ULV and generalized ULV subspace tracking adaptive algorithms

Author

Hosur, Srinath ; Tewfik, Ahmed H. ; Boley, Daniel

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., Minnesota Univ., Minneapolis, MN, USA

Volume

46

Issue

5

fYear

1998

fDate

5/1/1998 12:00:00 AM

Firstpage

1282

Lastpage

1297

Abstract

Traditional adaptive filters assume that the effective rank 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 ULV decomposition (Stewart 1992) to track and adapt in the signal subspace. The second adaptive algorithm is a subspace tracking least-mean-squares (LMS) algorithm that 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 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

Keywords

adaptive filters; convergence of numerical methods; least squares approximations; recursive filters; singular value decomposition; tracking filters; GULV decomposition; ULV; adaptive filters; convergence speed; dominant signal subspace; filter length; generalized ULV; input covariance matrix; input signal; low-rank recursive-least-squares algorithm; performance; signal subspace; subspace dimension; subspace tracking adaptive algorithms; subspace tracking least-mean-squares algorithm; well-conditioned singular value clusters; Adaptive algorithm; Adaptive filters; Adaptive signal processing; Clustering algorithms; Convergence; Covariance matrix; Least squares approximation; Matrix decomposition; Resonance light scattering; Signal processing algorithms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.668792

Filename

668792