{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T22:42:15Z","timestamp":1776897735531,"version":"3.51.2"},"reference-count":39,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2016,11,11]],"date-time":"2016-11-11T00:00:00Z","timestamp":1478822400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2019s 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.<\/jats:p>","DOI":"10.3390\/e18110396","type":"journal-article","created":{"date-parts":[[2016,11,11]],"date-time":"2016-11-11T10:05:56Z","timestamp":1478858756000},"page":"396","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Kernel Density Estimation on the Siegel Space with an Application to Radar Processing"],"prefix":"10.3390","volume":"18","author":[{"given":"Emmanuel","family":"Chevallier","sequence":"first","affiliation":[{"name":"Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot 7610001, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thibault","family":"Forget","sequence":"additional","affiliation":[{"name":"Thales Air Systems, Surface Radar Business Line, Advanced Radar Concepts Business Unit, Voie Pierre-Gilles de Gennes, Limours 91470, France"},{"name":"CMM-Centre de Morphologie Math\u00e9matique, MINES ParisTech, PSL-Research University, Paris 75006, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3664-3609","authenticated-orcid":false,"given":"Fr\u00e9d\u00e9ric","family":"Barbaresco","sequence":"additional","affiliation":[{"name":"Thales Air Systems, Surface Radar Business Line, Advanced Radar Concepts Business Unit, Voie Pierre-Gilles de Gennes, Limours 91470, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jesus","family":"Angulo","sequence":"additional","affiliation":[{"name":"CMM-Centre de Morphologie Math\u00e9matique, MINES ParisTech, PSL-Research University, Paris 75006, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,11,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/j.spl.2005.04.004","article-title":"Kernel density estimation on Riemannian manifolds","volume":"73","author":"Pelletier","year":"2005","journal-title":"Stat. 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