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A general Bayesian nonlinear estimation method using resampled Smooth Particle Hydrodynamics solutions of the underlying Fokker–Planck Equation

Duffy, Michael and Chung, Soon-Jo and Bergman, Lawrence (2022) A general Bayesian nonlinear estimation method using resampled Smooth Particle Hydrodynamics solutions of the underlying Fokker–Planck Equation. International Journal of Non-Linear Mechanics, 146 . Art. No. 104134. ISSN 0020-7462. doi:10.1016/j.ijnonlinmec.2022.104134. https://resolver.caltech.edu/CaltechAUTHORS:20220705-346228000

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Abstract

The effectiveness of nonlinear filters depends on many factors, but one of the most important is how accurately the filter is able to predict the state dynamics of the underlying system between measurements. For a wide class of Gaussian white noise driven nonlinear systems the Bayesian optimal prior can be obtained by solving the system’s corresponding Fokker–Planck Equation (FPE). Unfortunately the Fokker–Planck Equation is a partial differential equation with dimension equal to the number of states in the underlying dynamical system, making it extremely difficult to solve for realistic systems due to Curse of Dimensionality scaling issues. As a result it has been and still largely remains computationally impractical to simulate higher dimensional Fokker–Planck equations, at least while obtaining very high accuracy across the entire transient probability density function. This paper presents a general nonlinear filter based on solving the transient Fokker–Planck equation via Smooth Particle Hydrodynamics (SPH) at lower resolution, which turns out to still allow for accurate state estimation. The filter is enabled by an efficient heuristic resampling scheme of the SPH solution also presented here. The FPE-SPH Filter is able to replicate the accuracy of the Particle Filter and Extended Kalman filter (EKF) for lower-dimensional systems, while also being more robust than the EKF on certain classes of system.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.ijnonlinmec.2022.104134DOIArticle
ORCID:
AuthorORCID
Duffy, Michael0000-0002-6467-8748
Chung, Soon-Jo0000-0002-6657-3907
Bergman, Lawrence0000-0003-3346-8649
Additional Information:© 2022 Elsevier. Received 15 December 2021, Revised 19 May 2022, Accepted 24 June 2022, Available online 30 June 2022. Dedicated to the memory of Professor Leonid Isakovich Manevitch. CRediT authorship contribution statement: Michael Duffy: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing – Original draft, Writing – reviewing and editing, Visualization. Soon-Jo Chung: Conceptualization, Methodology, Writing – review & editing, Supervision. Lawrence Bergman: Conceptualization, Methodology, Writing – review & editing, Supervision. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Subject Keywords:Fokker–Planck equation (FPE); Nonlinear filtering; Smooth particle hydrodynamics (SPH); Stochastic process; Resampling
DOI:10.1016/j.ijnonlinmec.2022.104134
Record Number:CaltechAUTHORS:20220705-346228000
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220705-346228000
Official Citation:Michael Duffy, Soon-Jo Chung, Lawrence Bergman, A general Bayesian nonlinear estimation method using resampled Smooth Particle Hydrodynamics solutions of the underlying Fokker–Planck Equation, International Journal of Non-Linear Mechanics, Volume 146, 2022, 104134, ISSN 0020-7462, https://doi.org/10.1016/j.ijnonlinmec.2022.104134.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115320
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:07 Jul 2022 23:37
Last Modified:02 Aug 2022 16:29

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