Asymptotic properties of robust covariance matrix estimates

Abstract : In many statistical signal processing applications, the estimation of nuisance parameters and parameters of interest is strongly linked to the resulting performance. Generally, these applications deal with complex data. This paper focuses on covariance matrix estimation problems in non-Gaussian environments, and particularly the M -estimators in the context of elliptical distributions. First, this paper extends to the complex case the results of Tyler in [D. Tyler, "Robustness and Efficiency Properties of Scatter Matrices," Biometrika, vol. 70, no. 2, p. 411, 1983]. More precisely, the asymptotic distribution of these estimators as well as the asymptotic distribution of any homogeneous function of degree 0 of the M -estimates are derived. On the other hand, we show the improvement of such results on two applications: directions of arrival (DOA) estimation using the MUltiple SIgnal Classification (MUSIC) algorithm and adaptive radar detection based on the Adaptive Normalized Matched Filter (ANMF) test.
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Article dans une revue
IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2013, 61 (13), pp.3348-3356. 〈10.1109/TSP.2013.2259823〉
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Contributeur : Anne-Hélène Picot <>
Soumis le : mardi 21 janvier 2014 - 16:48:46
Dernière modification le : jeudi 11 janvier 2018 - 06:18:42

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Mélanie Mahot, Frédéric Pascal, Philippe Forster, Jean-Philippe Ovarlez. Asymptotic properties of robust covariance matrix estimates. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2013, 61 (13), pp.3348-3356. 〈10.1109/TSP.2013.2259823〉. 〈hal-00934246〉

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