A novel suboptimal method for solving polynomial filtering problems

• Xue Luo ^[1] ; Yang Jiao ^[3] ; Wen-Lin Chiou ^[4] ; Stephen S-T. Yau ^[2]
  1. [1] Beihang University

     Beihang University

     China

     
  2. [2] Tsinghua University

     Tsinghua University

     China

     
  3. [3] University of Illinois at Chicago;USA
  4. [4] Fu-Jen University, New Taipei City, Taiwan

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• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 62, 2015, págs. 26-31
• Idioma: inglés
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• Resumen

  • 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., ff, gg and hh 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 (Germani et al., 2007). 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.