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Séparation aveugle d'un mélange instantané de sources autorégressives par la méthode du vraisemblance exact

Abstract : This thesis deals with the problem of blind separation of an instantaneous mixture of Gaussian autoregressive sources, without additive noise, by the exact maximum likelihood approach. The maximization of the likelihood is divided, using relaxation, into two sub-optimization problems, still solved by relaxation techniques. The first one consists in the estimation of the separating matrix when the autoregressive structure of the sources is fixed. The second one aims to estimate this structure when the separating matrix is fixed. We show that the first problem is equivalent to the determinant maximization of the separating matrix under nonlinear constraints. We propose in this paper an algorithm to compute the solution of such a problem and we look at its convergence properties. We show that the maximum likelihood estimator exists and is consistent. We also give the expression of Fisher's information matrix and we propose a new index to measure the performances of separating methods. Then we study, by computer simulation, the performance of our estimator and show the improvement of its achievements with respect to the quasi-maximum likelihood estimator as well as other second order methods.
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https://tel.archives-ouvertes.fr/tel-00006754
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Submitted on : Wednesday, August 25, 2004 - 9:11:40 AM
Last modification on : Friday, November 6, 2020 - 4:11:22 AM
Long-term archiving on: : Friday, April 2, 2010 - 9:03:39 PM

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  • HAL Id : tel-00006754, version 1

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Abdelhamid Zaidi. Séparation aveugle d'un mélange instantané de sources autorégressives par la méthode du vraisemblance exact. Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 2000. Français. ⟨tel-00006754⟩

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