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Nonlinear Bearing Only Target Tracking Filter

방위각 정보만을 이용한 비선형 표적추적필터

  • Yoon, Jangho (Dept. of Aviation Maintenance, Far East University)
  • 윤장호 (극동대학교 항공정비학과)
  • Received : 2015.10.16
  • Accepted : 2015.12.21
  • Published : 2016.03.31

Abstract

The optimal estimation of a bearing only target tracking problem be achieved through the solution of the Fokker-Planck equation and the Bayesian update. Recently, a nonlinear filtering algorithm using a direct quadrature method of moments in which the associated Fokker-Planck equation can be propagated efficiently and accurately was proposed. Although this approach has demonstrated its promising in the field of nonlinear filtering in several examples, the "degeneracy" phenomenon, similar to that which exists in a typical particle filter, occasionally appears because only the weights are updated in the modified Bayesian rule in this algorithm. Therefore, in this paper to enhance the performance, a more stable measurement update process based upon the update equation in the Extended Kalman filters and a more accurate initialization and re-sampling strategy for weight and abscissas are proposed. Simulations are used to show the effectiveness of the proposed filter and the obtained results are promising.

Keywords

References

  1. A. Jazwinski, Stochastic Process and Filtering Theory, Academic Press, New York, NY, 2007 (re-publication of the version of 1970).
  2. L. Aggoun, and R. J. Elliott, Measure Theory and Filtering, Cambridge University Press, Cambridge, U.K., 2005.
  3. 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
  4. A. Gelb, Applied Optimal Estimation, MIT Press, Cambridge, MA, 1974.
  5. 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.
  6. 김민호, 송현민, 김정래 "저가형 GPS와 INS를 이용한 복합항법 시스템 개발," 항공우주시스템공학회지, Vol.4, No.3, pp.17-23, 2010
  7. 문근환, 김완범, 이정표, 최주호 "몬테 카를로 시뮬레이션을 이용한 하이브리드 로켓의 신뢰성 분석," 항공우주시스템공학회지, Vol.7, No.4, pp.1-11, 2013
  8. 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
  9. 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
  10. 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
  11. 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.
  12. J. Yoon and Y. Xu, "Relative position estimation using fokker-planck and bayes' equations," In AIAA GNC Conference and Exhibit, Hilton Head, South Carolina, August 2007. AIAA.
  13. 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
  14. 윤장호 "궤도결정을 위한 비선형 필터," 항공우주시스템공학회지, Vol.10, No.1, 2016 (게재예정)
  15. 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
  16. V. Aidala, "Kalman Filter Behavior in Bearing-Only Tracking Applications", IEEE Transactions on Aerospace Electronic Systems,Vol.15, January1979.
  17. X. Lin, T. Krubarajan, Y. Bar-Shalom, and S. Maskell, "Comparison of EKF, Pseudomeasurement and Particle Filters for a Bearing-only Target Tracking Problem," Proc. of SPIE Vol. 4728, Signal and Data Processing of Small Targets 2002, pp. 240-250A.
  18. Fokker, "Die mittlerer energie rotierender elektrischer dipole im strahlungsfeld," Annalen der Physik, vol. 43, pp. 810-820, 1914.
  19. M. Planck, "Uber einen satz der statistischen dynamik und seine erweiterung in der quantentheorie," Sitzungsber. Pr.