On a Class of Orthonormal Algorithms for Principal and Minor Subspace Tracking

Authors:
K. Abed-Meraim;A. Chkeif;Y. Hua;S. Attallah
Affiliations:
Telecom Paris, TSI Department 46, rue Barrault, 75634, Paris Cedex 13, France;Telecom Paris, TSI Department 46, rue Barrault, 75634, Paris Cedex 13, France;Department of Electrical Engineering, University of California, Riverside, 92521, CA, USA;School of Electrical & Computer Engineering, Curtin University of Technology, GPO Box U1987 Perth 6845, Australia
Venue:
Journal of VLSI Signal Processing Systems
Year:
2002

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Abstract

This paper elaborates on a new class of orthonormal power-based algorithms for fast estimation and tracking of the principal or minor subspace of a vector sequence. The proposed algorithms are closely related to the natural power method that has the fastest convergence rate among many power-based methods such as the Oja method, the projection approximation subspace tracking (PAST) method, and the novel information criterion (NIC) method. A common feature of the proposed algorithms is the exact orthonormality of the weight matrix at each iteration. The orthonormality is implemented in a most efficient way. Besides the property of orthonormality, the new algorithms offer, as compared to other power based algorithms, a better numerical stability and a linear computational complexity.