본문 바로가기
HOME> 논문 > 논문 검색상세

논문 상세정보

성능지표 선정을 통한 강인한 칼만필터 설계
Robust Kalman Filter Design via Selecting Performance Indices

정종철   (한양대학교 대학원 정밀기계공학과UU0001519  ); 허건수   (한양대학교 기계공학부UU0001519  );
  • 초록

    In this paper, a robust stationary Kalman filter is designed by minimizing selected performance indices so that it is less sensitive to uncertainties. The uncertainties include not only stochastic factors such as process noise and measurement noise, but also deterministic factors such as unknown initial estimation error, modeling error and sensing bias. To reduce the effect on the uncertainties, three performance indices that should be minimized are selected based on the quantitative error analysis to both the deterministic and the stochastic uncertainties. The selected indices are the size of the observer gain, the condition number of the observer matrix, and the estimation error variance. The observer gain is obtained by optimally solving the multi-objectives optimization problem that minimizes the indices. The robustness of the proposed filter is demonstrated through the comparison with the standard Kalman filter.


  • 주제어

    칼만필터 .   강인성 .   성능지표 .   최적화.  

  • 참고문헌 (24)

    1. Kalman, R. E. and Bucy, R. S., 1961, 'New Results in Linear Filtering and Prediction Theory,' Trans. of the ASME Series D: J. of Basic Engineering, Vol. 83, No.3, pp. 95-108 
    2. Bernstein, D. S. and Haddad, W. M., 1989, 'Steady-State Kalman Filtering with an $H_{\infty}$ Error Bound,' Systems and Control Letters, Vol. 12, No.1, pp. 9-16 
    3. Khargonekar, P. P. and Rotea, M. A., 1992, 'Mixed $H_2$/H_{\infty}$, Filtering,' Proc. of the 31st Conference on Decision and Control, pp. 2299-2304 
    4. Chen, X. and Zhou, K., 2002, '$H_{\infty}$ Gaussian Filter on Infinite Time Horizon,' IEEE Trans. on Circuits and Systems-I: Fundamental Theory and Applications, Vol. 49, No.5, pp. 674-679 
    5. I. R. Petersen, Optimal guaranteed cost control and filtering for uncertain linear systems, IEEE translation on Automatic Control, AC-37 pp. 1971-1977, 1994 
    6. Xie, L. and Soh, Y. C., 1994, 'Robust Kalman Filtering for Uncertain Systems,' Systems and Control Letters, Vol. 22, No.2, pp. 123-129 
    7. Fu, M., de Souza, C. E. and Luo, Z. Q., 2001, 'Finite-Horizon Robust Kalman Filter Design,' IEEE Trans. on Automatic Control, Vol. 49, No.9, pp. 2103-2112 
    8. Geromel, J. C., 1999, 'Optimal Linear Filtering Under Parameter Uncertainty,' IEEE Trans. on Signal Processing, Vol. 47, No. 1, pp. 168- 175 
    9. Shaked, U., Xie, L. and Soh, Y. C., 2001, 'New Approaches to Robust Minimum Variance Filter Design,' IEEE Trans. on Signal Processing, Vol. 49, No.11, pp. 2620-2629 
    10. Bertsekas, D. P. and Rhodes, I. B., 1971, 'Recursive State Estimation for a Set-membership Description of Uncertainty,' IEEE Trans. on Automatic Control, Vol. 16, No.2, pp. 117-128 
    11. Jain, B. N., 1975, 'Guaranteed Error Estimation in Uncertain Systems,' IEEE Trans. on Automatic Control, Vol. 20, No.2, pp. 230-232 
    12. Savkin, A. V. and Petersen, I. R., 1995, 'Recursive State Estimation for Uncertain Systems with an Integral Quadratic Constraint,' IEEE Trans. on Automatic Control, Vol. 40, No.6, pp. 1080-1083 
    13. Kwon, S., Chung, W. K. and Youm, Y., 2003, 'A Combined Observer for Robust State Estimation and Kalman Filtering,' Proc. of the American Control Conference, pp. 2459-2464 
    14. Mehra, R. K., 1970, 'On the Identification of Variances and Adaptive Kalman Filtering,' IEEE Trans. on Automatic Control, Vol. 15, No.2, pp. 175-184 
    15. Sage, A. P. and Melsa, J. L., 1971, Estimation Theory with Application to Communications and Control, McGraw-Hill, Inc. 
    16. Lee, B. S., 1997, 'Quantitative Performance Comparison of Observers with Uncertainties,' M. S. Thesis, Hanyang University, Seoul, Korea 
    17. Jung, J. and Huh, K., 2002, 'Design of the Well-Conditioned Observer Using the Non-Normality Measure,' Trans. of the KSME, A, Vol. 26, No.6, pp. 1114-1119     
    18. Huh, K. and Stein, J. L., 1994, 'A Quantitative Performance Index for Observer-Based Monitoring Systems,' Trans. of the ASME: J of Dynamic Systems, Measurement, and Control, Vol. 116, pp. 487-497. 
    19. Golub, G. H. and Van Loan, C. F., 1996, Matrix Computations, 3rd Ed., The Johns Hopkins University Press 
    20. Sasa, S., 1998, 'Robustness of a Kalman Filter Against Uncertainties of Noise Covariances,' Proc. of the American Control Conference, pp. 2344-2348 
    21. Huh, K., Jung, J. and Stein, J. L., 2001, 'DiscreteTime Well-Conditioned State Observer Design and Evaluation,' Trans. of the ASME:.J of Dynamic Systems, Measurement, and Control, Vol. 123, No.4, pp.615-622 
    22. Boyd, S., El Ghaoui, L., Feron, E. and Balakrishnan, V., 1994, Linear Matrix Inequalities in System and Control Theory, SIAM 
    23. El Ghaoui, L., Delebeque, F. and Nikoukhah, R., 1999, LMITOOL Ver. 2.1, available via anonymous ftp to ftp.ensta.fr, directory pub/elghaoui/lmitool-2.1 
    24. Oishi, J. and Balakrishnan, V., 2000, 'Linear Controller Design for the NEC Laser Bonder via Linear Matrix Inequality Optimization,' In Advances in Linear Matrix Inequality Methods in Control (Edited by El Ghaoui, L. and Niculescu, S.-L.), SIAM, Philadelphia, pp. 295-307 

