Implicit sampling is a sampling scheme for particle filters, designed to move particles one-by-one so that they remain in high-probability domains. We present a new derivation of implicit sampling, as well as a new iteration method for solving the resulting algebraic equations.
Keywords: implicit sampling, filter, reference density, jacobian, iteration, particles
@article{M2AN_2012__46_3_535_0,
author = {Chorin, Alexandre J. and Tu, Xuemin},
title = {An iterative implementation of the implicit nonlinear filter},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {535--543},
publisher = {EDP Sciences},
volume = {46},
number = {3},
year = {2012},
doi = {10.1051/m2an/2011055},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2011055/}
}
TY - JOUR AU - Chorin, Alexandre J. AU - Tu, Xuemin TI - An iterative implementation of the implicit nonlinear filter JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 535 EP - 543 VL - 46 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2011055/ DO - 10.1051/m2an/2011055 LA - en ID - M2AN_2012__46_3_535_0 ER -
%0 Journal Article %A Chorin, Alexandre J. %A Tu, Xuemin %T An iterative implementation of the implicit nonlinear filter %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 535-543 %V 46 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2011055/ %R 10.1051/m2an/2011055 %G en %F M2AN_2012__46_3_535_0
Chorin, Alexandre J.; Tu, Xuemin. An iterative implementation of the implicit nonlinear filter. ESAIM: Mathematical Modelling and Numerical Analysis , Special volume in honor of Professor David Gottlieb. Numéro spécial, Volume 46 (2012) no. 3, pp. 535-543. doi: 10.1051/m2an/2011055
[1] , , and , A tutorial on particle filters for online nonlinear/nongaussian Bayesia tracking. IEEE Trans. Signal Process. 50 (2002) 174-188.
[2] , and , Sharp failure rates for the bootstrap particle filter in high dimensions. IMS Collections : Pushing the Limits of Contemporary Statistics : Contributions in Honor of Jayanta K. Ghosh 3 (2008) 318-329. | MR
[3] , Digital and Kalman Filtering. Butterworth-Heinemann, Oxford (1994). | Zbl
[4] and , Dimensional reduction for a Bayesian filter. Proc. Natl. Acad. Sci. USA 101 (2004) 15013-15017. | Zbl | MR
[5] and , Implicit sampling for particle filters. Proc. Natl. Acad. Sc. USA 106 (2009) 17249-17254.
[6] , and , Implicit particle filters for data assimilation. Commun. Appl. Math. Comput. Sci. 5 (2010) 221-240. | Zbl | MR
[7] and , Particle filtering and smoothing : Fifteen years later, in Handbook of Nonlinear Filtering, edited by D. Crisan and B. Rozovsky, to appear.
[8] , and , On sequential Monte Carlo sampling methods for Bayesian filtering. Stat. Comput. 10 (2000) 197-208.
[9] , and , Sequential Monte Carlo Methods in Practice. Springer, New York (2001). | Zbl | MR
[10] , A sequential Monte Carlo approach for marine ecological prediction. Environmetrics 17 (2006) 435-455. | MR
[11] and , Following a moving target-Monte Carlo inference for dynamic Bayesian models. J. Roy. Statist. Soc. B 63 (2001) 127-146. | Zbl | MR
[12] and , Generalized Gibbs sampler and multigrid Monte Carlo for Bayesian computation. Biometrika 87 (2000) 353-369. | Zbl | MR
[13] , and , Sequential importance sampling for nonparametric Bayes models : the next generation. Can. J. Stat. 27 (1999) 251-267. | Zbl | MR
[14] , , and , A random map implementation of implicit filters. Submitted to J. Comput. Phys. | Zbl
[15] , , and , Obstacles to high-dimensional particle filtering. Mon. Weather Rev. 136 (2008) 4629-4640.
Cited by Sources:
