Mixture of uniform probability density functions for non linear state estimation using interval analysis

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 the light of interval analysis framework, is called Box Particle Filter (BPF). It has been show...

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Bibliographic Details
Published in2010 13th International Conference on Information Fusion pp. 1 - 8
Main Authors Gning, A, Mihaylova, L, Abdallah, F
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.07.2010
Subjects
Atmospheric measurements
Band pass filters
Bayesian Filters
Bayesian methods
Global Positioning System
Interval Analysis
Kalman Filters
Monte Carlo Methods
Noise
Non linear System
Particle measurements
Time measurement
Uniform distribution
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Summary: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 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.
DOI:10.1109/ICIF.2010.5712085