Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper › peer-review

Published

**Mixture of Uniform Probability Density Functions for non Linear State Estimation using Interval Analysis.** / Gning, A.; Mihaylova, L.; Abdallah, F.

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper › peer-review

Gning, A, Mihaylova, L & 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, 13th International Conference on Information Fusion, Edinburgh, UK, 26/07/10. <http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=5712085>

Gning, A., Mihaylova, L., & 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 *(pp. 1-8). IEEE. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=5712085

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

@inproceedings{9afb0996abef49c085e4a117af128653,

title = "Mixture of Uniform Probability Density Functions for non Linear State Estimation using Interval Analysis.",

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.",

keywords = "Non linear System, Bayesian Filters, Uniform distribution, Monte Carlo Methods, Kalman Filters, Interval Analysis",

author = "A. Gning and L. Mihaylova and F. Abdallah",

note = "Catalogue number: CFP10FUS-CDR ISBN:978-0-9824438-1-1; 13th International Conference on Information Fusion ; Conference date: 26-07-2010 Through 29-07-2010",

year = "2010",

month = jul,

day = "28",

language = "English",

isbn = "978-0-9824438-1-1",

pages = "1--8",

booktitle = "13th Conference on Information Fusion (FUSION), 2010",

publisher = "IEEE",

}

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T1 - Mixture of Uniform Probability Density Functions for non Linear State Estimation using Interval Analysis.

AU - Gning, A.

AU - Mihaylova, L.

AU - Abdallah, F.

N1 - Catalogue number: CFP10FUS-CDR ISBN:978-0-9824438-1-1

PY - 2010/7/28

Y1 - 2010/7/28

N2 - 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.

AB - 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.

KW - Non linear System

KW - Bayesian Filters

KW - Uniform distribution

KW - Monte Carlo Methods

KW - Kalman Filters

KW - Interval Analysis

M3 - Conference contribution/Paper

SN - 978-0-9824438-1-1

SP - 1

EP - 8

BT - 13th Conference on Information Fusion (FUSION), 2010

PB - IEEE

T2 - 13th International Conference on Information Fusion

Y2 - 26 July 2010 through 29 July 2010

ER -