An efficient numerical method for solving high-dimensional nonlinear filtering problems

Mei-Heng Yueh National Chiao Tung University Wen-Wei Lin National Chiao Tung University Shing-Tung Yau Harvard University

Optimization and Control mathscidoc:1608.27002

Communications in Information and Systems, 14, (4), 243--262, 2014
In this paper, a brief introduction of the nonlinear filtering problems and a review of the quasi-implicit Euler method are presented. The major contribution of this paper is that we propose a nonnegativity-preserving algorithm of Yau-Yau method for solving high-dimensional nonlinear filtering problems by applying quasi-implicit Euler method with discrete sine transform. Furthermore, our algorithms are directly applicable on the compact difference schemes, so that the number of spatial points can be substantially reduced and retain the same accuracy. Numerical results indicate that the proposed algorithm is capable of solving up to six-dimensional nonlinear filtering problems efficiently and accurately.
nonlinear filtering, Kolmogorov equations, discrete sine transform
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@inproceedings{mei-heng2014an,
  title={An efficient numerical method for solving high-dimensional nonlinear filtering problems},
  author={Mei-Heng Yueh, Wen-Wei Lin, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160822160043273011380},
  booktitle={Communications in Information and Systems},
  volume={14},
  number={4},
  pages={243--262},
  year={2014},
}
Mei-Heng Yueh, Wen-Wei Lin, and Shing-Tung Yau. An efficient numerical method for solving high-dimensional nonlinear filtering problems. 2014. Vol. 14. In Communications in Information and Systems. pp.243--262. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160822160043273011380.
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