Robust regularization of the recursive least-squares algorithm

This paper is dedicated to the memory of Steven L. Grant for his exceptional contributions to the echo cancellation problem. The regularization is mandatory in all ill-posed problems, especially in the presence of additive noise. In this paper, we consider the regularized recursive least-squares (RLS) algorithm and present a method to find its regularization parameter, depending on the signal-to-noise ratio. We also outline the robustness features of this solution, which could make the RLS algorithm to behave well even in non-stationary environments. Simulations performed in the context of echo cancellation support these findings.