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

Author

Champagne, Benoit

Author_Institution

Dept. of Electr. & Comput. Eng., McGill Univ., Montreal, Que.

Volume

48

Issue

1

fYear

2000

fDate

1/1/2000 12:00:00 AM

Firstpage

242

Lastpage

246

Abstract

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

Keywords

adaptive signal processing; convergence of numerical methods; covariance matrices; eigenvalues and eigenfunctions; matrix decomposition; numerical stability; tracking; ODE method; Proteus EVD trackers; Proteus-1; Proteus-2; adaptive implementation; asymptotic convergence; data covariance matrix; eigenvector estimates; numerical stability; previously; probability; signal-subspace methods; weak conditions; Approximation algorithms; Computational complexity; Computer simulation; Convergence of numerical methods; Councils; Covariance matrix; Eigenvalues and eigenfunctions; Numerical stability; Robustness; Signal processing algorithms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.815494

Filename

815494