NDLI: Multivariable feedback particle filter

Content Provider	IEEE Xplore Digital Library
Author	Tao Yang Laugesen, R.S. Mehta, P.G. Meyn, S.P.
Copyright Year	2012
Description	Author affiliation: Department of Electrical and Computer Engineering at University of Florida at Gainesville, USA (Meyn, S.P.) \|\| Coordinated Science Laboratory and the Department of Mechanical Science and Engineering at the University of Illinois at Urbana-Champaign, USA (Tao Yang; Mehta, P.G.) \|\| Math department at the University of Illinois at Urbana-Champaign, USA (Laugesen, R.S.)
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.
Starting Page	4063
Ending Page	4070
File Size	1253542
Page Count	8
File Format	PDF
ISBN	9781467320658
ISSN	07431546
e-ISBN	9781467320665
e-ISBN	9781467320641
DOI	10.1109/CDC.2012.6425937
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-12-10
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Mathematical model Equations Approximation methods Kalman filters Approximation algorithms Covariance matrix Poisson equations
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Modeling and Simulation

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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