Projection approximation subspace tracking

Subspace estimation plays an important role in a variety of modern signal processing applications. We present a new approach for tracking the signal subspace recursively. It is based on a novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem. We show that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation. The resulting algorithms have a computational complexity of O(nr) where n is the input vector dimension and r is the number of desired eigencomponents. Simulation results demonstrate that the tracking capability of these algorithms is similar to and in some cases more robust than the computationally expensive batch eigenvalue decomposition. Relations of the new algorithms to other subspace tracking methods and numerical issues are also discussed. >

[1]  Norman L. Owsley,et al.  Adaptive data orthogonalization , 1978, ICASSP.

[2]  J. Bunch,et al.  Rank-one modification of the symmetric eigenproblem , 1978 .

[3]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

[4]  T. Kailath,et al.  Least squares type algorithm for adaptive implementation of Pisarenko's harmonic retrieval method , 1982 .

[5]  E. Oja.  Simplified neuron model as a principal component analyzer , 1982, Journal of mathematical biology.

[6]  B. A. D. H. Brandwood.  A complex gradient operator and its applica-tion in adaptive array theory , 1983 .

[7]  R. Kumaresan,et al.  Estimating the Angles of Arrival of Multiple Plane Waves , 1983, IEEE Transactions on Aerospace and Electronic Systems.

[8]  Juha Karhunen,et al.  Adaptive algorithms for estimating eigenvectors of correlation type matrices , 1984, ICASSP.

[9]  Thomas Kailath,et al.  Detection of signals by information theoretic criteria , 1985, IEEE Trans. Acoust. Speech Signal Process..

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

[11]  Donald W. Tufts,et al.  Simple, effective computation of principal eigenvectors and their eigenvalues and application to high-resolution estimation of frequencies , 1986, IEEE Trans. Acoust. Speech Signal Process..

[12]  Ken Sharman,et al.  Adaptive algorithms for estimating the complete covariance eigenstructure , 1986, ICASSP '86. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[13]  Jar-Ferr Yang,et al.  Adaptive eigensubspace algorithms for direction or frequency estimation and tracking , 1988, IEEE Trans. Acoust. Speech Signal Process..

[14]  Tapan K. Sarkar,et al.  A survey of conjugate gradient algorithms for solution of extreme eigen-problems of a symmetric matrix , 1989, IEEE Trans. Acoust. Speech Signal Process..

[15]  Thomas Kailath,et al.  ESPRIT-estimation of signal parameters via rotational invariance techniques , 1989, IEEE Trans. Acoust. Speech Signal Process..

[16]  Joos Vandewalle,et al.  Updating Singular Value Decompositions. A Parallel Implementation. , 1989, Optics & Photonics.

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

[18]  Björn E. Ottersten,et al.  Detection and estimation in sensor arrays using weighted subspace fitting , 1991, IEEE Trans. Signal Process..

[19]  Harry B. Lee.  Eigenvalues and eigenvectors of covariance matrices for signals closely spaced in frequency , 1992, IEEE Trans. Signal Process..

[20]  Christian H. Bischof,et al.  On updating signal subspaces , 1992, IEEE Trans. Signal Process..

[21]  Ronald D. DeGroat,et al.  Noniterative subspace tracking , 1992, IEEE Trans. Signal Process..

[22]  G. W. Stewart,et al.  An updating algorithm for subspace tracking , 1992, IEEE Trans. Signal Process..

[23]  M.R. Azimi-Sadjadi,et al.  An adaptive approach for optimal data reduction using recursive least squares learning method , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[24]  Bin Yang,et al.  Rotation-based RLS algorithms: unified derivations, numerical properties, and parallel implementations , 1992, IEEE Trans. Signal Process..

[25]  Bin Yang,et al.  Subspace tracking based on the projection approach and the recursive least squares method , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[26]  Bin Yang,et al.  An adaptive algorithm of linear computational complexity for both rank and subspace tracking , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.