월쉬 단일항 전개를 이용한 비선형 확률 시스템의 상태추정

States Estimation of Nonlinear Stochastic System Using Single Term Walsh Series

  • 임윤식 (여주대학 방송영상제작과)
  • 발행 : 2008.06.01

초록

The EKF(Extended Kalman filter) method which is the state estimation algorithm of nonlinear stochastic system depends on the initial error and the estimated states. Therefore, the divergence of the estimated state can be caused if the initial values of the estimated states are not chosen as approximate real state values. In this paper, the demerit of the existing EKF method is improved using the EKF algorithm transformated by STWS(Single Term Walsh Series). This method linearizes each sampling interval of continous-time system through the derivation of an algebraic iterative equation without discretizing continuous system by the characteristic of STWS, the convergence of the estimated states can be improved. The validity of the proposed method is checked through comparison with the existing EKF method in simulation.

키워드

참고문헌

  1. J. E. Potter and R. G. Stern, " Statistical filtering of space navigation measurements", Proc. 1963 AIAA Guidance Contr. Conf., 1963
  2. T. L. Song, and J. L. Speyer, "A stochastic analysis of a modified extended Kalman filter with applications to estimation with bearing only measurements", IEEE. Trans. Automat Contr., Vol. AC-30, No. 10, pp.940-949 1985
  3. T. Kailath, " Some new algorithms for recursive estimation in constant linear systems", IEEE. Trans. Inform Theory., Vol. IT-19, pp. 750-760, 1973
  4. C. F. Chen and C. H Hsiao, "A State-Space Approach to Walsh Series Solution of linear Systems ", Int. J. Systems Sci., Vol. 6 , No.9, pp. 833-858, 1975 https://doi.org/10.1080/00207727508941868
  5. N. S. Hsu, and B. Cheng, " Analysis and Optimal control of time-varying linear Systems via block-pulse functions ", Int. J. Contr., Vol. 33, No.6, pp. 1107-1122, 1981 https://doi.org/10.1080/00207178108922979
  6. K. R. Palanisamy, "Analysis of Nonlinear System via Single Term Walsh Series Approach", Int. J. Systems. SCI., Vol. 13, No.8, pp.929-935, 1982 https://doi.org/10.1080/00207728208926400
  7. J. D. Pearson, "Approximation Methods in Optimal Control ", J Electron. Control., Vol. 13 , pp. 435-469, 1962
  8. J. P. Matuszewski , "Suboptimal Terminal Feedback Control of Nonstationary Nonlinear Systems ", IEEE. Trans, Automat. Contr., Vol. 18, pp. 271-274, 1973 https://doi.org/10.1109/TAC.1973.1100287
  9. A. Papoulis, Probability, Random Variables, and Stochastic Processes, McGraw-Hill, 1991
  10. R. E. Kalman, "A New Approach to Linear Filtering and Prediction Problems ", Journal of Basic Engineering, pp. 35-45, 1960
  11. M. S. Grewal and A. P. Andraws, Kalman filtering theory and practice, Prentice Hall, 1993
  12. M Afuans, " Suboptimal State Terminal Control of Nonlinear Systems from Discrete Noisy Measurements. " IEEE. Trans. Automat. Contr., Vol. AC-13, No.5, pp. 504-514, 1968