A parallelizable recursive least squares algorithm for adaptive filtering, with very good tracking properties

Abstract

In this paper, a new Recursive Least Squares(RLS)algorithm for Finite Window Adaptive Filtering is presented, that has a number of interesting and useful properties. First, owing to the specific structure of the updating formulas and due to the fact that the past information is, for the first time, directly dropped by means of a proper inversion Lemma stated and proved in this paper, the proposed algorithm is immediately parallelizable. Second, it is more robust than many RLS Kalman-type schemes, in the sense that it is more resistant to the finite precision error effects. At the same time, the proposed algorithm has very good tracking capabilities. Finally, it can constitute the basis for the development of 0(m)computational complexity algorithms that have very interesting properties, too, i.e. they are robust, parallelizable and they have particularly good tracking properties.