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continuous-discrete path integral filteringcontinuous-discrete路径积分滤波
Entropy 2009, 11, 402-430; doi:10.3390/e110300402 OPEN ACCESS entropy ISSN 1099-4300 /journal/entropy Article Continuous-Discrete Path Integral Filtering Bhashyam Balaji Radar Systems Section, Defence Research and Development Canada, Ottawa, 3701 Carling Avenue, Ottawa, ON, K1A 0Z4, Canada; E-Mail: Bhashyam.Balaji@drdc-rddc.gc.ca; Tel.: +1-613-998-2215; Fax: +1-613-990-8906 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 stochas- tic 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 nonlin- ear 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; continuous- discrete filters; nonlinear filtering; Dirac-Feynman approximation 1. Introduction The following continuous-discrete filte
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