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.
@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 - Mod\'elisation Math\'ematique et Analyse Num\'erique}, volume = {46}, year = {2012}, pages = {535-543}, doi = {10.1051/m2an/2011055}, language = {en}, url = {http://dml.mathdoc.fr/item/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 - Modélisation Mathématique et Analyse Numérique, Tome 46 (2012) pp. 535-543. doi : 10.1051/m2an/2011055. http://gdmltest.u-ga.fr/item/M2AN_2012__46_3_535_0/
[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 2459233
, and ,[3] Digital and Kalman Filtering. Butterworth-Heinemann, Oxford (1994). | Zbl 0593.93057
,[4] Dimensional reduction for a Bayesian filter. Proc. Natl. Acad. Sci. USA 101 (2004) 15013-15017. | MR 2099822 | Zbl 1135.93377
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 2765384 | Zbl 1229.60047
, 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 1847783 | Zbl 0967.00022
, and ,[10] A sequential Monte Carlo approach for marine ecological prediction. Environmetrics 17 (2006) 435-455. | MR 2240936
,[11] Following a moving target-Monte Carlo inference for dynamic Bayesian models. J. Roy. Statist. Soc. B 63 (2001) 127-146. | MR 1811995 | Zbl 0976.62021
and ,[12] Generalized Gibbs sampler and multigrid Monte Carlo for Bayesian computation. Biometrika 87 (2000) 353-369. | MR 1782484 | Zbl 0960.65015
and ,[13] Sequential importance sampling for nonparametric Bayes models : the next generation. Can. J. Stat. 27 (1999) 251-267. | MR 1704407 | Zbl 0957.62068
, and ,[14] A random map implementation of implicit filters. Submitted to J. Comput. Phys. | Zbl 1242.65012
, , and ,[15] Obstacles to high-dimensional particle filtering. Mon. Weather Rev. 136 (2008) 4629-4640.
, , and ,