The QS-Householder Sliding Window Bi-SVD Subspace Tracker
Peter Strobach · IEEE Transactions on Signal Processing · 2009
A fast algorithm for computing the sliding window bi-SVD subspace tracker is introduced. This algorithm produces, in each time step, a dominant rank-rSVD subspace approximant of anLtimesNrectangular sliding window data matrix. The method is based on theQS(orthonormal-square) decomposition. It uses two row-Householder transformations for updating and one nonorthogonal Householder transformation for downdating in each time step. The resulting algorithm is long-term stable and shows excellent numerical and structural properties, as known from pure Householder-type algorithms. The dominant complexity is4Lr+3Nrmultiplications per time update, which is also the lower bound in dominant complexity for an algorithm of this kind. A completely self-contained algorithm summary is provided and a Fortran subroutine of the algorithm is available for download from http://webuser.hs-furtwangen.de/~strobach/qsh-bisvd.for.