基于最优样条节点的导弹主动段弹道估计方法

doi:10.7527/S1000-6893.2015.0049

Abstract

Abstract:

Fitting the missile trajectory in boost phase and estimate its ballistic parameters is an important task of the space-based infrared system (SBIRS). Firstly, the cubic spline function is applied to describing the missile trajectory in boost phase, and the motion model and measurement model of the missile trajectory in boost phase are established. Secondly, by using the method of maximum likelihood, the estimation problem of missile trajectory is transformed into the optimal estimation problems of spline coefficients and the distribution of spline nodes under the criterion of nonlinear least squares. Finally, the above-memtioned estimation problems are separated by projection theorem, and the method for optimally determining the number of spline nodes is proposed by iterative approximation. The simulation and experimental results show that the proposed method not only has high fitting precision for missile trajectory in boost phase, but also reduces the number of parameters to be estimated, and simplifies the solving process. The proposed method can better solve the estimation problem of missile trajectory in boost phase without prior information.

Key words: trajectory parameter estimation, spline function, least squares, maximum likelihood estimation, space-based infrared system

CLC Number:

V557
TP274

ZHANG Tao, FAN Shiwei, XUE Yonghong, DING Yonghe. Trajectory estimation method of missile in boost phase using optimal knots spline[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(9): 3027-3033.

References

[1] Lei H, Dong L Q. Ballistic measurement and parameter estimation of ballistic missile with early warning satellite[J]. Advanced Materials Research, 2013, 712: 1960-1964.
[2] Li D, Zhou Y Y, Lyu T G, et al. Tactical parameter estimation of ballistic missile launch with space early warning system[J]. Journal of Astronautics, 2001, 22(6): 84-90 (in Chinese). 李盾, 周一宇, 吕彤光, 等. 空间预警系统对弹道导弹发射点战术参数估计方法[J]. 宇航学报, 2001, 22(6): 84-90.
[3] Li Y C, Bar-Shalom Y. Trajectory and launch point estimation for ballistic missiles from boost phase LOS measurements[C]//IEEE Conference Proceedings on Aerospace. Piscataway, NJ: IEEE Press, 1999: 425-442.
[4] Hutchins R G, Pace P E. Studies in trajectory tracking and launch point determination for ballistic missile defense[C]//Defense and Security Symposium. International Society for Optics and Photonics, 2006: 62360Y-1-8.
[5] Zhang Y, Xiao L X, Wang S H. Ballistics of ballistic missile[M]. Changsha: National University of Defence Technology Press, 2005: 31-144 (in Chinese). 张毅, 肖龙旭, 王顺宏. 弹道导弹弹道学[M]. 长沙: 国防科技大学出版社, 2005: 31-144.
[6] Shen Z, Qiang S, Yi D Y. Course head estimation method based on movement equation by single satellite's passive detection in boost phase[J]. Journal of Ballistics, 2010, 22(1): 7-10 (in Chinese). 申镇, 强胜, 易东云. 基于运动方程的单星无源主动段射向估计方法[J]. 弹道学报, 2010, 22(1): 7-10.
[7] Fan S W, Wang S W, Zhou B Z, et al. Evaluation of trajectory course by geometric relationship under the condition of a single camera[J]. Journal of Huazhong University of Science and Technology, 2005, 33(11): 9-11 (in Chinese). 樊士伟, 王树文, 周伯昭, 等. 单目条件下利用成像关系估计弹道导弹射向[J]. 华中科技大学学报, 2005, 33(11): 9-11.
[8] Li D, Yi D Y, Chen H W, et al. A polynomial approximation algorithm for free-fight trajectory estimation under the early warning of LEO satellite[J]. Journal of National University of Defense Technology, 2011, 33(4): 48-50 (in Chinese). 李冬, 易东云, 程洪玮, 等. 低轨预警自由段弹道估计的多项式逼近算法[J]. 国防科技大学学报, 2011, 33(4): 48-50.
[9] Wang S S, Feng J F, Wang F N, et al. Near space interception of ballistic missiles during boost phase[C]//2nd International Conference on Computing Control and Industrial Engineering. Piscataway, NJ: IEEE Press, 2011: 1-4.
[10] Zhang T, An W, Zhou Y Y, et al. Trajectory tracking method in boost phase using thrust acceleration profile[J]. Journal of Astronautics, 2006, 27(3): 385-389 (in Chinese). 张涛, 安玮, 周一宇, 等. 基于推力加速度模板的主动段弹道跟踪方法[J].宇航学报, 2006, 27(3): 385-389.
[11] Zhou Z, Liu J M, Guo X K. Adaptive tracking algorithm for reentry vehicle based on stochastic model approximation[J]. Journal of Beijing University of Aeronautics and Astronautics, 2014, 40(5): 651-657 (in Chinese). 周政, 刘进忙, 郭相科. 基于随机模型近似的再入目标自适应跟踪算法[J]. 北京航空航天大学学报, 2014, 40(5): 651-657.
[12] Zhang F, Tian K S, Xi M L. The ballistic missile tracking method using dynamic model[C]//2011 IEEE CIE International Conference on Radar. Piscataway, NJ: IEEE Press, 2011,1: 789-794.
[13] Sheng W D, Long Y L, Zhou Y Y. Analysis of target location accuracy in space based optical sensor network[J]. Acta Optica Sinica, 2011, 31(2): 247-253 (in Chinese). 盛卫东, 龙云利, 周一宇. 天基光学传感器网络目标定位精度分析[J]. 光学学报, 2011, 31(2): 247-253.
[14] Xue Y H, An W, Zhang T, et al. Real-time LOS calibration algorithm for high earth orbit infrared scanning sensor[J]. Acta Optica Sinica, 2013, 33(6): 313-318 (in Chinese). 薛永宏, 安玮, 张涛, 等. 高轨红外扫描相机视轴指向实时校正算法[J].光学学报, 2013, 33(6): 313-318.
[15] Taylor H. Cramer-Rao estimation error lower bound computation for deterministic nonlinear system[J]. IEEE Transactions on Automatic Control, 1979, AC-24(2): 343-344.
[16] Yang S Z, Wu Y, Xuan J P, et al. Time series analysis in engineering application[M]. Wuhan: Huazhong University of Science and Technology Press, 2007: 40-200 (in Chinese). 杨叔子, 吴雅, 轩建平, 等. 时间序列分析的工程应用[M]. 武汉: 华中科技大学出版社, 2007: 40-200.
[17] Zhang P, Yi D Y, Duan X J. Estimation of burnout time and precision analysis in space early warning system[J]. Missiles and Space Vehicles, 2004(6): 31-35 (in Chinese). 张萍, 易东云, 段晓君. 空间预警系统的关机点时间估计及精度分析[J]. 导弹与航天运载技术, 2004(6): 31-35.
[18] Bar-Shalom Y, Xiao R L. Estimation and tracking: Principles, techniques and software[M]. Boston, MA: Artech House, 1993: 23-46.

