Performances Analysis of a Givens Parametrized Adaptive Eigenspace Algorithm
Résumé
In this paper, we address an adaptive estimation method for eigenspaces of covariance matrices. We are interested in a gradient procedure based on coupled maximizations or minimizations of Rayleigh quotients where the constraints are replaced by a Givens parametrization. This enables us to provide a canonic orthonormal eigenbasis estimator. We study the convergence of this algorithm with the help of the associated ordinary di erential equation (ODE), and we propose a performance evaluation by computing the variances of the estimated eigenvectors and of the estimated projection matrices on eigenspaces for xed gain factors. In particular, we show that these misadjustments depend on whether the successive analyzed vector signals are correlated or not, and thus greatly depend on the origin of the covariance matrices of interest (spatial, temporal, spatio-temporal). More precisely, we show that these misadjustments can be smaller in the case of correlated observations than in the case of independent observations. Finally, we show that performance can be improved when the symmetriccentrosymmetric property of some of those covariance matrices is exploited.
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