Universal Nonlinear Filtering Using Feynman Path Integrals I: The Continuous-Discrete Model with Additive Noise

2007/08/02 by Bhashyam Balaji, Balaji, Bhashyam
Computer Science · Engineering · Physics and Astronomy · #Advanced Adaptive Filtering Techniques #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Image and Signal Denoising Methods #Other Condensed Matter (cond-mat.other) #cond-mat.other

paper · pdf · doi:10.48550/arxiv.0708.0354

Interdisciplinary, pedagogical, 37 pages, 2 figures

arxiv created 2007/08/02 · openalex publication_date 2007/08/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The continuous-discrete filtering problem requires the solution of a partial differential equation known as the Fokker-Planck-Kolmogorov forward equation (FPKfe). In this paper, the path integral formula for the fundamental solution of the FPKfe is derived and verified for the general additive noise case (i.e., explicitly time-dependent state model and with state-independent rectangular diffusion vielbein). The solution is universal in the sense that the initial distribution may be arbitrary. The practical utility is demonstrated via some examples.

Citations

• The Principles of Quantum Mechanics
• Space-Time Approach to Non-Relativistic Quantum Mechanics

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