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Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold

School of Electronic Science, National University of Defence Technology, Changsha 410073, China
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Entropy 2018, 20(4), 219; https://doi.org/10.3390/e20040219
Received: 25 February 2018 / Revised: 12 March 2018 / Accepted: 12 March 2018 / Published: 23 March 2018
(This article belongs to the Section Information Theory, Probability and Statistics)
This paper proposes a class of covariance estimators based on information divergences in heterogeneous environments. In particular, the problem of covariance estimation is reformulated on the Riemannian manifold of Hermitian positive-definite (HPD) matrices. The means associated with information divergences are derived and used as the estimators. Without resorting to the complete knowledge of the probability distribution of the sample data, the geometry of the Riemannian manifold of HPD matrices is considered in mean estimators. Moreover, the robustness of mean estimators is analyzed using the influence function. Simulation results indicate the robustness and superiority of an adaptive normalized matched filter with our proposed estimators compared with the existing alternatives. View Full-Text
Keywords: information divergence; Riemannian manifold; covariance estimation; mean estimator; heterogeneous clutter information divergence; Riemannian manifold; covariance estimation; mean estimator; heterogeneous clutter
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Hua, X.; Cheng, Y.; Wang, H.; Qin, Y. Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold. Entropy 2018, 20, 219.

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