Optimal Reduction of Dirac Mixture Densities on the 2-Sphere. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Frisch, Daniel; Li, Kailai; Hanebeck, Uwe D.
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 1282
• Page End: 1287
• Publication Date: 2020
• Subjects: Probability density function -- function approximation -- optimization problems -- least-squares approximation -- parameter estimation -- Dirac mixture approximation -- samples -- manifolds -- target tracking -- system state estimation -- Kalman filters -- density approximation; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.1856
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This paper is concerned with optimal approximation of a given Dirac mixture density on the S 2 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 S 2 manifold. Second, the L 2 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.