Analytic solution of the exact Daum-Huang flow equation for particle filters

State estimation for nonlinear systems, especially in high dimensions, is a generally intractable problem, despite the ever-increasing computing power. Efficient algorithms usually apply a finite-dimensional model for approximating the probability density of the state vector or treat the estimation...

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Bibliographic Details
Published in:arXiv.org 2022-12
Main Authors: Törő, Olivér, Bécsi, Tamás
Format: Article
Language:English
Subjects:
Algorithms
Bayesian analysis
Differential equations
Exact solutions
Flow equations
Nonlinear systems
State estimation
State vectors
Online Access:Get full text
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Summary:State estimation for nonlinear systems, especially in high dimensions, is a generally intractable problem, despite the ever-increasing computing power. Efficient algorithms usually apply a finite-dimensional model for approximating the probability density of the state vector or treat the estimation problem numerically. In 2007 Daum and Huang introduced a novel particle filter approach that uses a homotopy-induced particle flow for the Bayesian update step. Multiple types of particle flows were derived since with different properties. The exact flow considered in this work is a first-order linear ordinary time-varying inhomogeneous differential equation for the particle motion. An analytic solution in the interval [0,1] is derived for the scalar measurement case, which enables significantly faster computation of the Bayesian update step for particle filters.
ISSN:2331-8422
DOI:10.48550/arxiv.2209.00089