Title :
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.
fDate :
1/1/2000 12:00:00 AM
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;
Journal_Title :
Signal Processing, IEEE Transactions on
