Commun. Comput. Phys., 16 (2014), pp. 382-402.


An Implicit Algorithm of Solving Nonlinear Filtering Problems

Feng Bao 1, Yanzhao Cao 2*, Xiaoying Han 1

1 Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA.
2 Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA; School of Mathematics and Computational Sciences, Sun Yat-sen University, China.

Received 18 March 2013; Accepted (in revised version) 13 February 2014
Available online 9 May 2014
doi:10.4208/cicp.180313.130214a

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.

AMS subject classifications: 60G35, 62M20, 93E11

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Key words: Kalman filter, particle filter, implicit filter, Monte Carlo method, stochastic differential equations.

*Corresponding author.
Email: fzb0005@auburn.edu (F. Bao), yzc0009@auburn.edu (Y. Cao), xzh0003@auburn.edu (X. Han)
 

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