基于拦截概率的多弹区域协同覆盖制导方法

doi:10.12305/j.issn.1001-506X.2025.06.29

摘要/Abstract

摘要：

针对低精度指示条件下远程防空多弹协同拦截任务中, 弹道散布大, 各弹拦截区差异明显问题, 提出一种基于拦截概率的多弹区域协同覆盖制导方法。首先, 通过对蒙特卡罗打靶得到的脱靶量落入概率分布进行非线性拟合, 建立覆盖拦截区的拦截概率模型, 作为区域覆盖优化问题中的覆盖节点, 将区域拦截概率最高作为覆盖优化指标。其次, 设计采用改进的Circle与Tent映射混合策略自适应粒子群优化(Circle and Tent mapping hybrid strategy adaptive particle swarm optimization, CT-HAPSO)区域覆盖算法, 在目标误差区域内对各弹的拦截区进行覆盖优化分配, 将分配后的各节点位置作为各弹中制导末段的导引点, 通过高概率拦截区拼接及低概率拦截区叠加, 扩大整体高概率拦截区, 提高覆盖区域的整体拦截概率。最后, 通过三维场景下的制导仿真, 验证了所提方法的有效性。

关键词: 拦截概率, 协同覆盖, 目标误差区域, 粒子群优化算法

Abstract:

A cooperative coverage guidance method for multiple missiles region based on interception probability is proposed to address issues of significant ballistic dispersion and differences in missile interception regions in long-range air defense multiple missiles cooperative interception missions with the condition of low-accuracy. Firstly, a nonlinear fitting of the miss distance probability distribution obtained by Monte Carlo simulations is performed to establish an interception probability model for interception coverage regions. This model serves as a coverage node in the regional coverage optimization problem, with the highest regional interception probability as the coverage optimization criterion. Secondly, an improved Circle and Tent mapping hybrid strategy adaptive particle swarm optimization (CT-HAPSO) regional coverage algorithm is designed. The proposed algorithm optimizes the allocation of interception region of each missile within the target error region. The allocated node positions are used as the midcourse guidance points for each missile. By merging high-probability interception regions and low-probability overlapping interception regions, the overall high-probability interception region is expanded, improving the overall interception probability of coverage region. Finally, the effectiveness of the proposed method is verified through guidance simulations in a three-dimensional scenario.

Key words: interception probability, cooperative coverage, target error region, particle swarm optimization (PSO) algorithm

中图分类号:

V448.23

华子清, 魏明英, 李运迁, 柳立坤, 崔正达. 基于拦截概率的多弹区域协同覆盖制导方法[J]. 系统工程与电子技术, 2025, 47(6): 2015-2024.

Ziqing HUA, Mingying WEI, Yunqian LI, Likun LIU, Zhengda CUI. Cooperative coverage guidance method for multiple missiles region based on interception probability[J]. Systems Engineering and Electronics, 2025, 47(6): 2015-2024.

