A parallel adaptation algorithm for recursive-least-squares adaptive filters in nonstationary environments

An accurate new expression for the steady-state tracking performance of exponentially weighted recursive-least-squares (RLS) adaptive filters in a random walk scenario is derived. This relation is then used to provide a detailed comparison between RLS-performance and that of normalized least-mean-squares adaptive filters. Further, a variable-forgetting-factor algorithm referred to as the parallel adaptation algorithm that approximately achieves the theoretical minimum mean-squared-error performance in a random walk scenario is developed. Extensive simulation results are presented to support the present findings and demonstrate the improved performance of the proposed algorithm in a number of different applications