XIE Li-qing,HE La-mei.The Equivalence of Two Kinds of Ensemble Kalman Filter with Linear Equality Constraints[J].Journal of Chengdu University of Information Technology,2016,(03):285-290.
线性等式约束下两种集合卡尔曼滤波的等价性
- Title:
- The Equivalence of Two Kinds of Ensemble Kalman Filter with Linear Equality Constraints
- 文章编号:
- 2096-1618(2016)03-0285-06
- Keywords:
- For the problem of state estimation for nonlinear systems with linear state equality constraints; the method that combines ensemble Kalman filter with estimate projection approaches is presented. According to the different objects; there are two different
- 分类号:
- TN713
- 文献标志码:
- A
- 摘要:
- 针对含线性等式约束的非线性动力系统状态估计问题,考虑将集合卡尔曼滤波算法和估计投影方法相结合,根据不同的处理对象,提出两种不同的含线性等式状态约束的集合卡尔曼滤波算法:(1)运用估计投影方法对每个粒子进行修正之后再加权平均;(2)直接对加权平均后的状态估计向量使用估计投影方法。在约束矩阵退化为常向量,约束向量退化为常数的情况下,给出了上述两种滤波结果的等价性证明。数值模拟实例验证了这一结论。
- Abstract:
- For the problem of state estimation for nonlinear systems with linear state equality constraints, the method that combines ensemble Kalman filter with estimate projection approaches is presented. According to the different objects, there are two different algorithms of the ensemble Kalman filter with linear equality constraints:(1)calculating weighted average after using estimate projection method to correct each particle;(2)applying estimate projection method to calculating weighted average of the unconstrained state estimation vector. It is theoretically proved that the state estimation results of the two proposed algorithms are equivalent when the constraint matrix reduces to a constant vector, and the constraint vector reduces to a constant. Simulation results verify this conclusion.
参考文献/References:
[1] Simon D. Optimal State Estimation [M].New York: INC. Press, John Wiley & Sons, 2006: 212-217, 400-468.
[2] 陈金广, 李洁, 高新波. 等式状态约束下的粒子滤波算法 [J]. 电子科技大学学报, 2011, 40(4): 596-601.
[3] 杜航原, 郝燕玲, 赵玉新. 基于集合卡尔曼滤波的改进粒子滤波算法 [J]. 系统工程与电子技术, 2011, 33(7): 1653-1657.
[4] Bengtsson T, Bickel P, Li B. Curse-of-dimensionality revisited: collapse of the particle filter in very large scale systems [J]. IMS Collections, 2008,(2): 316-334.
[5] Snyder C, Bengtsson T, Bickel P, et al. Obstacles to high-dimensional particle filtering [J]. Mon. Weather Rev., 2008, 136: 4629-4640.
[6] Evensen G. Sequential data assimilation with a non-linear quasi-geostrophic model using Monte Carlo methods to forecast error statistics [J]. Journal of Geophysical research, 1994, 99(C5): 10,143-10,162.
[7] Burgers G,van Leeuwen P J,Evensen G.Analysis scheme in the ensemble Kalman Filter[J].Monthly Weather Review,1998,126:1719-1724.
[8] Evensen G. The Ensemble Kalman Filter: theoretical formulation and practical implementation [J]. Ocean Dynamics, 2003, 53(4): 343-367.
[9] Gillijins S,Mendoza O B, Chandrasekar J, et al. What is the ensemble Kalman filter and how well does it work [C].Proceedings of the American Control Conference, 2006: 4448-4453.
[10] Simon D.Kalman filtering with state constraints:a survey of linear and nonlinear algorithms[J].IET Control Theory Appl.,2010,4(8):1303-1318.
[11] Sangho Ko, Robert R Bitmead. State estimation for linear systems with state equality constraints [J]. Automatic, 2007, 43(8): 1363-1368.
[12] Xu Linfeng, Li X R. Modeling and state estimation for dynamic systems with linear equality constraints [J]. IEEE Transactions on Signal Processing, 2013, 61(11): 2927-2939.
[13] Duan Z S,Li X R. The role of pseudo measurements in equality-constrained state estimation [J]. IEEE Transactions on Aerospace and Electronic Systems, 2013, 49: 1654-1666.
[14] Prakash J, Patwardhan S C, Shah S L. Constrained state estimation using the ensemble Kalman filter [C].Proceedings of the 2008 American Control Conference, 2008: 3542-3547.
[15] Ishihara S, Yamakita M. Constrained state estimation for nonlinear systems with non-Gaussian noise [C].Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, 2009: 1279-1284.
[16] Simon D,Chia T L.Kalman filtering with state equality constraints[J].IEEE transactions on aerospace and electronic systems,2002,38(1):128-136.
[17] Chen Tianshi. Comments on “State estimation for linear systems with state equality constraints” [J]. IEEE Transactions on Automatic Control, 2010, 46(8): 1929-1932.
[18] 王兆敏,徐杰,何腊梅,等. 线性状态等式约束下两种H∞滤波的比较 [J]. 成都信息工程学院学报, 2011, 26(6): 642-646.
[19] Ungarala S.A direct sampling particle filter from approximate conditional density function supported on constrained state space[J].Computers and Chemical Engineering,2011,35(6):1110-1118.
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XIE Li-qing,HE La-mei.The Equivalence of Two Kinds of Ensemble Kalman
Filter with Linear Equality Constraints[J].Journal of Chengdu University of Information Technology,2016,(03):301.
备注/Memo
收稿日期:2015-02-11 基金项目:国家自然科学基金资助项目(61374027); 数学地质四川省重点实验室开放基金资助项目(scsxdz2011006)