Adaptive kernel principal component analysis
Signal Processing
Robust adaptive beamforming method using principal eigenpairs with modification of PASTd
Digital Signal Processing
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The author addresses the problem of computing the eigensystem of the modified Hermitian matrix, given the prior knowledge of the eigensystem of the original Hermitian matrix. Specifically, an additive rank-k modification corresponding to adding and deleting blocks of data to and from the covariance matrix is considered. An efficient and parallel algorithm which makes use of a generalized spectrum-slicing theorem is derived for computing the eigenvalues. The eigenvector can be computed explicitly in terms of the solution of a much-reduced (k ×k) homogeneous Hermitian system. The overall computational complexity is shown to be improved by an order of magnitude from O(N3) to O(N 2k), where N×N is the size of the covariance matrix. It is pointed out that these ideas can be applied to adaptive signal processing applications, such as eigen-based techniques for frequency or angle-of-arrival estimation and tracking. Specifically, adaptive versions of the principal eigenvector method and the total least squares method are derived