A New Nonlinear Set Membership Filter Based on Guaranteed Bounding Ellipsoid Algorithm
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摘要: 基于未知但有界噪声假设的集员滤波器为传统的概率化滤波方法提供了一种可行的替代选择, 然而其潜在的计算负担和保守性考虑制约了该方法的实际应用. 本文提出一种新的基于保证定界椭球近似的改进集员滤波方法, 用于解决针对非线性系统的状态估计问题,在保证实时性的前提下降低了算法的保守性. 首先,对非线性模型进行线性化处理,采用DC (Difference of convex)规划方法对线性化误差进行外包定界, 并通过椭球近似将其融合到系统噪声中; 在此基础上提出了一种结合了椭球直和计算和基于迭代外定界椭球算法的椭球--带交集计算 所构成的经典预测--更新步骤来估计得到状态的可行椭球集. 与常规的非线性扩展集员滤波方法的仿真比较表明了本文所提出算法的有效性和改进性能.Abstract: The framework of set membership filter (SMF) with unknown-but-bounded noise assumption provides an attractive alternative for probabilistic filters. However, the potential computational burden and conservation consideration may seriously limit the usage of this filter in practical applications. In this paper, based on guaranteed bounding ellipsoid approximation, a new enhanced set membership filter with better real-time property and reduced conservation is proposed for state estimation problem of nonlinear systems. The nonlinear model is firstly linearized and the DC programming method is used to outer-bound the linearization error, which is incorporated to the model noise with ellipsoidal approximations. A classical two-step prediction-correction procedure consisting vector sum computation between ellipsoids and an iterative outer-bounding ellipsoid algorithm to intersect ellipsoid with strip is presented to compute the ellipsoidal feasible set of the estimated states. Simulation results with comparisons to the nonlinear extended set membership filter are given to demonstrate the effectiveness and improved performances of our proposed algorithm.
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[1] Bar-Shalom Y, Li X R, Kirubarajan T. Estimation with Applications to Tracking and Navigation. New York: Willey, 2002. 200-217[2] Arulampalam M S, Maskell S, Gordon N, Clapp T. A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing, 2002, 50(2): 174-188[3] Einicke G A, White L B. Robust extended Kalman filtering. IEEE Transactions on Signal Processing, 1999, 47(9): 2596-2599[4] Di Marco M, Garulli A, Lacroix S, Vicino A. Set membership localization and mapping for autonomous navigation. International Journal of Robust and Nonlinear Control, 2001, 11(7): 709-743[5] Calafiore G. Reliable localization using set-valued nonlinear filters. IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans, 2005, 35(2): 189-197[6] Jaulin L. A nonlinear set membership approach for the localization and map building of underwater robots. IEEE Transactions on Robotics, 2009, 25(1): 88-98[7] Yu W, De Jesús Rubio J. Recurrent neural networks training with stable bounding ellipsoid algorithm. IEEE Transactions on Neural Networks, 2009, 20(6): 983-991[8] Fagarasan I, Ploix S, Gentil S. Causal fault detection and isolation based on a set-membership approach. Automatica, 2004, 40(12): 2099-2110[9] Combastel C, Zhang Q H. Robust fault diagnosis based on adaptive estimation and set-membership computations. In: Proceedings of the 6th IFAC Symposium on Fault Detection, Supervision and Safety of Technical. Beijing, China: IFAC, 2006. 7314-7319[10] Fogel E, Huang Y F. On the value of information in system identification — bounded noise case. Automatica, 1982, 18(2): 229-238[11] Kurzhanskiy A A, Varaiya P. Ellipsoidal techniques for reachability analysis of discrete-time linear systems. IEEE Transactions on Automatic Control, 2007, 52(1): 26-38[12] Kieffer M, Jaulin L, Walter E. Guaranteed recursive nonlinear state bounding using interval analysis. International Journal of Adaptive Control and Signal Processing, 2006, 16(3): 193-218[13] Chisci L, Garulli A, Zappa G. Recursive state bounding by parallelotopes. Automatica, 1996, 32(7): 1049-1055[14] Chisci L, Garulli A, Vicino A, Zappa G. Block recursive parallelotopic bounding in set membership identification. Automatica, 1998, 34(1): 15-22[15] Alamo T, Bravo J M, Camacho E F. Guaranteed state estimation by zonotopes. Automatica, 2005, 41(6): 1035-1073[16] Alamo T, Bravo J M, Redondo M J, Camacho E F. A set-membership state estimation algorithm based on DC programming. Automatica, 2008, 44(1): 216-224[17] Ros L, Sabaster A, Thomas F. An ellipsoidal calculus based on propagation and fuse. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2002, 32(4): 430-442[18] Schweppe F C. Recursive state estimation: unknown but bounded errors and system inputs. IEEE Transactions on Automatic Control, 1968, 13(1): 22-38[19] Bertsekas D P, Rhodes I B. Recursive state estimation for a set-membership description of uncertainty. IEEE Transactions on Automatic Control, 1971, 16(2): 117-128[20] Belforte G, Bona B. An improved parameter identification algorithm for signals with unknown-but-bounded errors. In: Proceedings of the 7th IFAC/IFORS Symposium on Identification and System Parameter Estimation. York, UK: IFAC, 1985. 1507-1511[21] Durieu C, Walter E, Polyak B T. Multi-input multi-output ellipsoidal state bounding. Journal of Optimization Theory and Applications, 2001, 111(2): 273-303[22] Chernousko F L, Rokityanskii D Y. Ellipsoidal bounds on reachable sets of dynamical systems with matrices subjected to uncertain perturbations. Journal of Optimization Theory and Applications, 2000, 104(1): 1-19[23] Maksarov D G, Norton J P. Computationally efficient algorithms for state estimation with ellipsoidal approximations. International Journal of Adaptive Control and Signal Processing, 2002, 16(6): 411-434[24] Shamma J S, Tu K Y. Approximate set-valued observers for nonlinear systems. IEEE Transactions on Automatic Control, 1997, 42(5): 648-658[25] Scholte E, Campell M E. A nonlinear set-membership filter for on-line applications. International Journal of Robust and Nonlinear Control, 2003, 13(15): 1337-1358[26] Horst R, Thoai N V. DC programming: overview. Journal of Optimization Theory and Applications, 1999, 103(1): 1-43[27] Boyd S, Vamdenberghe L. Convex Optimization. Cambridge: Cambridge University Press, 2004. 561-615[28] Zhou B, Han J D, Liu G J. A UD factorization-based nonlinear adaptive set-membership filter for ellipsoidal estimation. International Journal of Robust and Nonlinear Control, 2008, 18(16): 1513-1531
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