Bi-iteration SVD subspace tracking algorithms

We present a class of fast subspace tracking algorithms that arise from a straightforward extension of Bauer's (1957) classical bi-iteration to the sequential processing case. The bi-iteration concept has an unexpected potential in subspace tracking. Our new bi-SVD subspace trackers are well structured and show excellent convergence properties. They outperform the TQR-SVD subspace tracking algorithm. Detailed comparisons confirm our claims. An application to rank and data adaptive signal reconstruction is also discussed.

[1]  G. Golub,et al.  Tracking a few extreme singular values and vectors in signal processing , 1990, Proc. IEEE.

[2]  V. Pisarenko.  The Retrieval of Harmonics from a Covariance Function , 1973 .

[3]  Georges Bienvenu,et al.  Adaptivity to background noise spatial coherence for high resolution passive methods , 1980, ICASSP.

[4]  Peter Strobach.  Fast recursive orthogonal iteration subspace tracking algorithms and applications , 1997, Signal Process..

[5]  Peter Strobach.  Low-rank detection of multichannel Gaussian signals using block matrix approximation , 1995, IEEE Trans. Signal Process..

[6]  F. L. Bauer.  Das Verfahren der Treppeniteration und verwandte Verfahren zur Lösung algebraischer Eigenwertprobleme , 1957 .

[7]  Charles L. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[8]  R. Kumaresan,et al.  Estimation of frequencies of multiple sinusoids: Making linear prediction perform like maximum likelihood , 1982, Proceedings of the IEEE.

[9]  Maurice Clint,et al.  A Simultaneous Iteration Method for the Unsymmetric Eigenvalue Problem , 1971 .

[10]  Peter Strobach.  Low rank detection of multichannel Gaussian signals using a constrained inverse , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[11]  J. H. Wilkinson.  The algebraic eigenvalue problem , 1966 .

[12]  J. Bunch,et al.  Updating the singular value decomposition , 1978 .

[13]  Louis L. Scharf,et al.  Low rank detectors for Gaussian random vectors , 1987, IEEE Trans. Acoust. Speech Signal Process..

[14]  Daniel R. Fuhrmann.  Adaptive Music , 1988, Optics & Photonics.

[15]  Ilkka Karasalo,et al.  Estimating the covariance matrix by signal subspace averaging , 1986, IEEE Trans. Acoust. Speech Signal Process..

[16]  G. Stewart.  Introduction to matrix computations , 1973 .

[17]  Ralph Otto Schmidt,et al.  A signal subspace approach to multiple emitter location and spectral estimation , 1981 .

[18]  G. Stewart.  Methods of Simultaneous Iteration for Calculating Eigenvectors of Matrices , 1975 .

[19]  L. Ammann.  Robust Singular Value Decompositions: A New Approach to Projection Pursuit , 1993 .

[20]  Louis L. Scharf,et al.  Rank reduction for modeling stationary signals , 1987, IEEE Trans. Acoust. Speech Signal Process..

[21]  Eric M. Dowling,et al.  A TQR-iteration based adaptive SVD for real time angle and frequency tracking , 1994, IEEE Trans. Signal Process..

[22]  P. Strobach.  Low-rank adaptive filters , 1996, IEEE Trans. Signal Process..

[23]  Louis L. Scharf,et al.  Data adaptive rank-shaping methods for solving least squares problems , 1995, IEEE Trans. Signal Process..

[24]  Peter Strobach.  Fast recursive eigensubspace adaptive filters , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[25]  Peter Strobach.  Fast recursive low-rank linear prediction frequency estimation algorithms , 1996, IEEE Trans. Signal Process..