反舰导弹大前置角下三维剩余飞行时间估计方法

doi:10.12382/bgxb.2023.0613

摘要/Abstract

摘要：

为解决导弹开启末制导时初始前置角过大或前置角变化幅度较大的问题,设计适用于多种导弹制导律的前置角三维剩余飞行时间估计方法。将导弹速度和目标速度投影分解,在地面坐标系的Oxy面和Oxz面上建立弹目相对运动关系方程,以此为基础建立三维弹目相对运动模型。利用弹目相对运动关系方程和比例导引控制方程,建立1阶非线性微分方程,解析弹目距离与前置角的关系,并利用麦克劳林展开式求解方程。根据视线角速度变化选择合适的内框角,对前置角进行补偿,同时使用中位值平均滤波法降低前置角波动造成的误差。利用已建立的三维弹目相对运动模型进行仿真实验。仿真结果表明,在小角度假设不能成立时,尤其是因制导律进行角度控制而导致前置角变化较大时,前置角剩余飞行时间(Time-to-go,TGO)估计方法的估计值误差收敛时间和最大误差值要小于其他TGO估计方法,估计效果最佳。

关键词: 反舰导弹, 前置角, 制导律, 剩余飞行时间估计, 机动目标

Abstract:

To solve the problem of large initial lead angle or significant change in lead angle when missile terminal guidance starts, a 3D time-to-go(TGO)estimation method for lead angle is designed for various missile guidance laws. The missile velocity and target velocity projections are decomposed to establish the relationship equations of relative motion between missile and target on Oxy and Oxz surfaces of ground coordinate system. Based on this, a three-dimensional missile-target relative motion model is established. A first-order nonlinear differential equation is established by using the relative motion equation and proportional navigation control equation of missile and target. The relationship between missile-target distance and lead angle is analyzed. The first-order nonlinear differential equation is solved by using McLaughlin formula. An appropriate inner frame angle is selected based on the change in line-of-sight angular velocity to compensate for the lead angle, and the median average filtering method is used to reduce the error caused by the fluctuation of lead angle. The simulation experiments are conducted by using the proposed three-dimensional missile-target relative motion model. The simulated results show that, when the small angle assumption cannot be established, especially when the angle control of guidance law results in significant changes in the lead angle, the convergence time and maximum error value of estimated error of the lead angle TGO estimation method are smaller than those of other TGO estimation methods.

Key words: anti-ship missile, lead angle, guidance law, time-to-go estimation, maneuvering target

中图分类号:

吴浩, 李东光, 王泳安. 反舰导弹大前置角下三维剩余飞行时间估计方法[J]. 兵工学报, 2024, 45(5): 1449-1459.

WU Hao, LI Dongguang, WANG Yong’an. Time-to-go Estimation Method for Anti-ship Missiles with Large Lead Angle in Three-dimensional Space[J]. Acta Armamentarii, 2024, 45(5): 1449-1459.

图/表 14

图1 弹目相对运动关系

Fig.1 Relative movement relationship between missile and target

图2 APNG弹目运动轨迹

Fig.2 Missile-target motion trajectory of APNG

图3 APNG前置角

Fig.3 Lead angle of APNG

图4 APNG的TGO估计误差

Fig.4 TGO estimated error of APNG

图5 APNG的TGO估计误差(无中位值平均滤波法)

Fig.5 TGO estimated error of APNG (without median value average filtering method)

表1 APNG仿真结果

Table 1 APNG simulated results

方法	收敛时间/s	收敛时的估计值/s	最大误差值/s	最大误差值出现时间/s
TGO1	72.23	-1	47.56	0.02
TGO2	71.64	-1	39.98	0.02
TGO3	32.73	1	32.49	0.01
TGO4			25.88	0.01

图6 BPNG弹目运动轨迹

Fig.6 Missile-target motion trajectory of BPNG

图7 BPNG前置角

Fig.7 Lead angle of BPNG

图8 BPNG的TGO估计误差

Fig.8 TGO estimated error of BPNG

表2 BPNG仿真结果

Table 2 BPNG simulated results

方法	收敛时间/s	收敛时的估计值/s	最大误差值/s	最大误差值出现的时间/s
TGO1	88.39	-1.00	44.08	14.61
TGO2	84.12	-1.00	38.07	15.43
TGO3	16.93	1.00	38.55	0.01
TGO4	7.60	0.99	31.94	0.01

