, we show that a convex combination between one LMS and one RLS filters with their optimum settings may have a tracking performance close to the optimal excess mean-square error (EMSE) and mean-square deviation (MSD) obtained via Kalman filter, but with lower computational complexity (linear in the filter length instead of quadratic - in the case of diagonal matrices in the Kalman model - or cubic, for general Kalman models).