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Volume 32 Issue 12
Dec.  2006
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Journal of Beijing University of Aeronautics and Astronautics  > 2006  >  32(12): 1447-1450.
Wang Yuhui, Zhang Yuru, Wang Dangxiaoet al. Haptic rendering algorithm based on discrete energy optimization method of preparation of human tooth[J]. Journal of Beijing University of Aeronautics and Astronautics, 2005, 31(07): 785-788. (in Chinese)
Citation: Chai Wei, Sun Xianfang. Robust ellipsoidal state bounding algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2006, 32(12): 1447-1450. (in Chinese)
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Robust ellipsoidal state bounding algorithm

  • School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics,Beijing 100083, China

  • Received Date: 19 Dec 2005
  • Publish Date: 31 Dec 2006
    Abstract
  • A numerically robust algorithm for computing ellipsoidal bounds on the state of a linear, discrete-time dynamic system was proposed. The algorithm employed ellipsoidal outer approximation of the feasible set assuming instantaneous process and observation noise vectors and the initial state to be bounded by known ellipsoids. The time and observation updates produced, respectively, the vector sum and intersection of two ellipsoids. Cholesky decomposition was used in the propagation of the shape-defining matrix of the ellipsoid to keep it positive definite in the presence of roundoff errors. Besides, a subminimal-volume ellipsoid was selected from a family of ellipsoids as the observation-updated ellipsoid to circumvent the complex optimization affected by ill-conditioned matrix inverse. Monte Carlo simulations on a digital computer were performed to compare the performance of the proposed algorithm with that of the optimal algorithm. Simulation results show that the proposed algorithm not only matches the performance of the optimal algorithm closely in terms of ellipsoid volumes and mean-square errors, but also is less vulnerable to roundoff errors. The proposed algorithm also features the capability to be realized on a parallel computer.

     

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