Performances analysis of parameterized adaptive eigenspace algorithms

We address adaptive estimation methods of eigenspaces of covariance matrices. We are interested in methods based on several coupled maximizations or minimizations of Rayleigh ratios where the constraints are replaced by appropriate parameterizations (Givens and mixed Givens/Householder). We prove the convergence of these algorithms with the help of the associated ordinary differential equation, and we propose an evaluation of the performance by computing the variances of the estimated eigenvectors for fixed gain factors. We show that these variances are very sensitive to the difference between two consecutive eigenvalues. Moreover, they also 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). Finally we show that the performance can be improved when the centro-symmetric property of some of those covariance matrices is taken into account