A Novel Suboptimal Method for Solving Polynomial Filtering Problems

Xue Luo Beihang University Yang Jiao University of Illinois at Chicago Wen-Lin Chiou Fu-Jen University Stephen S.-T. Yau Tsinghua University

Optimization and Control mathscidoc:1611.27002

Automatica , 62, 26-31, 2015
In this paper we derive the stochastic differentials of the conditional central moments of the nonlinear filtering problems, especially those of the polynomial filtering problem, and develop a novel suboptimal method by solving this evolution equation. The basic idea is to augment the state of the original nonlinear system by including the original states' conditional central moments such that the augmented states form a so-called bilinear system after truncating. During our derivation, it is clear to see that the stochastic differentials of the conditional central moments of the linear filtering problem (i.e., $f$, $g$ and $h$ are all at most degree one polynomials) form a closed system automatically without truncation. This gives one reason for the existence of optimal filtering for linear problems. On the contrary, the conditional central moments form an infinite dimensional system, in general. To reduce it to a closed-form, we let all the high enough central moments to be zero, as one did in the Carleman approach \cite{GMP}. Consequently, a novel suboptimal method is developed by dealing with the bilinear system. Numerical simulation is performed for the cubic sensor problem to illustrate the accuracy and numerical stability.
polynomial filtering problems; suboptimal filter; recursive algorithm; estimation theory
[ Download ] [ 2016-11-26 01:26:46 uploaded by xluo ] [ 450 downloads ] [ 0 comments ]
@inproceedings{xue2015a,
  title={A Novel Suboptimal Method for Solving Polynomial Filtering Problems},
  author={Xue Luo, Yang Jiao, Wen-Lin Chiou, and Stephen S.-T. Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161126012646029443656},
  booktitle={Automatica },
  volume={62},
  pages={26-31},
  year={2015},
}
Xue Luo, Yang Jiao, Wen-Lin Chiou, and Stephen S.-T. Yau. A Novel Suboptimal Method for Solving Polynomial Filtering Problems. 2015. Vol. 62. In Automatica . pp.26-31. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161126012646029443656.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved