Asymptotic Properties of Robust Complex Covariance Matrix Estimates

Mélanie Mahot (1, 2) , Frédéric Pascal (1) , Philippe Forster (3) , Jean-Philippe Ovarlez (1, 2)

1 SONDRA - Sondra, CentraleSupélec, Université Paris-Saclay (COmUE)
2 ONERA - The French Aerospace Lab [Palaiseau]
3 SATIE - Systèmes et Applications des Technologies de l'Information et de l'Energie

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 re- sults 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.

Mots clés: ROBUST ESTIMATION; TYLER ESTIMATOR; M-ESTIMATORS

Domaines: Traitement du signal et de l'image [eess.SP]; Autres [stat.ML]; Applications [stat.AP]

Mélanie Mahot, Frédéric Pascal, Philippe Forster, Jean-Philippe Ovarlez. Asymptotic Properties of Robust Complex Covariance Matrix Estimates. IEEE Transactions on Signal Processing, 2013, 61 (13), page 3348 - 3356. ⟨10.1109/TSP.2013.2259823⟩. ⟨hal-01705126⟩