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An Implicit Algorithm of Solving Nonlinear Filtering Problems

Published online by Cambridge University Press:  03 June 2015

Feng Bao ,
Yanzhao Cao  and
Xiaoying Han
Feng Bao*
Affiliation:
Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA
Yanzhao Cao*
Affiliation:
Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA School of Mathematics and Computational Sciences, Sun Yat-sen University, China
Xiaoying Han*
Affiliation:
Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA
*
Email:fzb0005@auburn.edu
Corresponding author.Email:yzc0009@auburn.edu
Email:xzh0003@auburn.edu
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Abstract

Nonlinear filter problems arise in many applications such as communications and signal processing. Commonly used numerical simulation methods include Kalman filter method, particle filter method, etc. In this paper a novel numerical algorithm is constructed based on samples of the current state obtained by solving the state equation implicitly. Numerical experiments demonstrate that our algorithm is more accurate than the Kalman filter and more stable than the particle filter.

Keywords

60G3562M2093E11Kalman filterparticle filterimplicit filterMonte Carlo methodstochastic differential equations.
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 2 , August 2014 , pp. 382 - 402
Copyright
Copyright © Global Science Press Limited 2014

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