Regularized Particle Filter with Langevin Resampling Step

Lian Duan; Chris L. Farmer; Irene M. Moroz

doi:10.1063/1.3497827

Regularized Particle Filter with Langevin Resampling Step

Lian Duan, Chris L. Farmer, Irene M. Moroz

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

The solution of an inverse problem involves the estimation of variables and parameters values given by the state-space system. While a general (infinite-dimensional) optimal filter theory [1, 2] exists for nonlinear systems with Gaussian or non-Gaussian noise, applications rely on (finite-dimensional) suboptimal approximations to the optimal filter for practical implementations. The most widely-studied filters of this kind include the Regularized Particle Filter (RPF) [3, 4] and the Ensemble Square Root Filter (EnSRF) [5]. The latter is an ad-hoc approximation to the Bayes Filter, while the former is rigorously formulated, based upon the Glivenko-Cantelli theorem. By introducing a new global resampling step to the RPF, the EnSRF is proved to approximate the RPF in a special case.

Original language	English (US)
Title of host publication	International Conference on Numerical Analysis and Applied Mathematics
Publisher	AMER INST PHYSICS
Pages	1080-+
Number of pages	1079
DOIs	https://doi.org/10.1063/1.3497827
State	Published - 2010
Externally published	Yes

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@inproceedings{7ed6f92165454632bad7d7d9c3754211,

title = "Regularized Particle Filter with Langevin Resampling Step",

abstract = "The solution of an inverse problem involves the estimation of variables and parameters values given by the state-space system. While a general (infinite-dimensional) optimal filter theory [1, 2] exists for nonlinear systems with Gaussian or non-Gaussian noise, applications rely on (finite-dimensional) suboptimal approximations to the optimal filter for practical implementations. The most widely-studied filters of this kind include the Regularized Particle Filter (RPF) [3, 4] and the Ensemble Square Root Filter (EnSRF) [5]. The latter is an ad-hoc approximation to the Bayes Filter, while the former is rigorously formulated, based upon the Glivenko-Cantelli theorem. By introducing a new global resampling step to the RPF, the EnSRF is proved to approximate the RPF in a special case.",

author = "Lian Duan and Farmer, {Chris L.} and Moroz, {Irene M.}",

note = "KAUST Repository Item: Exported on 2022-06-23 Acknowledged KAUST grant number(s): KUK-C1-013-04 Acknowledgements: This publication was based on work supported in part by Award No KUK-C1-013-04 , made by King Abdullah University of Science and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2010",

doi = "10.1063/1.3497827",

language = "English (US)",

pages = "1080--+",

booktitle = "International Conference on Numerical Analysis and Applied Mathematics",

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AU - Duan, Lian

AU - Farmer, Chris L.

AU - Moroz, Irene M.

N1 - KAUST Repository Item: Exported on 2022-06-23 Acknowledged KAUST grant number(s): KUK-C1-013-04 Acknowledgements: This publication was based on work supported in part by Award No KUK-C1-013-04 , made by King Abdullah University of Science and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2010

Y1 - 2010

N2 - The solution of an inverse problem involves the estimation of variables and parameters values given by the state-space system. While a general (infinite-dimensional) optimal filter theory [1, 2] exists for nonlinear systems with Gaussian or non-Gaussian noise, applications rely on (finite-dimensional) suboptimal approximations to the optimal filter for practical implementations. The most widely-studied filters of this kind include the Regularized Particle Filter (RPF) [3, 4] and the Ensemble Square Root Filter (EnSRF) [5]. The latter is an ad-hoc approximation to the Bayes Filter, while the former is rigorously formulated, based upon the Glivenko-Cantelli theorem. By introducing a new global resampling step to the RPF, the EnSRF is proved to approximate the RPF in a special case.

AB - The solution of an inverse problem involves the estimation of variables and parameters values given by the state-space system. While a general (infinite-dimensional) optimal filter theory [1, 2] exists for nonlinear systems with Gaussian or non-Gaussian noise, applications rely on (finite-dimensional) suboptimal approximations to the optimal filter for practical implementations. The most widely-studied filters of this kind include the Regularized Particle Filter (RPF) [3, 4] and the Ensemble Square Root Filter (EnSRF) [5]. The latter is an ad-hoc approximation to the Bayes Filter, while the former is rigorously formulated, based upon the Glivenko-Cantelli theorem. By introducing a new global resampling step to the RPF, the EnSRF is proved to approximate the RPF in a special case.

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UR - http://aip.scitation.org/doi/abs/10.1063/1.3497827

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U2 - 10.1063/1.3497827

DO - 10.1063/1.3497827

M3 - Conference contribution

SP - 1080-+

BT - International Conference on Numerical Analysis and Applied Mathematics

PB - AMER INST PHYSICS

ER -

Regularized Particle Filter with Langevin Resampling Step

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