图/表 17

图1

图2

图3

图4

图5

图6

图7

表1

图8

图9

表2

图10

表3

图11

表4

图12

表5

参考文献 32

1	魏明英. 远程防空导弹飞行控制方法研究[M]. 北京: 中国宇航出版社, 2022.
	WEI M Y . Research on flight control methods of long-range air defense missiles[M]. Beijing: China Astronautics Publishing House, 2022.
2	魏明英, 崔正达, 李运迁. 多弹协同拦截综述与展望[J]. 航空学报, 2020, 41 (S1): 29- 36.
	WEI M Y , CUI Z D , LI Y Q . Review and future development of multi-missile coordinated interception[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41 (S1): 29- 36.
3	LIU Y Z , ZHANG X R , DU H F , et al. Construction and simulation of Lanchester battle equations based on space-based information support[J]. Journal of Physics: Conference Series, 2022, 2384 (1): 012011. doi: 10.1088/1742-6596/2384/1/012011
4	YANG K , DANINO M , BAR-SHALOM Y , et al. Track segment association in target selection for interdiction using a single passive sensor[J]. IEEE Trans.on Aerospace and Electronic Systems, 2021, 57 (5): 3268- 3278. doi: 10.1109/TAES.2021.3087813
5	DJEDJIGA B , YAAKOV S B , PETER W . Single space based sensor bias estimation using a single target of opportunity[J]. IEEE Trans.on Aerospace and Electronic Systems, 2019, 56 (3): 1676- 1684.
6	SU W S , SHIN H , CHEN L , et al. Cooperative interception strategy for multiple inferior missiles against one highly maneuvering target[J]. Aerospace Science and Technology, 2018, 80, 91- 100. doi: 10.1016/j.ast.2018.06.026
7	SU W S , LI K B , CHEN L . Coverage-based three-dimensional cooperative guidance strategy against highly maneuvering target[J]. Aerospace Science and Technology, 2018, 85, 556- 566.
8	肖惟, 于江龙, 董希旺, 等. 过载约束下的大机动目标协同拦截[J]. 航空学报, 2020, 41 (S1): 184- 194.
	XIAO W , YU J L , DONG X W , et al. Cooperative interception against highly maneuvering target with acceleration constraints[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41 (S1): 184- 194.
9	于江龙, 董希旺, 李清东, 等. 拦截机动目标的分布式协同围捕制导方法[J]. 航空学报, 2022, 43 (9): 521- 541.
	YU J L , DONG X W , LI Q D , et al. Distributed cooperative encirclement hunting guidance method for intercepting maneuvering target[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43 (9): 521- 541.
10	LIU S X , YAN B B , ZHANG T , et al. Coverage-based coope-rative guidance law for intercepting hypersonic vehicles with overload constraint[J]. Aerospace Science and Technology, 2022, 126, 107651.
11	LIU S X , YAN B B , ZHANG T , et al. Three-dimensional cove- rage-based cooperative guidance law with overload constraints to intercept a hypersonic vehicle[J]. Aerospace Science and Technology, 2022, 130, 107908.
12	CHEN Z Y , YU J L , DONG X W , et al. Three-dimensional cooperative guidance strategy and guidance law for intercepting highly maneuvering target[J]. Chinese Journal of Aeronautics, 2021, 34 (5): 485- 495.
13	ZHANG B L , ZHOU D , LI J L , et al. Coverage-based coope-rative guidance strategy by controlling flight path angle[J]. Journal of Guidance, Control, and Dynamics, 2022, 45 (5): 972- 981.
14	MA L B, HE F H, YAO Y. A 2-D coverage-based guidance algorithm for the multi-stage cooperative interception[C]// Proc. of the Chinese Control Conference, 2019.
15	王龙. 基于区域覆盖的多飞行器协同拦截优化设计方法研究[D]. 哈尔滨: 哈尔滨工业大学, 2018.
	WANG L. Study on optimization and design approach for mutiple flight vehicles cooperative interception based on area coverage[D]. Harbin: Harbin Institute of Technology, 2018.
16	LI K B , BAI Z H , SHIN H , et al. Capturability of 3D RTPN guidance law against true-arbitrarily maneuvering target with maneuverability limitation[J]. Chinese Journal of Aeronautics, 2022, 35 (7): 75- 90.
17	RAMANA V M , KOTHARI M . Pursuit strategy to capture high-speed evaders using multiple pursuers[J]. Journal of Guidance, Control, and Dynamics, 2016, 40 (1): 139- 149.
