摘要：AbstractThis paper is concerned with optimal approximation of a given Dirac mixture density on the S2manifold, 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 S2manifold. Second, theL2norm 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.
关键词：KeywordsProbability density functionfunction approximationoptimization problemsleast-squares approximationparameter estimationDirac mixture approximationsamplesmanifoldstarget trackingsystem state estimationKalman filtersdensity approximation
