AN ITERATIVE IMPLEMENTATION OF THE IMPLICIT NONLINEAR FILTER

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.

[1]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[2]  Paul Krause,et al.  Dimensional reduction for a Bayesian filter. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[3]  P. Bickel,et al.  Obstacles to High-Dimensional Particle Filtering , 2008 .

[4]  W. Gilks,et al.  Following a moving target—Monte Carlo inference for dynamic Bayesian models , 2001 .

[5]  Simon J. Godsill,et al.  On sequential Monte Carlo sampling methods for Bayesian filtering , 2000, Stat. Comput..

[6]  Matthias Morzfeld,et al.  Implicit sampling for data assimilation , 2014 .

[7]  Timothy J. Robinson,et al.  Sequential Monte Carlo Methods in Practice , 2003 .

[8]  Matthias Morzfeld,et al.  A random map implementation of implicit filters , 2011, J. Comput. Phys..

[9]  P. Bickel,et al.  Sharp failure rates for the bootstrap particle filter in high dimensions , 2008, 0805.3287.

[10]  Jun S. Liu,et al.  Sequential importance sampling for nonparametric Bayes models: The next generation , 1999 .

[11]  A. Chorin,et al.  Implicit sampling for particle filters , 2009, Proceedings of the National Academy of Sciences.

[12]  S. M. Bozic.  Digital and Kalman filtering , 1979 .

[13]  M. Dowd.  A sequential Monte Carlo approach for marine ecological prediction , 2006 .

[14]  Matthias Morzfeld,et al.  Implicit particle filters for data assimilation , 2010, 1005.4002.

[15]  Jun S. Liu,et al.  Generalised Gibbs sampler and multigrid Monte Carlo for Bayesian computation , 2000 .

[16]  Neil J. Gordon,et al.  Editors: Sequential Monte Carlo Methods in Practice , 2001 .

[17]  Arnaud Doucet,et al.  Particle Filtering and Smoothing: Fifteen years later , 2008 .