Recursive regularisation parameter selection for sparse RLS algorithm

Abstract

In this Letter, the authors propose a recursive regularisation parameter selection method for sparse recursive least squares (RLS) algorithm. The proposed RLS algorithm is regularised by a convex function, which equals the linear combination of two convex functions, one to cope with random sparsity, and the other to cope with group sparsity. The normal equations corresponding to the RLS algorithm with the proposed convex regularised penalty function are derived, and a recursive algorithm to update the regularisation parameters (i.e. the coefficients of the linear combination) is proposed. As an example, by using the linear combination of an l 0 -norm and an l 2 , 0 -norm as the penalty function, simulation results show that the proposed sparse RLS with recursive regularisation parameter selection can achieve better performance in terms of mean square error for a slowly time-varying sparse system with both random sparsity and group sparsity.