# An iterative implementation of the implicit nonlinear filter

Alexandre J. Chorin; Xuemin Tu

- Volume: 46, Issue: 3, page 535-543
- ISSN: 0764-583X

## Access Full Article

top## Abstract

top## How to cite

topChorin, Alexandre J., and Tu, Xuemin. "An iterative implementation of the implicit nonlinear filter." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 46.3 (2012): 535-543. <http://eudml.org/doc/273153>.

@article{Chorin2012,

abstract = {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.},

author = {Chorin, Alexandre J., Tu, Xuemin},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {implicit sampling; filter; reference density; jacobian; iteration; particles; Jacobian},

language = {eng},

number = {3},

pages = {535-543},

publisher = {EDP-Sciences},

title = {An iterative implementation of the implicit nonlinear filter},

url = {http://eudml.org/doc/273153},

volume = {46},

year = {2012},

}

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 - Modélisation Mathématique et Analyse Numérique

PY - 2012

PB - EDP-Sciences

VL - 46

IS - 3

SP - 535

EP - 543

AB - 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.

LA - eng

KW - implicit sampling; filter; reference density; jacobian; iteration; particles; Jacobian

UR - http://eudml.org/doc/273153

ER -

## References

top- [1] M. Arulampalam, S. Maskell, N. Gordon and T. Clapp, A tutorial on particle filters for online nonlinear/nongaussian Bayesia tracking. IEEE Trans. Signal Process.50 (2002) 174–188.
- [2] P. Bickel, B. Li and T. Bengtsson, 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. MR2459233
- [3] S. Bozic, Digital and Kalman Filtering. Butterworth-Heinemann, Oxford (1994). Zbl0593.93057
- [4] A.J. Chorin and P. Krause, Dimensional reduction for a Bayesian filter. Proc. Natl. Acad. Sci. USA101 (2004) 15013–15017. Zbl1135.93377MR2099822
- [5] A.J. Chorin and X. Tu, Implicit sampling for particle filters. Proc. Natl. Acad. Sc. USA106 (2009) 17249–17254.
- [6] A.J. Chorin, M. Morzfeld and X. Tu, Implicit particle filters for data assimilation. Commun. Appl. Math. Comput. Sci.5 (2010) 221–240. Zbl1229.60047MR2765384
- [7] A. Doucet and A. Johansen, Particle filtering and smoothing : Fifteen years later, in Handbook of Nonlinear Filtering, edited by D. Crisan and B. Rozovsky, to appear. Zbl05919872
- [8] A. Doucet, S. Godsill and C. Andrieu, On sequential Monte Carlo sampling methods for Bayesian filtering. Stat. Comput.10 (2000) 197–208.
- [9] A. Doucet, N. de Freitas and N. Gordon, Sequential Monte Carlo Methods in Practice. Springer, New York (2001). Zbl0967.00022MR1847783
- [10] M. Dowd, A sequential Monte Carlo approach for marine ecological prediction. Environmetrics17 (2006) 435–455. MR2240936
- [11] W. Gilks and C. Berzuini, Following a moving target-Monte Carlo inference for dynamic Bayesian models. J. Roy. Statist. Soc. B63 (2001) 127–146. Zbl0976.62021MR1811995
- [12] J. Liu and C. Sabatti, Generalized Gibbs sampler and multigrid Monte Carlo for Bayesian computation. Biometrika87 (2000) 353–369. Zbl0960.65015MR1782484
- [13] S. Maceachern, M. Clyde and J. Liu, Sequential importance sampling for nonparametric Bayes models : the next generation. Can. J. Stat.27 (1999) 251–267. Zbl0957.62068MR1704407
- [14] M. Morzfeld, X. Tu, E. Atkins and A.J. Chorin, A random map implementation of implicit filters. Submitted to J. Comput. Phys. Zbl1242.65012
- [15] C. Snyder, T. Bengtsson, P. Bickel and J. Anderson, Obstacles to high-dimensional particle filtering. Mon. Weather Rev.136 (2008) 4629–4640.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.