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Finite-dimensional filters with nonlinear drift. V: solution to Kolmogorov equation arising from linear filtering with non-Gaussian initial condition

Zhigang Liang SS-T Yau Shing-Tung Yau

Analysis of PDEs mathscidoc:1912.43632

IEEE transactions on aerospace and electronic systems, 33, (4), 1295-1308, 1997.10
Despite its usefulness, the Kalman-Bucy filter is not perfect. One of its weaknesses is that it needs a Gaussian assumption on the initial data. Recently Yau and Yau introduced a new direct method to solve the estimation problem for linear filtering with non-Gaussian initial data. They factored the problem into two parts: (1) the on-line solution of a finite system of ordinary differential equations (ODEs), and (2) the off-line calculation of the Kolmogorov equation. Here we derive an explicit closed-form solution of the Kolmogorov equation. We also give some properties and conduct a numerical study of the solution.
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@inproceedings{zhigang1997finite-dimensional,
  title={Finite-dimensional filters with nonlinear drift. V: solution to Kolmogorov equation arising from linear filtering with non-Gaussian initial condition},
  author={Zhigang Liang, SS-T Yau, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204558483530196},
  booktitle={IEEE transactions on aerospace and electronic systems},
  volume={33},
  number={4},
  pages={1295-1308},
  year={1997},
}
Zhigang Liang, SS-T Yau, and Shing-Tung Yau. Finite-dimensional filters with nonlinear drift. V: solution to Kolmogorov equation arising from linear filtering with non-Gaussian initial condition. 1997. Vol. 33. In IEEE transactions on aerospace and electronic systems. pp.1295-1308. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204558483530196.
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