Feynman path integral inspired computational methods for nonlinear filtering

Bhashyam Balaji

doi:10.1117/12.849698

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27 April 2010 Feynman path integral inspired computational methods for nonlinear filtering

Bhashyam Balaji

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Proceedings Volume 7697, Signal Processing, Sensor Fusion, and Target Recognition XIX; 769708 (2010) https://doi.org/10.1117/12.849698
Event: SPIE Defense, Security, and Sensing, 2010, Orlando, Florida, United States

Abstract

The fundamental solution for the continuous-time filtering problems can be expressed in terms of Feynman path integrals. This enables one to view the solution of filtering problem in terms of an effective action that is a function of the signal and measurement models. 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 Fokker-Planck-Kolmogorov forward equation (termed the Dirac-Feynman approximation) can be applied to solve nonlinear continuous-discrete filtering problems quite accurately using sparse grid filtering and Monte-Carlo approaches.

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Bhashyam Balaji "Feynman path integral inspired computational methods for nonlinear filtering", Proc. SPIE 7697, Signal Processing, Sensor Fusion, and Target Recognition XIX, 769708 (27 April 2010); https://doi.org/10.1117/12.849698

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