改进的平方根UKF在再入滑翔目标跟踪中的应用
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摘要
针对临近空间高超声速再入滑翔目标跟踪问题,提出了一种基于新气动力模型的改进的平方根UKF滤波算法(ISR-UKF)。首先对气动力模型进行了变换。其次,在传统平方根UKF基础上,改用球形无迹变换来计算权系数以及sigma点;改进了平方根矩阵的分解方法;同时为解决矩阵求逆易出现奇异值使滤波失效的问题,提出在协方差矩阵更新中引入多重次稳定因子。最后将该算法分别与基于原气动力的ISR-UKF,基于新气动力的平方根UKF以及基于原气动力的平方根UKF进行仿真比较。仿真表明,该算法具有良好的滤波性能,而且能避免奇异值问题的出现,具有很好的可靠性。
To improve the tracking problem of the hypersonic reentry glide targets in near space, an improved square root UKF filtering algorithm(ISR-UKF) based on the new aerodynamic model is proposed. Firstly, we improve the aerodynamic model. Secondly, based on the traditional square root UKF algorithm, we use the spherical unscented transform to calculate the weight coefficient and the sigma point. And we improve the decomposition method of the square root matrix. At the same time, to solve the problem that the singular value makes the filter invalid when the matrix inversion occurs, multiple stability factors are introduced in the covariance matrix update. Finally, the algorithm is compared with the ISR-UKF based on the traditional aerodynamic force, square root UKF based on the new aerodynamic force, and square root UKF based on the traditional aerodynamic force. The results show that the algorithm has good filtering performance, and can avoid the occurrence of the singular value problems. So it also has good reliability.
To improve the tracking problem of the hypersonic reentry glide targets in near space, an improved square root UKF filtering algorithm(ISR-UKF) based on the new aerodynamic model is proposed. Firstly, we improve the aerodynamic model. Secondly, based on the traditional square root UKF algorithm, we use the spherical unscented transform to calculate the weight coefficient and the sigma point. And we improve the decomposition method of the square root matrix. At the same time, to solve the problem that the singular value makes the filter invalid when the matrix inversion occurs, multiple stability factors are introduced in the covariance matrix update. Finally, the algorithm is compared with the ISR-UKF based on the traditional aerodynamic force, square root UKF based on the new aerodynamic force, and square root UKF based on the traditional aerodynamic force. The results show that the algorithm has good filtering performance, and can avoid the occurrence of the singular value problems. So it also has good reliability.
引文
[1] 黄伟,罗世彬,王振国.临近空间高超声速飞行器关键技术及展望[J].宇航学报, 2010, 31(5): 1259-1265.[Huang Wei, Luo Shi-bin, Wang Zhen-guo. Key techniques and prospect of near-space Hypersonic vehicle[J].Journal of Astronautics, 2010,31(5): 1259-1265.]
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[3] 刘源,张翔宇,王国宏,等.一种新的临近空间高超声速目标跟踪算法[J].电光与控制,2016,23(7):34-38.[Liu Yuan, Zhang Xiang-yu, Wang Guo-hong, et al. A new algorithm for tracking of hypersonic target in near space[J].Electronics Optics &Control, 2016,23(7):34-38.]
[4] 李广华,张洪波,汤国建.高超声速滑翔飞行器典型弹道特性分析[J].宇航学报,2015,36(4):397-403.[Li Guang-hua, Zhang Hong-bo, Tang Jian-guo. Typical trajectory characteristics of hypersonic glide vehicle[J].Journal of Astronautics, 2015,36(4):397-403.]
[5] Shen Q K, Jiang B, Cocquempot V. Fuzzy logic systems-based adaptive fault-tolerant control for near-space vehicle attitude dynamics with actuator faults[J].IEEE Transactions on Fuzzy Systems, 2013,21(2):289-300.
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[9] 张凯,熊家军,韩春耀,等.一种基于气动力模型的高超声速滑翔目标跟踪算法[J].宇航学报, 2017, 38(2):123-130. [Zhang Kai, Xiong Jia-jun, Han Chun-yao, et al. A tracking algorithm of hypersonic glide reentry vehicle via aerodynamic model[J]. Journal of Astronautics,2017,38(2):123-130.]
[10] Lerro D, Bar-shalom Y K. Tracking with debiased consistent converted measurements versus EKF[J]. IEEE Transactions on Aerospace and Electronics Systems,1993,29(3):1015-1022.
[11] 王成飞,胡英娣,张丕旭. 基于平方根UKF的海上多平台误差配准方法[J].海军工程大学学报, 2016, 28(1):103-112. [Wang Cheng-fei, Hu Ying-di, Zhang Pi-xu. Error registration method based on square-root UKF for maritime multi-platforms[J]. Journal of Naval university of Engineering, 2016, 28(1):103-112. ]
[12] Laviola J J. A comparison of unscented and extended Kalman filtering for estimating quaternion motion[C]. Proc. of the American Control Conference,2003.
[13] 李鹏,宋申民,陈兴林.自适应平方根无迹卡尔曼滤波算法[J].控制理论与应用,2010, 27(2):143-146. [Qing Peng, Song Shen-min, Chen Xing-lin. Adaptive square-root unscented Kalman filter algorithm[J]. Control Theory & Applications, 2010, 27(2):143-146.]
