-
摘要: 卡尔曼滤波在高斯白噪声的假设下是一种最优滤波, 基于区间数学理论的集员滤波 (Set-membership filter, SMF)能够有效处理有界噪声假设下的滤波问题. 然而, 随机噪声和有界噪声在许多情况下会同时干扰控制系统. 由于两种滤波算法都受到各自适用范围的限制, 使用单一滤波算法难以得到理想的估计结果. 本文通过建立具有双重不确定性系统的模型, 提出了一种基于贝叶斯估计联合滤波算法. 该算法用卡尔曼滤波处理系统的随机不确定性, 用集员滤波处理系统的有界不确定性, 得出一个易于实现的滤波器. 最后通过对雷达跟踪系统的仿真, 结果表明, 较单一滤波算法, 联合滤波具有更强的噪声适应性和有效性.Abstract: Kalman filter is optimal under the assumption of Gaussian white noise, while the set-membership filter (SMF), which is based on interval mathematics, can deal with bounded noise efficiently. However, in many situations, the actual control system is usually interrupted by both random noises and bounded noises simultaneously. It is not easy to obtain expected results by using only one single filter, due to the limited application fields of the two filtering algorithms. In this paper, according to the established system model with dual uncertainties, a new kind of filter named combined filter is proposed, which is based on Bayesian estimation. This algorithm can deal with random uncertainties by applying Kalman filter, and can deal with bounded uncertainties by applying set-membership filter. Accordingly, a new kind of easy filter is produced. The effectiveness of the new filtering algorithm is verified in a radar tracking simulation system. From the simulation results, the combined filter algorithm can produce better adaptability and effectiveness than any one single filter.
-
Key words:
- Kalman filter /
- set-membership filter (SMF) /
- dual uncertainties /
- combined filter
-
表 1 RMSE 均值对比
Table 1 Comparison of RMSE means
算法 RMSE 均值 位移(m) 速度(m/s) EKF 11.2541 1.9795 ESMF 17.7999 3.3716 New -lter 13.5249 2.1869 
下载: 导出CSV
-
[1] 丁原志, 宋晓梅. 雷达跟踪系统的随机干扰自适应. 自动化学报, 1989, 15(3): 209-216 http://www.aas.net.cn/CN/abstract/abstract14905.shtmlDing Yuan-Zhi, Song Xiao-Mei. Adaptation of tracking systems to random disturbances. Acta Automatica Sinica, 1989, 15(3): 209-216 http://www.aas.net.cn/CN/abstract/abstract14905.shtml [2] 石勇, 韩崇昭. 自适应UKF算法在目标跟踪中的应用. 自动化学报, 2011, 37(6): 755-759 http://www.aas.net.cn/CN/abstract/abstract17491.shtmlShi Yong, Han Chong-Zhao. Adaptive UKF method with applications to target tracking. Acta Automatica Sinica, 2011, 37(6): 755-759 http://www.aas.net.cn/CN/abstract/abstract17491.shtml [3] 祁武超, 邱志平. 基于区间分析的结构非概率可靠性优化设计. 中国科学: 物理学 力学 天文学, 2013, 43(1): 85-93 http://www.cnki.com.cn/Article/CJFDTOTAL-JGXK201301013.htmQi Wu-Chao, Qiu Zhi-Ping. Non-probabilistic reliability-based structural design optimization based on interval analysis methods. Scientia Sinica-Physica, Mechanica & Astronomica, 2013, 43(1): 85-93 http://www.cnki.com.cn/Article/CJFDTOTAL-JGXK201301013.htm [4] Wei G L, Liu S A, Song Y, Liu Y R. Probability-guaranteed set-membership filtering for systems with incomplete measurements. Automatica, 2015, 60: 12-16 doi: 10.1016/j.automatica.2015.06.037 [5] Witsenhausen H S. Sets of possible states of linear systems given perturbed observations. IEEE Transactions on Automatic Control, 1968, 13(5): 556-558 doi: 10.1109/TAC.1968.1098995 [6] Cerone V, Lasserre J B, Piga D, Regruto D. A unified framework for solving a general class of conditional and robust set-membership estimation problems. IEEE Transactions on Automatic Control, 2014, 59(11): 2897-2909 doi: 10.1109/TAC.2014.2351695 [7] 王超, 张胜修, 秦伟伟, 郑建飞. 具有自适应噪声边界的Tube可达集鲁棒预测控制. 控制理论与应用, 2014, 31(1): 11-18 http://www.cnki.com.cn/Article/CJFDTOTAL-KZLY201401002.htmWang Chao, Zhang Sheng-Xiu, Qin Wei-Wei, Zheng Jian-Fei. Tube-reachable set-based robust model predictive control with adaptive disturbances boundaries. Control Theory & Applications, 2014, 31(1): 11-18 http://www.cnki.com.cn/Article/CJFDTOTAL-KZLY201401002.htm [8] 吴昊, 陈树新, 杨宾峰, 陈坤. 