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Entropy 2016, 18(11), 396; doi:10.3390/e18110396

Kernel Density Estimation on the Siegel Space with an Application to Radar Processing

1
Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot 7610001, Israel
2
Thales Air Systems, Surface Radar Business Line, Advanced Radar Concepts Business Unit, Voie Pierre-Gilles de Gennes, Limours 91470, France
3
CMM-Centre de Morphologie Mathématique, MINES ParisTech, PSL-Research University, Paris 75006, France
This paper is an extended version of our paper published in the 2nd conference on Geometric Science of Information, Paris, France, 28–30 October 2015.
*
Author to whom correspondence should be addressed.
Academic Editors: Arye Nehorai, Satyabrata Sen and Murat Akcakaya
Received: 13 August 2016 / Revised: 26 October 2016 / Accepted: 31 October 2016 / Published: 11 November 2016
(This article belongs to the Special Issue Differential Geometrical Theory of Statistics)
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Abstract

This paper studies probability density estimation on the Siegel space. The Siegel space is a generalization of the hyperbolic space. Its Riemannian metric provides an interesting structure to the Toeplitz block Toeplitz matrices that appear in the covariance estimation of radar signals. The main techniques of probability density estimation on Riemannian manifolds are reviewed. For computational reasons, we chose to focus on the kernel density estimation. The main result of the paper is the expression of Pelletier’s kernel density estimator. The computation of the kernels is made possible by the symmetric structure of the Siegel space. The method is applied to density estimation of reflection coefficients from radar observations. View Full-Text
Keywords: kernel density estimation; Siegel space; symmetric spaces; radar signals kernel density estimation; Siegel space; symmetric spaces; radar signals
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Chevallier, E.; Forget, T.; Barbaresco, F.; Angulo, J. Kernel Density Estimation on the Siegel Space with an Application to Radar Processing. Entropy 2016, 18, 396.

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