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In this paper, we introduce a new interpretation of the signal subspace as the solution of an unconstrained minimization problem. We show that recursive least squares techniques can be applied to track the signal subspace recursively by making an appropriate projection approximation of the cost function. The resulting algorithms have a computational complexity of O(nr) where n is the input vector dimension and r(r<n) is the number of desired eigen components. We demonstrate that this approach can also be extended to track the rank, i.e. the number of signals, at the same order of linear (approximately n) computational complexity. Simulation results show that our algorithms offer a comparable and in some cases more robust performance than the spherical tracker by DeGroat, the URV updating by Stewart, and even the exact eigenvalue decomposition.
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Bin Yang "Recursive least-squares-based subspace tracking", Proc. SPIE 2296, Advanced Signal Processing: Algorithms, Architectures, and Implementations V, (28 October 1994);

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