Communications in Information and Systems
Volume 14 (2014)
An efficient numerical method for solving high-dimensional nonlinear filtering problems
Pages: 243 – 262
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
2010 Mathematics Subject Classification
Primary 60G35, 62M20, 93E11. Secondary 65M06, 65M12.