基于广义M估计的鲁棒容积卡尔曼滤波目标跟踪算法. 物理学报, 2015, 64(21): 218401-1-218401-8 http://www.cnki.com.cn/Article/CJFDTOTAL-WLXB201521049.htmWu Hao, Chen Shu-Xin, Yang Bin-Feng, Chen Kun. Robust cubature Kalman filter target tracking algorithm based on genernalized M-estiamtion. Acta Physica Sinica, 2015, 64(21): 218401-1-218401-8 http://www.cnki.com.cn/Article/CJFDTOTAL-WLXB201521049.htm [9] Cerone V, Razza V, Regruto D. Set-membership estimation of fiber laser physical parameters from input-output power measurements. Automatica, 2015, 61: 211-217 doi: 10.1016/j.automatica.2015.08.019 [10] Zhai S C, Wang W, Ye H. Auxiliary signal design for active fault detection based on set-membership. IFAC-PapersOnLine, 2015, 48(21): 452-457 doi: 10.1016/j.ifacol.2015.09.568 [11] Guo L. Estimating time-varying parameters by the Kalman filter based algorithm: stability and convergence. IEEE Transactions on Automatic Control, 1990, 35(2): 141-147 doi: 10.1109/9.45169 [12] Oberkampf W L, Helton J C, Joslyn C A, Wojtkiewicz S F, Ferson S. Challenge problems: uncertainty in system response given uncertain parameters. Reliability Engineering & System Safety, 2004, 85(1-3): 11-19 http://cn.bing.com/academic/profile?id=2037662824&encoded=0&v=paper_preview&mkt=zh-cn [13] Hanbeck U D, Horn J, Schmidt G. On combining statistical and set-theoretic estimation. Automatica, 1999, 35(6): 1101-1109 doi: 10.1016/S0005-1098(99)00011-4 [14] Noack B, Klumpp V, Hanebeck U D. State estimation with sets of densities considering stochastic and systematic errors. In: Proceedings of the 12th International Conference on Information Fusion. Seattle USA: IEEE, 2009. 1751-1758 [15] Klumpp V, Noack B, Baum M, Hanebeck U D. Combined set-theoretic and stochastic estimation: a comparison of the SSI and the CS filter. In: Proceedings of the 13th Conference on Information Fusion. Edinburgh, United Kingdom: IEEE, 2010. 1-8 [16] Henningsson T. Recursive state estimation for linear systems with mixed stochastic and set-bounded disturbances. In: Proceedings of the 47th IEEE Conference on Decision and Control. Cancun, Mexico: IEEE, 2008. 678-683 [17] Liu Y S, Zhao Y. Ellipsoidal set filter combined set-membership and statistics uncertainties for bearing-only maneuvering target tracking. In: Proceedings of the 2014 IEEE/ION Position, Location and Navigation Symposium (PLANS 2014). Monterey, CA: IEEE, 2014. 753-759 [18] Fogel E, Huang Y F. On the value of information in system identification-bounded noise case. Automatica, 1982, 18(2): 229-238 doi: 10.1016/0005-1098(82)90110-8 [19] Morrell D R, Stirling W C. An extended set-valued Kalman filter. In: Proceedings of the 2003 International Symposium on Imprecise Probabilities and Their Applications (ISIPTA). Lugano, Switzerland, 2003. 395-407 [20] Milanese M, Novara C. Unified set membership theory for identification, prediction and filtering of nonlinear systems. Automatica, 2011, 47(10): 2141-2151 doi: 10.1016/j.automatica.2011.03.013 [21] 宋大雷, 吴冲, 齐俊桐, 韩建达. 基于MIT规则的自适应扩展集员估计方法. 自动化学报, 2012, 38(11): 1847-1860 doi: 10.3724/SP.J.1004.2012.01847Song Da-Lei, Wu Chong, Qi Jun-Tong, Han Jian-Da. A MIT-based nonlinear adaptive set-membership filter for ellipsoidal estimation. Acta Automatica Sinica, 2012, 38(11): 1847-1860 doi: 10.3724/SP.J.1004.2012.01847 -
图(5) / 表(1)
计量
- 文章访问数: 2216
- HTML全文浏览量: 237
- PDF下载量: 1040
- 被引次数: 0
