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Paper data
Generalized Gerschgorin's theorem for source number detection

Caspary Olivier, CRAN (Centre de Recherche en Automatique de Nancy)

Page numbers in the proceedings:
Volume I pp 189-192

Parameter Estimation and Statistical Signal Analysis

Paper abstract
A new family of source number estimators has appeared from the information provided by Gerschgorin radii and the centers of a unitary transformed covariance matrix. We suggest using a generalization of Gerschgorin's theorem developed for the eigenvalue problem A*x=lambda*B*x. This generalization can be applied to the perturbation of multiple eigenvalues and the usual theorem of Gerschgorin appears only as a particular case. For this, we need defining regions that bound a distance called the chordal metric. The techniques of diagonalization based on unitary transformation are necessary to exploit the estimated covariance matrix too. With sinusoidal signals embedded in a colored noise, the used criterion GDEdist with this generalization shows a better detection rate compared to that obtained by the simple Gerschgorin theorem.

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