Title
A Quadrature-Based Method Of Moments For Nonlinear Filtering
Keywords
Estimation; Filtering algorithms; Fokker-Planck equation; Nonlinear filtering; Stochastic differential equation
Abstract
According to the nonlinear filtering theory, optimal estimates of a general continuous-discrete nonlinear filtering problem can be obtained by solving the Fokker-Planck equation, coupled with a Bayesian update rule. This procedure does not rely on linearizations of the dynamical and/or measurement models. However, the lack of fast and efficient methods for solving the Fokker-Planck equation presents challenges in real time nonlinear filtering problems. In this paper, a direct quadrature method of moments is introduced to solve the Fokker-Planck equation efficiently and accurately. This approach involves representation of the state conditional probability density function in terms of a finite collection of Dirac delta functions. The weights and locations (abscissas) in this representation are determined by moment constraints and modified using the Bayes' rule according to measurement updates. As demonstrated by numerical examples, this approach appears to be promising in the field of nonlinear filtering. © 2009 Elsevier Ltd. All rights reserved.
Publication Date
5-1-2009
Publication Title
Automatica
Volume
45
Issue
5
Number of Pages
1291-1298
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1016/j.automatica.2009.01.015
Copyright Status
Unknown
Socpus ID
65049087213 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/65049087213
STARS Citation
Xu, Yunjun and Vedula, Prakash, "A Quadrature-Based Method Of Moments For Nonlinear Filtering" (2009). Scopus Export 2000s. 11906.
https://stars.library.ucf.edu/scopus2000/11906