Science China Information Sciences

, Volume 53, Issue 2, pp 258–270 | Cite as

Least trace extended set-membership filter

Research Papers Special Focus

Abstract

To improve the consistency of estimation result, a least-trace extended set-membership filter (LTESMF) is presented for a class of nonlinear stochastic systems, which has linear output and unknown-but-bounded noise. Feedback technique is used instead of the intersection of ellipsoid-sets in the measurement update. The feedback parameter is optimized in order to minimize the trace of error bounded ellipsoid’s envelop matrix. A new stability analysis method was developed to prove the stochastic system’s stability by using the convergence of some measurement of the error bounded ellipsoid. Analysis result shows that the estimation error of LTESMF will converge to a bounded area. A simulation of SINS/GPS integrated alignment with large misalignment angles is conducted. The results demonstrate that the convergence speed and the consistency of LTESMF are much better than those of extended Kalman filter (EKF), in addition the steady estimation precision and computational complexity are close to that of EKF.

Keywords

set-membership estimation nonlinear system convergence upper bound least trace stability analysis 

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References

  1. 1.
    Zhu F L. Research on observers of nonlinear control systems (in Chinese). PhD thesis. Shanghai: Shanghai Jiaotong University, 2001Google Scholar
  2. 2.
    Xiong K, Zhang H Y. Application of particle filter in INS nonlinear alignment (in Chinese). J Chin Inertial Tech, 2003, 11: 20–26Google Scholar
  3. 3.
    Julier S J, Uhlmann J K, Hugh F D-W. A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Trans Automat Control, 2000, 45: 477–482MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    He Q. Study on method and application of set-membership estimation theory (in Chinese). PhD thesis. Hunan: Hunan University, 2002Google Scholar
  5. 5.
    He Q, Zhang J. A square root extended set membership algorithm with applications to nonlinear system estimation. In: IEEE Proceed Int Conf on Intelligent Computation Tech and Automation, Changsha, Hunan, China, 2008. 559–562Google Scholar
  6. 6.
    He Q, Zhang J. Set membership state estimation for nonlinear systems in the presence of bounded disturbances. In: IEEE Proceedings The 26th Chin Control Conf, Zhangjiajie, Hunan, China, 2007. 196–201Google Scholar
  7. 7.
    Scholte E, Campell M E. A nonlinear set-membership filter for on-line applications. Int J Robust Nonlinear Control, 2003, 13: 1337–1358MATHCrossRefGoogle Scholar
  8. 8.
    Scholte E, Campell M E. Robust nonlinear model predictive control with partial state information. IEEE Trans Control Syst Tech, 2008, 16: 636–651CrossRefGoogle Scholar
  9. 9.
    Schlaepfer F M, Schweppe F C. Continuous-time state estimation under disturbances bounded by convex sets. IEEE Trans Automat Control, 1972, 17: 197–205MATHCrossRefGoogle Scholar
  10. 10.
    Alamo T, Bravo J M, Camacho E F. Guaranteed state estimation by zonotopes. Automatica, 2005, 41: 1035–1043MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Zhou B, Han J D. A UD factorization-based adaptive extended set-membership filter (in Chinese). Acta Automat Sin, 2008, 34: 150–158MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Zhou B, Han J D. A UD factorization-based nonlinear adaptive set-membership filter for ellipsoidal estimation. Int J Robust Nonlin Control, 2008, 18: 1513–1531MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Zhou B, Han J D. An enhanced adaptive set-membership filter for nonlinear ellipsoidal estimation. In: Proceedings IEEE American Control Conference, New York, USA, 2007. 5135–5140Google Scholar
  14. 14.
    Laurent E G, Giuseppe C. Robust filtering for discrete-time systems with bounded noise and parametric uncertainty. IEEE Trans Automat Control, 2001, 46: 1084–1089MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Cheng P. Theory of Linear System (in Chinese). Beijing: BUAA Press, 2004. 89–94Google Scholar
  16. 16.
    Gao J Y. Computer Control System (in Chinese). Beijing: Higher Education Press, 2004. 169–174Google Scholar
  17. 17.
    Jean-Jacques E S, Wei P L. Applied Nonlinear Control. Upper Saddle River, NJ: Prentice-Hall, 1992. 36–48Google Scholar

Copyright information

© Science in China Press and Springer Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.National Key Laboratory of Science and Technology on Integrated Control Technology, School of Automation Science and Electric EngineeringBeihang UniversityBeijingChina

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