Finite-window RLS algorithms

Two recursive least-squares (RLS) adaptive filtering algorithms are most often used in practice, the exponential and sliding (rectangular) window RLS algorithms. This popularity is mainly due to existence of low-complexity versions of these algorithms. However, these two windows are not always the best choice for identification of fast time-varying systems, when the identification performance is most important. In this paper, we show how RLS algorithms with arbitrary finite-length windows can be implemented at a complexity comparable to that of exponential and sliding window RLS algorithms. Then, as an example, we show an improvement in the performance when using the proposed finite-window RLS algorithm with the Hanning window for identification of fast time-varying systems.