Optimal Reduction of Dirac Mixture Densities on the 2-Sphere

Autor

Uwe D. Hanebeck, Kailai Li

Korrespondierender Autor

Daniel Frisch

Beteiligtes Institut

Institut für Anthropomatik und Robotik (IAR)

Genre

Veranstaltung

Beschreibung

This paper is concerned with optimal approximation of a given Dirac mixture density on the S2 manifold, i.e., a set of weighted samples located on the unit sphere, by an equally weighted Dirac mixture with a reduced number of components. The sample locations of the approximating density are calculated by minimizing a smooth global distance measure, a generalization of the well-known Cramér-von Mises Distance. First, the Localized Cumulative Distribution (LCD) together with the von Mises–Fisher kernel provides a continuous characterization of Dirac mixtures on the S2 manifold. Second, the L2 norm of the difference of two LCDs is a unique and symmetric distance between the corresponding Dirac mixtures. Thereby we integrate over all possible kernel sizes instead of choosing one specific kernel size. The resulting approximation method facilitates various efficient nonlinear sample-based state estimation methods.

Schlagwörter

deterministic sampling, sample reduction, nonlinear optimization, localized cumulative distribution

Laufzeit (hh:mm:ss)

00:15:55

Publiziert am

22.04.2026

Fachgebiet

Informatik

Lizenz

KITopen-Lizenz

Aufrufe

115