Communications in Information and Systems

Volume 14 (2014)

Number 4

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

Pages: 243 – 262

DOI: http://dx.doi.org/10.4310/CIS.2014.v14.n4.a2

Authors

Mei-Heng Yueh (Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan)

Wen-Wei Lin (Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan)

Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)

Abstract

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.

Keywords

nonlinear filtering, Kolmogorov equations, discrete sine transform

2010 Mathematics Subject Classification

Primary 60G35, 62M20, 93E11. Secondary 65M06, 65M12.

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