Journal
INFORMATION FUSION
Volume 92, Issue -, Pages 247-255Publisher
ELSEVIER
DOI: 10.1016/j.inffus.2022.11.027
Keywords
Particle filter; Particle flow; State estimation; Nonlinear filtering; Log-homotopy
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State estimation for nonlinear systems is a challenging problem, especially in high dimensions, despite advances in computing power. A novel particle filter approach was introduced in 2007 by Daum and Huang, which utilizes a homotopy-induced particle flow for the Bayesian update step. 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 is derived for the scalar measurement case, enabling faster computation of the Bayesian update step 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 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.
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