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Entropy 2009, 11(1), 42-58; doi:10.3390/e11010042

Euclidean Quantum Mechanics and Universal Nonlinear Filtering

Radar Systems Section, Defence Research and Development Canada, Ottawa, 3701 Carling Avenue, Ottawa ON K1A 0Z4 Canada
Received: 1 January 2009 / Accepted: 6 February 2009 / Published: 12 February 2009

Abstract

An important problem in applied science is the continuous nonlinear filtering problem, i.e., the estimation of a Langevin state that is observed indirectly. In this paper, it is shown that Euclidean quantum mechanics is closely related to the continuous nonlinear filtering problem. The key is the configuration space Feynman path integral representation of the fundamental solution of a Fokker-Planck type of equation termed the Yau Equation of continuous-continuous filtering. A corollary is the equivalence between nonlinear filtering problem and a time-varying Schr¨odinger equation.
Keywords: Bayesian filtering and estimation; Fokker-Planck Equation; Kolmogorov Equation; stochastic differential equations; Duncan-Mortensen-Zakai (DMZ) Equation; nonlinear filtering; Feynman path integral Bayesian filtering and estimation; Fokker-Planck Equation; Kolmogorov Equation; stochastic differential equations; Duncan-Mortensen-Zakai (DMZ) Equation; nonlinear filtering; Feynman path integral
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. Euclidean Quantum Mechanics and Universal Nonlinear Filtering. Entropy 2009, 11, 42-58.

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