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## 留言板

 引用本文: 张勇刚, 黄玉龙, 武哲民, 李宁. 一种高阶无迹卡尔曼滤波方法. 自动化学报, 2014, 40(5): 838-848.
ZHANG Yong-Gang, HUANG Yu-Long, WU Zhe-Min, LI Ning. A High Order Unscented Kalman Filtering Method. ACTA AUTOMATICA SINICA, 2014, 40(5): 838-848. doi: 10.3724/SP.J.1004.2014.00838
 Citation: ZHANG Yong-Gang, HUANG Yu-Long, WU Zhe-Min, LI Ning. A High Order Unscented Kalman Filtering Method. ACTA AUTOMATICA SINICA, 2014, 40(5): 838-848.

## A High Order Unscented Kalman Filtering Method

Funds:

Supported by National Natural Science Foundation of China (61001154, 61201409, 61371173), China Postdoctoral Science Foundation (2013M530147), Heilongjiang Postdoctoral Fund (LBH-Z13052), and Fundamental Research Funds for the Central Universities of Harbin Engineering University (HEUCFX41307)

• 摘要: 现有的研究中，高阶无迹变换（Unscented transform，UT）还不存在具体的解析解，因此，无法利用高阶无迹变换获得具备更高精度的高阶无迹卡尔曼滤波器（Unscented Kalman filter，UKF）.为了解决这一问题，本文在五阶容积变换（Cubature transform，CT）的基础上，通过引入一个自由参数κ，得到高阶无迹变换的解析解，从而获得了高阶无迹卡尔曼滤波器（Unscented Kalman filter，UKF）.同时验证了现有的五阶容积变换和五阶无迹变换分别是本文所提出的高阶无迹变换在κ=2和κ=6-n时的两个特例.进而分析和讨论了高阶无迹卡尔曼滤波器在系统不同维数条件下κ值的最优选取，并讨论了其稳定性.纯方位跟踪模型和弹道目标再入模型仿真验证了本文方法的正确性，且与现有方法相比具有更高的精度.
•  [1] Wu Y X, Hu D W, Wu M P, Hu X P. A numerical-integration perspective on Gaussian filters. IEEE Transactions on Signal Processing, 2006, 54(8): 2910-2921 [2] Julier S J, Uhlman J K, Durrant-Whyte H F. A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Transactions on Automatic Control, 2000, 45(3): 477-482 [3] Julier S J, Uhlman J K. Unscented filtering and nonlinear estimation. Proceedings of the IEEE, 2004, 92(3): 401-422 [4] Lefebvre T, Bruyninckx H, de Schuller J. Comment on "A new method for the nonlinear transformation of means and covariances in filters and estimators" [and author's reply]. IEEE Transactions on Automatic Control, 2002, 47(8): 1406-1409 [5] Zhao Lin, Wang Xiao-Xu, Sun Ming, Ding Ji-Cheng, Yan Chao. Adaptive UKF filtering algorithm based on maximum a posterior estimation and exponential weighting. Acta Automatica Sinica, 2010, 36(7): 1007-1019(赵琳, 王小旭, 孙明, 丁继成, 闫超. 基于极大后验估计和指数加权的自适应UKF 滤波算法. 自动化学报, 2010, 36(7): 1007-1019) [6] Sun Yao, Zhang Qiang, Wan Lei. Small autonomous underwater vehicle navigation system based on adaptive UKF algorithm. Acta Automatica Sinica, 2010, 37(3): 342-353 (孙尧, 张强, 万磊. 基于自适应UKF 算法的小型水下机器人导航系统. 自动化学报, 2010, 37(3): 342-353) [7] Wang Lu, Li Guang-Chun, Qiao Xiang-Wei, Wang Zhao-Long, Ma Tao. An adaptive UKF algorithm based on maximum likelihood principle and expectation maximization algorithm. Acta Automatica Sinica, 2012, 38(7): 1200-1210(王璐, 李光春, 乔相伟, 王兆龙, 马涛. 基于极大似然准则和最大期望算法的自适应UKF 算法. 自动化学报, 2012, 38(7): 1200-1210) [8] Arasaratnam I, Haykin S. Cubature Kalman filters. IEEE Transactions on Automatic Control, 2009, 54(6): 1254-1269 [9] Jia B, Xin M, Cheng Y. High-degree cubature Kalman filter. Automatica, 2013, 49(2): 510-518 [10] Julier S J, Uhlman J K. The scaled unscented transformation. In: Proceedings of the 2000 American Control Conference. Anchorage, AK, USA: IEEE, 2002, 6: 4555-4559 [11] Chang L B, Hu B Q, Li A, Qin F J. Transformed unscented Kalman filter. IEEE Transactions on Automatic Control, 2013, 58(1): 252-257 [12] Julier S J, Uhlman J K. A consistent, debiased method for converting between polar and Cartesian coordinate systems. In: Proceedings of Acquisition, Tracking and Pointing XI. Orlando, 1997, 3086. 110-121 [13] Lerner U N. Hybrid Bayesian Networks for Reasoning about Complex Systems [Ph.D. dissertation], Stanford University, USA, 2002 [14] Ito K, Xiong K Q. Gaussian filters for nonlinear filtering problems. IEEE Transactions on Automatic Control, 2000, 45(5): 910-927 [15] Xiong K, Zhang H Y, Chan C W. Performance evaluation of UKF-based nonlinear filtering. Automatica, 2006, 42(2): 261-270 [16] Dunik J, Simandl M, Straka O. Unscented Kalman filter: aspects and adaptive setting of scaling parameter. IEEE Transactions on Automatic Control, 2012, 57(9): 2411-2416 [17] Nφrgaard M, Poulsen N K, Ravn O. New developments in state estimation for nonlinear systems. Automatica, 2000, 36(11): 1627-1638
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##### 出版历程
• 收稿日期:  2013-06-05
• 修回日期:  2013-08-28
• 刊出日期:  2014-05-20

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