图9 OGL弹目运动轨迹

Fig.9 Missile-target motion trajectory of OGL

图10 OGL前置角

Fig.10 Lead angle of OGL

图11 OGL的TGO估计误差

Fig.11 TGO estimated error of OGL

表3 OGL仿真结果

Table 3 BPNG simulated results

方法	收敛时间/s	收敛时的估计值/s	最大误差值/s	最大误差值出现的时间/s
TGO1	81.73	-1	45.35	0.02
TGO2	78.52	-1	37.77	0.02
TGO3	26.31	1	34.7	0.01
TGO4	14.40	1	28.09	0.01

参考文献 26

[1]	TAHK M J, SHIM S W, HONG S M, et al. Impact time control based on time-to-go prediction for sea-skimming antiship missiles[J]. IEEE Transactions on Aerospace and Electronic Systems, 2018, 54(4):2043-2052.
[2]	李文, 尚腾, 姚寅伟, 等. 速度时变情况下多飞行器时间协同制导方法研究[J]. 兵工学报, 2020, 41(6):1096-1110. doi: 10.3969/j.issn.1000-1093.2020.06.006
	LI W, SHANG T, YAO Y W, et al. Research on time coordinated guidance method for multiple aircraft under time varying velocity[J]. Acta Armamentarii, 2020, 41(6):1096-1110. (in Chinese)
[3]	FUMIAKI I. Some aspects of a realistic three-dimensional pursuit-evasion game[J]. Journal of Guidance Control & Dynamics, 1993, 16(2):289-293.
[4]	ZHU J W, SU D L, XIE Y, et al. Impact time and angle control guidance independent of time-to-go prediction[J]. Aerospace Science and Technology, 2019, 86(Mar.): 818-825.
[5]	王思卓, 范世鹏, 林德福, 等. 考虑目标机动和落角约束的二阶滑模制导律[J]. 兵工学报, 2022, 43(12):3048-3061.
	WANG S Z, FAN S P, LIN D F, et al. Second order sliding mode guidance law considering target maneu-vering and landing angle constraints[J]. Acta Armamentarii, 2022, 43(12):3048-3061. (in Chinese)
[6]	ADLER F P. Missile guidance by three-dimensional proportional navigation[J]. Journal of Applied Physics, 1956, 27(5): 500-507.
[7]	YAN X D, LÜ S. A two-side cooperative interception guidance law for active air defense with a relative time-to-go deviation[J]. Aerospace Science and Technology, 2020, 100(5):105787.
[8]	ZHUANG Z H, TU J P, WANG H B. Prediction of time to go during missile-target encounter[J]. Journal of Astronautics, 2002, 23(5):32-38.
[9]	李辕, 赵继广, 白国玉, 等. 基于预测碰撞点的剩余飞行时间估计方法[J]. 北京航空航天大学学报, 2016, 42(8):1667-1674.
	LI Y, ZHAO J G, BAI G Y, et al. A method for estimating remaining flight time based on predicting collision points[J]. Journal of Beijing University of Aeronautics and Astronautics, 2016, 42(8):1667-1674. (in Chinese)
[10]	史绍琨, 赵久奋, 尤浩. 基于预测碰撞点带落角约束的导引律设计[J]. 火力与指挥控制, 2019, 44(10):148-152.
	SHI S K, ZHAO J F, YOU H. Guidance law design based on predicting collision points with falling angle constraints[J]. Fire Control & Command Control, 2019, 44(10):148-152. (in Chinese)
[11]	吕永佳, 王宝贵, 陈晓刚. 剩余飞行时间估计改进算法研究[J]. 弹箭与制导学报, 2012, 32(3):24-26.
	LÜ Y J, WANG B G, CHEN X G. Research on improved algorithms for estimating remaining flight time[J]. Journal of Projectiles,Rockets,Missiles and Guidance, 2012, 32(3):24-26. (in Chinese)
[12]	HOU Z W, LIU L, WANG Y J. Time-to-go estimation for terminal sliding mode based impact angle constrained guidance[J]. Aerospace Science and Technology, 2017, 71(2):685-694.
[13]	张友安, 马国欣. 大前置角下比例导引律的剩余时间估计算法[J]. 哈尔滨工程大学学报, 2013, 34(11):1409-1414.
