On the asymptotic convergence and numerical stability of the Proteus EVD trackers

摘要

The asymptotic convergence and numerical stability of the previously introduced subspace tracking algorithms Proteus-1 and -2 are investigated by means of the ODE method. It is shown that (1) under weak conditions, both algorithms globally converge with probability one to the desired eigenvalue decomposition (EVD) components of the data covariance matrix, and (2) they have a built-in mechanism that prevents deviation from orthonormality in the eigenvector estimates over long periods of operation, i.e., numerical stability.