FIFTH ANNUAL
ASAP '97 WORKSHOP

Fast Approximate
Subspace Tracking

¹ Sanders, A Lockheed Martin Company
PTP2-A001, P.O. Box 868
Nashua, NH 03061-0868
email: r eal@rocket.sanders.com

² University of Rhode Island
Department of Electrical Engineering
Kingston, RI 02881
email: cooley@ele.uri.edu

Abstract A new fast and accurate algorithm for tracking singular values, singular vectors and the dimension of the signal subspace through an overlapping sequence of data matrices is presented. The accuracy of the algorithm approaches that of the Prony-Lanczos (PL) method [1] with speed and accuracy superior to both the PAST and PASTd algorithms [2] for moderate to large size problems. The algorithm is described for the special case of changes to two columns of the matrix prior to each update of principle singular vectors and values; although the approach is not limited to two column updates. Comparisons of speed and accuracy are made with the algorithms named above. Specifically, we introduce a new algorithm for efficiently tracking the principle singular values and the associated left (or right) singular vectors of successive data matrices formed from observations of a nonstationary signal in non-stationary noise. The dimension of the signal subspace is tracked simultaneously with the singular values and vectors. The ability to do this accurately and in real time is a critical requirement of many signal processing applications in areas such as radar, sonar, communications, pattern recognition, and speech processing.