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The QS-Householder Sliding Window Bi-SVD Subspace Tracker

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1 Author(s)
Strobach, P. ; AST-Consulting Inc., Rohrnbach, Germany

A fast algorithm for computing the sliding window bi-SVD subspace tracker is introduced. This algorithm produces, in each time step, a dominant rank-r SVD subspace approximant of an L timesN rectangular sliding window data matrix. The method is based on the QS (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 is 4Lr +3Nr multiplications 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

Published in:

Signal Processing, IEEE Transactions on  (Volume:57 ,  Issue: 11 )