Continuous-Discrete Path Integral Filtering

TL;DR

This paper explores the connection between stochastic process equations and path integral methods, demonstrating a practical, simple filtering algorithm for nonlinear problems that can be used in real-time applications.

Contribution

It introduces a novel application of the Dirac-Feynman path integral approach to solve nonlinear continuous-discrete filtering problems efficiently.

Findings

Path integral approximation effectively solves nonlinear filtering.

The Dirac-Feynman algorithm is simple and suitable for real-time use.

Demonstrated accuracy on nontrivial examples.

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.