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궤도결정을 위한 비선형 필터

윤장호
Yoon, Jangho

  • 투고 : 2015.10.27
  • 심사 : 2015.12.21
  • 발행 : 2016.03.31

초록

Orbit determination problems have been interest of many researchers for long time. Due to the high nonlinearity of the equation of motion and the measurement model, it is necessary to linearize the both equations. To avoid linearization, the filter based on Fokker-Planck equation is designed. with the extended Kalman filter update mechanism, in which the associated Fokker-Planck equation was solved efficiently and accurately via discrete quadrature and the measurement update was done through the extended Kalman filter update mechanism. This filter based on the DQMOM and the EKF update is applied to the orbit determination problem with appropriate modification to mitigate the filter smugness. Unlike the extended Kalman filter, the hybrid filter based on the DQMOM and the EKF update does not require the burdensome evaluation of the Jacobian matrix and Gaussian assumption for the system, and can still provide more accurate estimations of the state than those of the extended Kalman filter especially when measurements are sparse. Simulation results indicate that the advantages of the hybrid filter based on the DQMOM and the EKF update make it a promising alternative to the extended Kalman filter for orbit estimation problems.

키워드

Nonlinear Estimation;Kalman Filter;Fokker-Planck Equation;Bearing Only Tracking

참고문헌

  1. E. G. Forbes, "Gauss and the Discovery of Ceres," Journal for the History of Astronomy Vol. 2, pp. 195-199, 1971 https://doi.org/10.1177/002182867100200305
  2. 정옥철, 임현정, 김화영, 안상일 "우주환경 변화에 따른 저궤도 위성의 궤도변화 분석," 항공우주시스템공학회지 제9권 제2호, pp. 57-62, 2015
  3. J. R. Vetter, "Fifty Years of Orbit Determination: Development of Modern Astrodynamics Methods," Johns Hopkins APL Technical Digest, Vol. 27 No. 7, pp. 239-252, 2007
  4. A. Jazwinski, Stochastic Process and Filtering Theory, Academic Press, New York, NY, 2007 (re-publication of the version of 1970).
  5. L. Aggoun, and R. J. Elliott, Measure Theory and Filtering, Cambridge University Press, Cambridge, U.K., 2005.
  6. F. Michael, and M. D. Johnson, "Financial Market Dynamics," Physica A: Statistical Mechanics and its Applications, Vol. 320, pp. 525-534, March 2003. https://doi.org/10.1016/S0378-4371(02)01558-3
  7. 유성숙, 김정래, 송용규 "위성발사체 궤도추적을 위한 융합필터 연구," 항공우주시스템공학회지 제1권 제3호 pp. 37-42 2007
  8. A. Gelb, Applied Optimal Estimation, MIT Press, Cambridge, MA, 1974.
  9. R. G. Brown and P. Y. Hwhang, Introduction to Random Signals and Applied Kalman Filtering, John Wiley & Sons, Inc., New York, NY, 3rd edition, 1997.
  10. J. Yoon, and Y. Xu, "Alternating Direction Implicit Method Enhanced Nonlinear Filtering for Relative Orbit Estimation," ASCE Journal of Aerospace Engineering, Vol 23, Iss 3, pp 186-196. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000024
  11. S. Challa, Y. Bar-Shalom, and V. Krishnamurthy, "Nonlinear Filtering via Generalized Edgeworth Series and Gauss Hermite Quadrature," IEEE Transactions on Signal Processing, Vol. 48, No. 6, pp. 1816-1820, June 2000. https://doi.org/10.1109/78.845944
  12. S. Challa and Y. Bar-Shalom, "Nonlinear filter design using fokker-planck- kolmogorov probability density evolutions," IEEE Transactions on Aerospace and Electronic Systems, 36(1):309-315, January 2000. https://doi.org/10.1109/7.826335
  13. S. Musick, J. Greenswald, C. Kreucher and K, Kastella, "Comparison of particle method and finite difference nonlinear filters for low snr target tracking," In 4th International Conference on Information Fusion, 2001.
  14. J. Yoon and Y. Xu, "Relative position estimation using fokker-planck and bayes' equations," In AIAA Guidance, Navigation and Control Conference and Exhibit, Hilton Head, South Carolina, August 2007. AIAA.
  15. Y. Xu and P. Vedula, "A quadrature based method of moments for nonlinear filtering," Automatica, vol. 45, no. 5, pp. 1291-1298, May 2009. https://doi.org/10.1016/j.automatica.2009.01.015
  16. Fokker, "Die mittlerer energie rotierender elektrischer dipole im strahlungsfeld," Annalen der Physik, vol. 43, pp. 810-820, 1914.
  17. M. Planck, "Uber einen satz der statistischen dynamik und seine erweiterung in der quantentheorie," Sitzungsber. Pr.
  18. P. J. Attar and P. Vedula, "Direct quadrature method of moments solution of the fokker-planck equation," Journal of Sound and Vibration, vol. 317 issues 1-2, pp. 265-272, 2008. https://doi.org/10.1016/j.jsv.2008.02.037
  19. J. Yoon, "Nonlinear Bearing Only Target Tracking Filter," Journal of The Society for Aerospace System Engineering, Submitted.
  20. D. A. Vallado, Fundamentals of Astrodynamics and Applications, Ch. 6, Microcosm Press, NY, NY, 2001.
  21. R. R. Bate, D. D. Mueller, and J. E. White, Fundamentals of Astrodynamics, Ch. 2, Dover, NY, NY, 1972.