[14] Torrieri D J. Fundamental limitations on repeater jamming of frequency-hopping Communications[J].1989,7(4):569-575.
[15] 尤悦,王华,Christophe P,等.基于SRUKF的偏心仅测角相对导航方法[J]. 宇航学报,2016, 37(11): 1312- 1322.[You Yue, Wang Hua, Christophe P, et al. Square root unscented kalman filter-based angles-only relative navigation using camera offset[J].Journal of Astronautics,2016,37(11): 1312-1322.]
[16] Li X R, Jilkov V P. Survey of maneuvering target tracking. Part II: motion models of ballistic and space targets[J].IEEE Transactions on Aerospace and Electronic Systems.2010,46(1):96-119.
[2] Wang W Q. Near-space vehicle:Supply a gap between satellites and airplanes for remote sensing[J]. IEEE Transactions on Aerospace and Electronic Systems Magazine, 2011, 26(4):4-9.
[3] 刘源,张翔宇,王国宏,等.一种新的临近空间高超声速目标跟踪算法[J].电光与控制,2016,23(7):34-38.[Liu Yuan, Zhang Xiang-yu, Wang Guo-hong, et al. A new algorithm for tracking of hypersonic target in near space[J].Electronics Optics &Control, 2016,23(7):34-38.]
[4] 李广华,张洪波,汤国建.高超声速滑翔飞行器典型弹道特性分析[J].宇航学报,2015,36(4):397-403.[Li Guang-hua, Zhang Hong-bo, Tang Jian-guo. Typical trajectory characteristics of hypersonic glide vehicle[J].Journal of Astronautics, 2015,36(4):397-403.]
[5] Shen Q K, Jiang B, Cocquempot V. Fuzzy logic systems-based adaptive fault-tolerant control for near-space vehicle attitude dynamics with actuator faults[J].IEEE Transactions on Fuzzy Systems, 2013,21(2):289-300.
[6] 李林,王国宏,于洪波,等.一种临近空间高超声速目标检测前跟踪算法[J].宇航学报,2017,38(4): 420- 427.[Li Lin, Wang Guo-hong, Yu Hong-bo, et al. A TBD algorithm for near space hypersonic target[J]. Journal of Astronautics,2017,38(4):420-427.]
[7] Fesq L, Aljabri A, Anderson C,et al. Spacecraft autonomy in the new millennium[C]. Proc. of the Annual AAS Rocky Mountain Guidance and Control Conference,1996.
[8] 赵艳丽,高向东,戚宗锋,等.基于空气动力模型的助推-滑翔导弹跟踪[J].导弹与航天运载技术,2010(5):24-29. [Zhao Yan-li, Gao Xiang-dong,Qi Zhong-fen, et al. Tracking for boost-glide missile based on aerodynamic model[J]. Missiles and Space Vehicles, 2010(5):24-29. ]
[9] 张凯,熊家军,韩春耀,等.一种基于气动力模型的高超声速滑翔目标跟踪算法[J].宇航学报, 2017, 38(2):123-130. [Zhang Kai, Xiong Jia-jun, Han Chun-yao, et al. A tracking algorithm of hypersonic glide reentry vehicle via aerodynamic model[J]. Journal of Astronautics,2017,38(2):123-130.]
[10] Lerro D, Bar-shalom Y K. Tracking with debiased consistent converted measurements versus EKF[J]. IEEE Transactions on Aerospace and Electronics Systems,1993,29(3):1015-1022.
[11] 王成飞,胡英娣,张丕旭. 基于平方根UKF的海上多平台误差配准方法[J].海军工程大学学报, 2016, 28(1):103-112. [Wang Cheng-fei, Hu Ying-di, Zhang Pi-xu. Error registration method based on square-root UKF for maritime multi-platforms[J]. Journal of Naval university of Engineering, 2016, 28(1):103-112. ]
[12] Laviola J J. A comparison of unscented and extended Kalman filtering for estimating quaternion motion[C]. Proc. of the American Control Conference,2003.
[13] 李鹏,宋申民,陈兴林.自适应平方根无迹卡尔曼滤波算法[J].控制理论与应用,2010, 27(2):143-146. [Qing Peng, Song Shen-min, Chen Xing-lin. Adaptive square-root unscented Kalman filter algorithm[J]. Control Theory & Applications, 2010, 27(2):143-146.]
[14] Torrieri D J. Fundamental limitations on repeater jamming of frequency-hopping Communications[J].1989,7(4):569-575.
[15] 尤悦,王华,Christophe P,等.基于SRUKF的偏心仅测角相对导航方法[J]. 宇航学报,2016, 37(11): 1312- 1322.[You Yue, Wang Hua, Christophe P, et al. Square root unscented kalman filter-based angles-only relative navigation using camera offset[J].Journal of Astronautics,2016,37(11): 1312-1322.]
[16] Li X R, Jilkov V P. Survey of maneuvering target tracking. Part II: motion models of ballistic and space targets[J].IEEE Transactions on Aerospace and Electronic Systems.2010,46(1):96-119.