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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
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
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MDPI and ACS Style
Balaji, B. Continuous-Discrete Path Integral Filtering. Entropy 2009, 11, 402-430.
Balaji B. Continuous-Discrete Path Integral Filtering. Entropy. 2009; 11(3):402-430.
Balaji, Bhashyam. 2009. "Continuous-Discrete Path Integral Filtering." Entropy 11, no. 3: 402-430.