ULV and generalized ULV subspace tracking adaptive algorithms

Traditional adaptive lters assume that the eective rank of the input signal is the same as the input covariance matrix or the lter length N. Therefore, if the input signal lives in a subspace of dimension less than N, these lters fail to perform satisfactorily. In this paper we present two new algorithms for adapting only in the dominant signal subspace. The rst of these is a low-rank recursive-least-squares (RLS) algorithm which uses a ULV decomposition to track and adapt in the signal subspace. The second adaptive algorithm is a subspace tracking least-mean-squares (LMS) algorithm which uses a generalized ULV (GULV) decomposition, developed in this paper, to track and adapt in subspaces corresponding to several well conditioned singular value clusters. The algorithm also has an improved convergence speed compared to that of the LMS algorithm. Bounds on the quality of subspaces isolated using the GULV decomposition are derived and the performance of the adaptive algorithms are analyzed.