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Density Approximation Based on Dirac Mixtures with Regard to Nonlinear Estimation and Filtering

Schrempf, Oliver C.; Brunn, Dietrich; Hanebeck, Uwe D.


A deterministic procedure for optimal approximation of arbitrary probability density functions by means of Dirac mixtures with equal weights is proposed. The optimality of this approximation is guaranteed by minimizing the distance of the approximation from the true density. For this purpose a distance measure is required, which is in general not well defined for Dirac mixtures. Hence, a key contribution is to compare the corresponding cumulative distribution functions. This paper concentrates on the simple and intuitive integral quadratic distance measure. For the special case of a Dirac mixture with equally weighted components, closed-form solutions for special types of densities like uniform and Gaussian densities are obtained. Closed-form solution of the given optimization problem is not possible in general. Hence, another key contribution is an efficient solution procedure for arbitrary true densities based on a homotopy continuation approach. In contrast to standard Monte Carlo techniques like particle filters that are based on random sampling, the proposed approach is deterministic and ensures an optimal approximation with respect to a given distance measure. ... mehr

Volltext §
DOI: 10.5445/IR/1000013888
DOI: 10.1109/cdc.2006.376759
Zitationen: 21
Cover der Publikation
Zugehörige Institution(en) am KIT Fakultät für Informatik – Institut für Anthropomatik (IFA)
Publikationstyp Proceedingsbeitrag
Publikationsjahr 2006
Sprache Englisch
Identifikator ISBN: 1-4244-0171-2
KITopen-ID: 1000013888
Erschienen in Proceedings / 45th IEEE Conference on Decision and Control, 2006, 13 - 15 Dec. 2006, San Diego, CA, USA
Verlag IEEE Service Center
Seiten 1709 - 1714
Nachgewiesen in Dimensions
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