OATAO - Open Archive Toulouse Archive Ouverte Open Access Week

Covariance matrix estimation with heterogeneous samples

Besson, Olivier and Bidon, Stéphanie and Tourneret, Jean-Yves Covariance matrix estimation with heterogeneous samples. (2008) IEEE Transactions on Signal Processing, 5 (3). 909-920. ISSN 1053-587X

(Document in English)

PDF (Author's version) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader

Official URL: http://dx.doi.org/10.1109/TSP.2007.908995


We consider the problem of estimating the covariance matrix Mp of an observation vector, using heterogeneous training samples, i.e., samples whose covariance matrices are not exactly Mp. More precisely, we assume that the training samples can be clustered into K groups, each one containing Lk, snapshots sharing the same covariance matrix Mk. Furthermore, a Bayesian approach is proposed in which the matrices Mk. are assumed to be random with some prior distribution. We consider two different assumptions for Mp. In a fully Bayesian framework, Mp is assumed to be random with a given prior distribution. Under this assumption, we derive the minimum mean-square error (MMSE) estimator of Mp which is implemented using a Gibbs-sampling strategy. Moreover, a simpler scheme based on a weighted sample covariance matrix (SCM) is also considered. The weights minimizing the mean square error (MSE) of the estimated covariance matrix are derived. Furthermore, we consider estimators based on colored or diagonal loading of the weighted SCM, and we determine theoretically the optimal level of loading. Finally, in order to relax the a priori assumptions about the covariance matrix Mp, the second part of the paper assumes that this matrix is deterministic and derives its maximum-likelihood estimator. Numerical simulations are presented to illustrate the performance of the different estimation schemes.

Item Type:Article
Additional Information:Thanks to IEEE. The original PDF can be found on the IEEE website : http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
HAL Id:hal-03610264
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Laboratory name:
Délégation Générale pour l'Armement (DGA) - Thales Systèmes Aéroportés
Deposited On:10 Sep 2008 14:25

Repository Staff Only: item control page