5 May 2011 The exact fundamental solution for the Benes filter: a Feynman path integral derivation
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Abstract
The Benes filtering problem has been shown to be related to the quantum mechanical simple harmonic oscillator. In a previous paper, the exact fundamental solution for the filtering problem was derived. The methods employed included the method of separation of variables for solving PDEs, results from Strum-Liouville theory, and properties of the Hermite special function. In this paper, the results are rederived more simply and directly using Feynman path integral methods. Numerical examples are included that demonstrate the correctness of formulas and their utility in solving continuous-discrete filtering problems with Benes drift and nonlinear measurement model.
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Bhashyam Balaji, Bhashyam Balaji, "The exact fundamental solution for the Benes filter: a Feynman path integral derivation", Proc. SPIE 8050, Signal Processing, Sensor Fusion, and Target Recognition XX, 80500Y (5 May 2011); doi: 10.1117/12.883547; https://doi.org/10.1117/12.883547
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