Gning, A. and Mihaylova, L. and Abdallah, F. (2010) *Mixture of Uniform Probability Density Functions for non Linear State Estimation using Interval Analysis.* In: 13th Conference on Information Fusion (FUSION), 2010. IEEE, pp. 1-8. ISBN 978-0-9824438-1-1

## Abstract

In this work, a novel approach to nonlinear non-Gaussian state estimation problems is presented based on mixtures of uniform distributions with box supports. This class of filtering methods, introduced in [1] in the light of interval analysis framework, is called Box Particle Filter (BPF). It has been shown that weighted boxes, estimating the state variables, can be propagated using interval analysis tools combined with Particle filtering ideas. In this paper, in the light of the widely used Bayesian inference, we present a different interpretation of the BPF by expressing it as an approximation of posterior probability density functions, conditioned on available measurements, using mixture of uniform distributions. This interesting interpretation is theoretically justified. It provides derivation of the BPF procedures with detailed discussions.

Item Type: | Contribution in Book/Report/Proceedings |
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Additional Information: | Catalogue number: CFP10FUS-CDR ISBN:978-0-9824438-1-1 |

Uncontrolled Keywords: | Non linear System ; Bayesian Filters ; Uniform distribution ; Monte Carlo Methods ; Kalman Filters ; Interval Analysis |

Subjects: | Q Science > QA Mathematics > QA75 Electronic computers. Computer science |

Departments: | Faculty of Science and Technology > School of Computing & Communications |

ID Code: | 33959 |

Deposited By: | Dr L Mihaylov |

Deposited On: | 05 Aug 2010 09:40 |

Refereed?: | No |

Published?: | Published |

Last Modified: | 04 Dec 2016 02:39 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/33959 |

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