Trajectory estimation method of missile in boost phase using optimal knots spline

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	CHEN Zhiqiang, LIU Zhanhe, MIAO Nan, FENG Wei. Parametric reduced-order model of unsteady aerodynamics based on incremental learning algorithm [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(7): 125103-125103.
[2]	XING Huaixi, ZHANG Yuhui, CHEN You, ZHOU Yipeng, HE Wenbo. Single station passive localization with phase difference change rate based on MCIS technology [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(3): 324278-324278.
[3]	GUO Qiang, LI Wentao. Passive location method based on TDOA/FDOA in case of 4 receivers [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(2): 324236-324236.
[4]	CHEN Senlin, GAO Zhenghong, ZHU Xinqi, PANG Chao, DU Yiming, CHEN Shusheng. Unsteady aerodynamic modeling of unstable dynamic process [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(8): 123675-123675.
[5]	REN Ziqiang, SI Xiaosheng, HU Changhua, WANG Xi. Remaining useful life prediction method for engine combining multi-sensors data [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(12): 223312-223312.
[6]	ZHOU Zhou, GUO Jilian, ZHOU Yijiao, SHEN Anwei. Application of PLS-SEM in core parameter of armament cost estimation [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(3): 221705-221705.
[7]	WANG Ding, YIN Jiexin, WU Zhidong, LIU Ruirui. Direct localization method for constant modulus source based on Doppler frequency shifts [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(9): 321084-321084.
[8]	CHEN Lu, BI Daping, CUI Rui, HAN Jiahui. DOA estimation algorithm based on maximum likelihood estimation for nested array [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(11): 321212-321212.
[9]	ZHU Yingtong, DONG Chunxi, LIU Songyang, DONG Yangyang, ZHAO Guoqing. Passive localization using retransmitted TDOA measurements in the presence of sensor position errors [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(2): 706-716.
[10]	DU Yanshen, WEI Ping, ZHANG Huaguo. A novel solution for passive source localization algorithm using TDOA and GROA measurements [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(9): 3034-3040.
[11]	LIU Yang, YANG Le, GUO Fucheng, JIANG Wenli. Moving targets TDOA/FDOA passive localization algorithm based on localization error refinement [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(5): 1617-1626.
[12]	YU Fei, TAO Jianwu, QIAN Lilin. Airspeed measurement method based on propagation time estimation of acoustic waves [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(4): 1285-1298.
[13]	TDOA and FDOA measurements ZHOU Cheng, HUANG Gaoming, SHAN Hongchang, GAO Jun. Bias compensation algorithm based on maximum likelihood estimation for passive localization using TDOA and FDOA measurements [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(3): 979-986.
[14]	XU Zheng, QU Changwen, LUO Huizi. Novel Multiple Moving Observers TDOA Localization Algorithm Without Introducing Intermediate Variable [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(6): 1665-1672.
[15]	LI Luogang, JING Wuxing, GAO Changsheng. Tracking Near Space Vehicle Using Early-warning Satellite [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(1): 105-115.