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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30 September 2010
ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010
19–25 September 2010
Rhodes (Greece)
Research Article|
September 30 2010
Regularized Particle Filter with Langevin Resampling Step
Lian Duan;
Lian Duan
aOxford Centre for Collaborative Applied Mathematics, Mathematical Institute, University of Oxford, OX1 3LB
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Chris L. Farmer;
Chris L. Farmer
aOxford Centre for Collaborative Applied Mathematics, Mathematical Institute, University of Oxford, OX1 3LB
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Irene M. Moroz
Irene M. Moroz
bOxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, OX1 3LB
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AIP Conf. Proc. 1281, 1080–1083 (2010)
Citation
Lian Duan, Chris L. Farmer, Irene M. Moroz; Regularized Particle Filter with Langevin Resampling Step. AIP Conf. Proc. 30 September 2010; 1281 (1): 1080–1083. https://doi.org/10.1063/1.3497827
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