Tracking directions-of-arrival with invariant subspace updating

Abstract A new method for solving directions-of-arrival (DOA) tracking problems is presented. It is based on a practical method for updating invariant subspaces, introduced by G.W. Stewart. This method is O( L 2 ), where L is the number of array sensors. One advantage gained by using the invariant subspace updating method is the ability to track rapidly changing DOAs. In addition, it is possible to track sources as they appear or disappear in the incoming data. The results are indistinguishable from those obtained from a full eigendecomposition at every step.

[1]  K. J. Ray Liu,et al.  URV ESPRIT for tracking time-varying signals , 1994, IEEE Trans. Signal Process..

[2]  L. Dieci,et al.  Some numerical considerations and Newton's method revisited for solving algebraic Riccati equations , 1991 .

[3]  Craig Scott Macinnes,et al.  Analysis of small and large perturbations of matrix subspaces , 1995 .

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

[5]  Marc Moonen,et al.  SVD and Signaling Processing III: Algorithms, Architectures, and Applications , 1995 .

[6]  Benoît Champagne,et al.  Adaptive eigendecomposition of data covariance matrices based on first-order perturbations , 1994, IEEE Trans. Signal Process..

[7]  Petko Hr. Petkov,et al.  Perturbation Analysis of Matrix Quadratic Equations , 1990, SIAM J. Sci. Comput..

[8]  Bin Yang,et al.  Projection approximation subspace tracking , 1995, IEEE Trans. Signal Process..

[9]  G. W. Stewart,et al.  Stochastic Perturbation Theory , 1990, SIAM Rev..

[10]  Å. Björck.  Solving linear least squares problems by Gram-Schmidt orthogonalization , 1967 .

[11]  D. Luenberger.  Optimization by Vector Space Methods , 1968 .

[12]  H. Keller,et al.  Analysis of Numerical Methods , 1969 .

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

[14]  G. Stewart.  Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems , 1973 .

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

[16]  Alan J. Laub,et al.  Local convergence analysis of conjugate gradient methods for solving algebraic Riccati equations , 1992 .

[17]  P. Lancaster,et al.  Invariant subspaces of matrices with applications , 1986 .

[18]  F. Gersemsky,et al.  Adaptive direction-of-arrival estimation based on rank and subspace tracking , 1995 .

[19]  R. D. DeGroat,et al.  Efficient, numerically stabilized rank-one eigenstructure updating [signal processing] , 1990, IEEE Trans. Acoust. Speech Signal Process..

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

[21]  Eric M. Dowling,et al.  Adaptation dynamics of the spherical subspace tracker , 1992, IEEE Trans. Signal Process..

[22]  Gene H. Golub,et al.  Matrix computations , 1983 .

[23]  A. Laub,et al.  Generalized eigenproblem algorithms and software for algebraic Riccati equations , 1984, Proceedings of the IEEE.