This paper proposes a systematic procedure for approximating arbitrary probability density functions by means of Dirac mixtures. For that purpose, a distance measure is required, which is in general not well defined for Dirac mixture densities. Hence, a distance measure comparing the corresponding cumulative distribution functions is employed. Here, we focus on the weighted Cramer-von Mises distance, a weighted integral quadratic distance measure, which is simple and intuitive. Since a closed-form solution of the given optimization problem is not possible in general, an efficient solution procedure based on a homotopy continuation approach is proposed. Compared to a standard particle approximation, the proposed procedure ensures an optimal approximation with respect to a given distance measure. Although useful in their own respect, the results also provide the basis for a recursive nonlinear filtering mechanism as an alternative to the popular particle filters

Zugehörige Institution(en) am KIT |
Institut für Anthropomatik (IFA) |

Publikationstyp |
Proceedingsbeitrag |

Jahr |
2006 |

Sprache |
Englisch |

Identifikator |
ISBN: 1-424-40566-1 KITopen-ID: 1000013897 |

Erschienen in |
Proceedings / 2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems, 3 - 4 Sept. 2006, Heidelberg, Germany |

Verlag |
IEEE Service Center, Piscataway (NJ) |

Seiten |
512 - 517 |

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