ULV and generalized ULV subspace tracking adaptive algorithms

Traditional adaptive filters assume that the effective rark of the input signal is the same as the input covariance matrix or the filter length N. Therefore, if the input signal lives in a subspace of dimension less than N, these filters fail to perform satisfactorily. In this paper, we present two new algorithms for adapting only in the dominant signal subspace. The first of these is a low-rank recursive-least-squares (RLS) algorithm that uses a ULY decomposition to track and adapt in the signal subspace. The second adaptive algorithm is a subspace tracking leastmean-squares (LMS) algorithm that uses a generalized ULV (GULV) decomposition, which has been developed in this paper, to track and adapt in subspaces corresponding to several well-conditioned singular cue clusters. The algorithm also has an improved convergence speed compared with 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.