Complete Real Time Solution of the General Nonlinear Filtering Problem without Memory

Xue Luo Beihang University Stephen S.-T. Yau Tsinghua University

Optimization and Control mathscidoc:1701.27015

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 58, (10), 2563-2578, 2013.10
It is well known that the nonlinear filtering problem has important applications in both military and civil industries. The central problem of nonlinear filtering is to solve the Duncan-Mortensen-Zakai (DMZ) equation in real time and in a memoryless manner. In this paper, we shall extend the algorithm developed previously by S.-T. Yau and the second author to the most general setting of nonlinear filterings, where the explicit time-dependence is in the drift term, observation term, and the variance of the noises could be a matrix of functions of both time and the states. To preserve the off-line virture of the algorithm, necessary modifications are illustrated clearly. Moreover, it is shown rigorously that the approximated solution obtained by the algorithm converges to the real solution in the $L^1$ sense. And the precise error has been estimated. Finally, the numerical simulation support the feasibility and efficiency of our algorithm.
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@inproceedings{xue2013complete,
  title={Complete Real Time Solution of the General Nonlinear Filtering Problem without Memory},
  author={Xue Luo, and Stephen S.-T. Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170129111421487049134},
  booktitle={IEEE TRANSACTIONS ON AUTOMATIC CONTROL},
  volume={58},
  number={10},
  pages={2563-2578},
  year={2013},
}
Xue Luo, and Stephen S.-T. Yau. Complete Real Time Solution of the General Nonlinear Filtering Problem without Memory. 2013. Vol. 58. In IEEE TRANSACTIONS ON AUTOMATIC CONTROL. pp.2563-2578. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170129111421487049134.
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