On the Recursions of Robust COMET Algorithm for Convexly Structured Shape Matrix

B. Meriaux (1) , C. Ren (1) , A. Breloy (2) , M.N. El Korso (2) , Philippe Forster (3) , J.-P. Ovarlez (4, 1)

1 SONDRA - Sondra, CentraleSupélec, Université Paris-Saclay
2 LEME - Laboratoire Energétique Mécanique Electromagnétisme
3 SATIE - Systèmes et Applications des Technologies de l'Information et de l'Energie
4 DEMR, ONERA, Université Paris Saclay (COmUE) [Palaiseau]

This paper addresses robust estimation of structured shape (normalized covariance) matrices. Shape matrices most often own a particular structure depending on the application of interest and taking this structure into account improves estimation accuracy. In the framework of robust estimation, we introduce a recursive robust shape matrix estimation technique based on Tyler's M-estimate for convexly structured shape matrices. We prove that the proposed estimator is consistent, asymptotically efficient and Gaussian distributed and we notice that it reaches its asymptotic regime faster as the number of recursions increases. Finally, in the particular wide spreaded case of Hermitian persymmetric structure, we study the convergence of the recursions of the proposed algorithm.

Mots clés: Robust shape matrix estimation elliptical distributions Tyler's M -estimator structured estimation; Robust shape matrix estimation; elliptical distributions; Tyler's M -estimator; structured estimation

Domaines: Traitement du signal et de l'image [eess.SP]

B. Meriaux, C. Ren, A. Breloy, M.N. El Korso, Philippe Forster, et al.. On the Recursions of Robust COMET Algorithm for Convexly Structured Shape Matrix. 2019 27th European Signal Processing Conference (EUSIPCO), Sep 2019, A Coruna, France. ⟨10.23919/EUSIPCO.2019.8903167⟩. ⟨hal-04472691⟩