Generalised particle filters with Gaussian mixtures
File(s)
Accepted version
Author(s)
Crisan, D
Li, K
Type
Journal Article
Abstract
Stochastic filtering is defined as the estimation of a partially observed dynamical system. Approximating the solution of the filtering problem with Gaussian mixtures has been a very popular method since the 1970s. Despite nearly fifty years of development, the existing work is based on the success of the numerical implementation and is not theoretically justified. This paper fills this gap and contains a rigorous analysis of a new Gaussian mixture approximation to the solution of the filtering problem. We deduce the <sup>L2</sup>-convergence rate for the approximating system and show some numerical examples to test the new algorithm.
Date Issued
2015-02-02
Date Acceptance
2015-01-26
Citation
Stochastic Processes and their Applications, 2015, 125 (7), pp.2643-2673
ISSN
0304-4149
Publisher
Elsevier
Start Page
2643
End Page
2673
Journal / Book Title
Stochastic Processes and their Applications
Volume
125
Issue
7
Copyright Statement
© 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/H000550/1
Subjects
Statistics & Probability
0104 Statistics
1502 Banking, Finance And Investment
Publication Status
Published