Generalized URV Subspace Tracking LMS Algorithm 1

The convergence rate of the Least Mean Squares (LMS) algorithm is poor whenever the adaptive lter input auto-correlation matrix is ill-conditioned. In this paper we propose a new LMS algorithm to alleviate this problem. It uses a data dependent signal transformation. The algorithm tracks the subspaces corresponding to clusters of eigenvalues of the auto-correlation matrix of the input to the adaptive lter, which have the same order of magnitude. The algorithm up-dates the projection of the tap weights of the adaptive lter onto each subspace using LMS algorithms with dierent step sizes. The technique also permits adaptation only in those subspaces, which contain strong signal components leading to a lower excess Mean Squared Error (MSE) as compared to traditional algorithms.