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

Entropy

Jesus Angulo¹  Emmanuel Chevallier²  Thibault Forget³  Frédéric Barbaresco³ 

[1] CMM-Centre de Morphologie Mathématique, MINES ParisTech, PSL-Research University, Paris 75006, France;Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot 7610001, Israel;Thales Air Systems, Surface Radar Business Line, Advanced Radar Concepts Business Unit, Voie Pierre-Gilles de Gennes, Limours 91470, France;

关键词: kernel density estimation;    Siegel space;    symmetric spaces;    radar signals;   

DOI  :  10.3390/e18110396

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown