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.
Mots-clés : 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 = {http://archive.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 - http://archive.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 http://archive.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, Tome 46 (2012) no. 3, pp. 535-543. doi : 10.1051/m2an/2011055. http://archive.numdam.org/articles/10.1051/m2an/2011055/
[1] A tutorial on particle filters for online nonlinear/nongaussian Bayesia tracking. IEEE Trans. Signal Process. 50 (2002) 174-188.
, , and ,[2] 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
, and ,[3] Digital and Kalman Filtering. Butterworth-Heinemann, Oxford (1994). | Zbl
,[4] Dimensional reduction for a Bayesian filter. Proc. Natl. Acad. Sci. USA 101 (2004) 15013-15017. | MR | Zbl
and ,[5] Implicit sampling for particle filters. Proc. Natl. Acad. Sc. USA 106 (2009) 17249-17254.
and ,[6] Implicit particle filters for data assimilation. Commun. Appl. Math. Comput. Sci. 5 (2010) 221-240. | MR | Zbl
, and ,[7] Particle filtering and smoothing : Fifteen years later, in Handbook of Nonlinear Filtering, edited by D. Crisan and B. Rozovsky, to appear.
and ,[8] On sequential Monte Carlo sampling methods for Bayesian filtering. Stat. Comput. 10 (2000) 197-208.
, and ,[9] Sequential Monte Carlo Methods in Practice. Springer, New York (2001). | MR | Zbl
, and ,[10] A sequential Monte Carlo approach for marine ecological prediction. Environmetrics 17 (2006) 435-455. | MR
,[11] Following a moving target-Monte Carlo inference for dynamic Bayesian models. J. Roy. Statist. Soc. B 63 (2001) 127-146. | MR | Zbl
and ,[12] Generalized Gibbs sampler and multigrid Monte Carlo for Bayesian computation. Biometrika 87 (2000) 353-369. | MR | Zbl
and ,[13] Sequential importance sampling for nonparametric Bayes models : the next generation. Can. J. Stat. 27 (1999) 251-267. | MR | Zbl
, and ,[14] A random map implementation of implicit filters. Submitted to J. Comput. Phys. | Zbl
, , and ,[15] Obstacles to high-dimensional particle filtering. Mon. Weather Rev. 136 (2008) 4629-4640.
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