	ZHANG Y A, MA G X. A remaining time estimation algorithm for proportional guidance law with large leading angle[J]. Journal of Harbin Engineering University, 2013, 34(11): 1409-1414. (in Chinese)
[14]	ZHANG B L, ZHOU D, SHAO C T. Closed-form time-to-go estimation for proportional navigation guidance considering drag[J]. IEEE Transactions on Aerospace and Electronic Systems, 2022, 58(5): 4705-4717.
[15]	MONDAL S, PADHI R. Generalized explicit guidance with optimal time-to-go and realistic final velocity[J]. Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering, 2019, 233(13):4926-4942.
[16]	RA W S, SHIN H S, LEE Y, et al. Recursive time-to-go estimator for anti-ship missiles guided by pure proportional navigation[C]//Proceedings of 2019 Workshop on Research, Education and Development of Unmanned Aerial Systems. Singapore: IEEE, 2020.
[17]	TAHK M J, RYOO C K, CHO H. Recursive time-to-go estimation for homing guidance missiles[J]. IEEE Transactions on Aerospace and Electronic Systems, 2002, 38(1):13-24.
[18]	WHANG I H, RA W S. Time-to-go estimation filter for anti-ship missile application[C]//Proceedings of the 2008 Sice Annual Conference. Chofu, Japan: IEEE, 2008.
[19]	HULL D G, RADKE J J. Time-to-go prediction for a homing missile based on minimum-time trajectories[J]. AIAA Journal, 2013, 14(5):865-871.
[20]	SHENGNAN F, XIAODONG L, WENJIE Z, et al. Multiconstraint adaptive three-dimensional guidance law using convex optimization[J]. Journal of Systems Engineering and Electronics, 2020, 31(4):791-803. doi: 10.23919/JSEE.2020.000054
[21]	李辕, 闫梁, 赵继广, 等. 顺轨拦截模式剩余飞行时间估计方法[J]. 航空学报, 2015, 36 (9): 3082-3091. doi: 10.7527/S1000-6893.2015.0107
	LI Y, YAN L, ZHAO J G, et al. Estimation method for remaining flight time in along orbit interception mode[J]. Acta Aeronautica et Astronautica Sinic, 2015, 36(9): 3082-3091. (in Chinese)
[22]	马帅, 王旭刚, 王中原, 等. 带初始前置角和末端攻击角约束的偏置比例导引律设计以及剩余飞行时间估计[J]. 兵工学报, 2019, 40(1):68-78. doi: 10.3969/j.issn.1000-1093.2019.01.009
	MA S, WANG X G, WANG Z Y, et al. BPNG law with arbitrary initial lead angle and terminal impact angle constraint and time-to-go estimation[J]. Acta Armamentarii, 2019, 40(1):68-78. (in Chinese) doi: 10.3969/j.issn.1000-1093.2019.01.009
[23]	钱杏芳, 林瑞雄, 赵亚男. 导弹飞行力学[M]. 北京: 北京理工大学出版社, 2013.
	QIAN X F, LIN R S, ZHAO Y A. Missile aircraft fight mechanics[M]. Beijing: Beijing Institute of Technology Press, 2013. (in Chinese)
[24]	张友安, 王星亮, 刘京茂, 等. 角度控制与时间控制导引律[M]. 北京: 电子工业出版社, 2017.
	ZHANG Y A, WANG X L, LIU J M, et al. Angle control and time control guidance law[M]. Beijing: Publishing House of Electronics Industry, 2017. (in Chinese)
[25]	张书森, 孟秀云, 丁晓. 有落角约束的参数可调最优制导律[J]. 飞行力学, 2021, 39(4): 57-60.
	ZHANG S S, MENG X Y, DING X. Parameter adjustable optimal guidance law with falling angle constraint[J]. Flight Dynamics, 2021, 39(4):57-60. (in Chinese)
[26]	ZUO E F, PING F L, PING S D. Optimal guidance with impact angle control based time-to-go estimation[C]//Proceedings of the International Conference on Guidance, Navigation and Control. Harbin, China: Springer, 2022.