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.
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References
Zhu F L. Research on observers of nonlinear control systems (in Chinese). PhD thesis. Shanghai: Shanghai Jiaotong University, 2001
Xiong K, Zhang H Y. Application of particle filter in INS nonlinear alignment (in Chinese). J Chin Inertial Tech, 2003, 11: 20–26
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: 477–482
He Q. Study on method and application of set-membership estimation theory (in Chinese). PhD thesis. Hunan: Hunan University, 2002
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. 559–562
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. 196–201
Scholte E, Campell M E. A nonlinear set-membership filter for on-line applications. Int J Robust Nonlinear Control, 2003, 13: 1337–1358
Scholte E, Campell M E. Robust nonlinear model predictive control with partial state information. IEEE Trans Control Syst Tech, 2008, 16: 636–651
Schlaepfer F M, Schweppe F C. Continuous-time state estimation under disturbances bounded by convex sets. IEEE Trans Automat Control, 1972, 17: 197–205
Alamo T, Bravo J M, Camacho E F. Guaranteed state estimation by zonotopes. Automatica, 2005, 41: 1035–1043
Zhou B, Han J D. A UD factorization-based adaptive extended set-membership filter (in Chinese). Acta Automat Sin, 2008, 34: 150–158
Zhou B, Han J D. A UD factorization-based nonlinear adaptive set-membership filter for ellipsoidal estimation. Int J Robust Nonlin Control, 2008, 18: 1513–1531
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. 5135–5140
Laurent E G, Giuseppe C. Robust filtering for discrete-time systems with bounded noise and parametric uncertainty. IEEE Trans Automat Control, 2001, 46: 1084–1089
Cheng P. Theory of Linear System (in Chinese). Beijing: BUAA Press, 2004. 89–94
Gao J Y. Computer Control System (in Chinese). Beijing: Higher Education Press, 2004. 169–174
Jean-Jacques E S, Wei P L. Applied Nonlinear Control. Upper Saddle River, NJ: Prentice-Hall, 1992. 36–48
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Huang, Y., Chen, Z. & Wei, C. Least trace extended set-membership filter. Sci. China Inf. Sci. 53, 258–270 (2010). https://doi.org/10.1007/s11432-010-0024-x
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DOI: https://doi.org/10.1007/s11432-010-0024-x