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Entropy 2009, 11(3), 402-430; doi:10.3390/e110300402

Continuous-Discrete Path Integral Filtering

Radar Systems Section, Defence Research and Development Canada, Ottawa, 3701 Carling Avenue, Ottawa, ON, K1A 0Z4, Canada
Received: 19 February 2009 / Accepted: 6 August 2009 / Published: 17 August 2009
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Abstract

A summary of the relationship between the Langevin equation, Fokker-Planck-Kolmogorov forward equation (FPKfe) and the Feynman path integral descriptions of stochastic processes relevant for the solution of the continuous-discrete filtering problem is provided in this paper. The practical utility of the path integral formula is demonstrated via some nontrivial examples. Specifically, it is shown that the simplest approximation of the path integral formula for the fundamental solution of the FPKfe can be applied to solve nonlinear continuous-discrete filtering problems quite accurately. The Dirac-Feynman path integral filtering algorithm is quite simple, and is suitable for real-time implementation.
Keywords: Fokker-Planck equation; Kolmogorov equation; universal nonlinear filtering; Feynman path integrals; path integral filtering; data assimilation; tracking; continuousdiscrete filters; nonlinear filtering; Dirac-Feynman approximation Fokker-Planck equation; Kolmogorov equation; universal nonlinear filtering; Feynman path integrals; path integral filtering; data assimilation; tracking; continuousdiscrete filters; nonlinear filtering; Dirac-Feynman approximation
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Balaji, B. Continuous-Discrete Path Integral Filtering. Entropy 2009, 11, 402-430.

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