Fast Generalized Eigenvector Tracking Based on the Power Method

Abstract

This letter develops a power method-based algorithm for tracking generalized eigenvectors when stochastic signals having unknown correlation matrices are observed. The proposed approach is based on the fact that the generalized eigenvalue problem is reduced to a standard eigenvalue problem, for which the power method can be easily applied by changing the metric of the vector space. The difficulty of applying the power method to this problem lies in the computational load of the inverse of the square root of a matrix at every update. The proposed algorithm can avoid the computation of eigenvalue decomposition to obtain the inverse of the matrix square root. Experimental results show that the proposed tracking algorithm gives a similar performance in tracking to the direct computation of singular value decomposition (SVD), while the computation order of the proposed algorithm is lower than the SVD.