 저자의 다른 논문

  • 정종철 (7)

    1. 2002 "입력관측기의 정량적 성능지표 (I) -과도상태 해석-" 大韓機械學會論文集. Transactions of the Korean Society of Mechanical Engineers. A. A 26 (10): 2060~2066    
    2. 2002 "입력관측기의 정량적 성능지표 (II) -정상상태 해석-" 大韓機械學會論文集. Transactions of the Korean Society of Mechanical Engineers. A. A 26 (10): 2067~2072    
    3. 2002 "비정규지표를 이용한 Well-Conditioned 관측기 설계" 大韓機械學會論文集. Transactions of the Korean Society of Mechanical Engineers. A. A 26 (6): 1114~1119    
    4. 2003 "차세대 리소그라피 시스템을 위한 압전구동기의 동적 해석" 大韓機械學會論文集. Transactions of the Korean Society of Mechanical Engineers. A. A 27 (3): 472~477    
    5. 2004 "Well-Conditioned 관측기 설계 - A Linear Matrix Inequality Approach -" 大韓機械學會論文集. Transactions of the Korean Society of Mechanical Engineers. A. A 28 (5): 503~510    
    6. 2004 "차세대 리소그라피 시스템을 위한 2축 나노스테이지의 시뮬레이션 툴 구축" 大韓機械學會論文集. Transactions of the Korean Society of Mechanical Engineers. A. A 28 (10): 1541~1548    
    7. 2006 "최적화 기법에 의한 비선형 시스템에서의 강인한 적응 관측기 설계" 大韓機械學會論文集. Transactions of the Korean Society of Mechanical Engineers. A. A 30 (10): 1249~1254    
  • 허건수 (38)

 활용도 분석

  • 상세보기

    amChart 영역
  • 원문보기

    amChart 영역

원문보기

무료다운로드
유료다운로드

유료 다운로드의 경우 해당 사이트의 정책에 따라 신규 회원가입, 로그인, 유료 구매 등이 필요할 수 있습니다. 해당 사이트에서 발생하는 귀하의 모든 정보활동은 NDSL의 서비스 정책과 무관합니다.

원문복사신청을 하시면, 일부 해외 인쇄학술지의 경우 외국학술지지원센터(FRIC)에서
무료 원문복사 서비스를 제공합니다.

NDSL에서는 해당 원문을 복사서비스하고 있습니다. 위의 원문복사신청 또는 장바구니 담기를 통하여 원문복사서비스 이용이 가능합니다.

이 논문과 함께 출판된 논문 + 더보기