DocumentCode :
3161516
Title :
Multivariable feedback particle filter
Author :
Tao Yang ; Laugesen, R.S. ; Mehta, Prashant G. ; Meyn, Sean P.
Author_Institution :
Dept. of Mech. Sci. & Eng., Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA
fYear :
2012
fDate :
10-13 Dec. 2012
Firstpage :
4063
Lastpage :
4070
Abstract :
In recent work it is shown that importance sampling can be avoided in the particle filter through an innovation structure inspired by traditional nonlinear filtering combined with Mean-Field Game formalisms [9], [19]. The resulting feedback particle filter (FPF) offers significant variance improvements; in particular, the algorithm can be applied to systems that are not stable. The filter comes with an up-front computational cost to obtain the filter gain. This paper describes new representations and algorithms to compute the gain in the general multivariable setting. The main contributions are, (i) Theory surrounding the FPF is improved: Consistency is established in the multivariate setting, as well as well-posedness of the associated PDE to obtain the filter gain. (ii) The gain can be expressed as the gradient of a function, which is precisely the solution to Poisson´s equation for a related MCMC diffusion (the Smoluchowski equation). This provides a bridge to MCMC as well as to approximate optimal filtering approaches such as TD-learning, which can in turn be used to approximate the gain. (iii) Motivated by a weak formulation of Poisson´s equation, a Galerkin finite-element algorithm is proposed for approximation of the gain. Its performance is illustrated in numerical experiments.
Keywords :
Galerkin method; Poisson equation; approximation theory; diffusion; feedback; finite element analysis; game theory; importance sampling; nonlinear filters; partial differential equations; particle filtering (numerical methods); Galerkin finite element algorithm; MCMC diffusion; PDE; Poisson equation; Smoluchowski equation; consistency; feedback particle filter; function gradient; gain approximation; importance sampling; mean field game; multivariable FPF; nonlinear filter; optimal filtering approach; Approximation algorithms; Approximation methods; Covariance matrix; Equations; Kalman filters; Mathematical model; Poisson equations;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Decision and Control (CDC), 2012 IEEE 51st Annual Conference on
Conference_Location :
Maui, HI
ISSN :
0743-1546
Print_ISBN :
978-1-4673-2065-8
Electronic_ISBN :
0743-1546
Type :
conf
DOI :
10.1109/CDC.2012.6425937
Filename :
6425937
Link To Document :
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