18	江涌, 王林波, 王蒙一, 等. 基于覆盖理论的高速强机动目标协同围捕策略[J]. 工程科学学报, 2024, 46 (7): 1169- 1178.
	JIANG Y , WANG L B , WANG M Y , et al. Coverage-based cooperative encirclement strategy against high-speed and highly maneuvering targets[J]. Chinese Journal of Engineering, 2024, 46 (7): 1169- 1178.
19	ZHAI C, HE F H, HONG Y G. A coverage-based guidance algorithm of multiple interceptors for uncertain targets[C]//Proc. of the Chinese Control Conference, 2013.
20	ZHAI C , HE F H , HONG Y G , et al. Coverage-based interception algorithm of multiple interceptors against the target involving decoys[J]. Journal of Guidance, Control, and Dyna-mics, 2016, 39 (7): 1646- 1652.
21	SONG B, YU J Q, CHEN X, et al. A multi-missile coverage interception strategy[C]//Proc. of the Aerospace Mechatronics and Control Technology, 2021.
22	TAN L , ZHANG H T , LIU Y Z , et al. Quality-based irregular area coverage algorithm in aerial sensor networks[J]. Computers and Electrical Engineering, 2023, 112, 109003.
23	DING S X , ZHANG T , CHEN C , et al. An efficient particle swarm optimization with evolutionary multitasking for stochastic area coverage of heterogeneous sensors[J]. Information Sciences, 2023, 645, 119319.
24	KUMAR K S , SINGH D , ANAND V . Strategic node deployment scheme for maximizing coverage area and network lifetime in UASNS using voronoi-fuzzy c-means and salp swarm optimiza- tion[J]. IEEE Sensors Journal, 2024, 24 (10): 16926- 16934.
25	LI D L . Research on coverage holes repair in wireless sensor networks based on an improved artificial fish swarm algorithm[J]. International Journal of Autonomous and Adaptive Communications Systems, 2022, 15 (4): 312- 330.
26	宋明智, 杨乐. 基于改进自适应PSO算法的WSN覆盖优化方法[J]. 计算机应用研究, 2013, 30 (11): 3472- 3475.
	SONG M Z , YANG L . Improving coverage of wireless sensor network using enhanced adaptive PSO algorithm[J]. Application Research of Computers, 2013, 30 (11): 3472- 3475.
27	聂文梅, 宋晓霞. 基于自适应粒子群优化算法的无线传感器网络覆盖控制[J]. 沈阳工业大学学报, 2023, 45 (4): 459- 464.
	NIE W M , SONG X X . Coverage control of wireless sensor networks by using adaptive particle swarm optimization algorithm[J]. Journal of Shenyang University of Technology, 2023, 45 (4): 459- 464.
28	HASHIM F A , HUSSIEN A G . Snake optimizer: a novel meta- heuristic optimization algorithm[J]. Knowledge-Based Systems, 2022, 242, 108320.
29	LIU X , TIAN M , ZHOU J , et al. An efficient coverage method for SEMWSNs based on adaptive chaotic Gaussian variant snake optimization algorithm[J]. Mathematical Biosciences and Engineering, 2023, 20 (2): 3191- 3215.
30	JIN Z G , LI H Y , LIANG J W . A node deployment method based on improved snake optimizer for marine disasters[J]. IEEE Sensors Journal, 2024, 24 (9): 15446- 15456.
31	MANTEGNA R N . Fast, accurate algorithm for numerical simulation of Lévy stable stochastic processes[J]. Physical Review E: Statistical Physics Plasmas Fluids & Related Interdisciplinary Topics, 1994, 49 (5): 4677- 4683.
32	崔正达, 魏明英, 李运迁. 考虑阻力系数时变的下压段半解析时间预测方法[J]. 系统工程与电子技术, 2023, 45 (2): 530- 537. doi: 10.12305/j.issn.1001-506X.2023.02.25
	CUI Z D , WEI M Y , LI Y Q . Semi-analytical encounter time estimation method in dive phase with time-varying drag coefficient[J]. Systems Engineering and Electronics, 2023, 45 (2): 530- 537. doi: 10.12305/j.issn.1001-506X.2023.02.25

参数	拦截弹
参数	M₁	M₂	M₃	M₄	M₅
(x_M, y_M, z_M)/km	(0, 31, 0)	(0, 32, 0)	(0, 30, 0)	(0, 29, 0)	(0, 33, 0)
V_M/(m·s^-1)	1 900	1 800	1 700	1 650	1 500
θ/(°)	10	15	15	5	15
ψ/(°)	-2	-10	3	5	10

参数	拦截弹
参数	M₁	M₂	M₃	M₄	M₅
x_M/km	143.28	161.44	185.44	175.78	133.72
y_M/km	10.00	10.00	10.00	10.00	10.00
z_M/km	11.51	-26.352	-8.76	22.63	-19.67

中制导导引点	弹数	打靶仿真命中概率/%
目标误差区域五等分点目标误差区域六等分点协同覆盖优化分配点	5 6 5	79.25 98.75 98.35

参数	拦截弹
参数	M₁	M₂	M₃	M₄	M₅
x_M/km	174.01	140.09	167.19	188.49	142.82
y_M/km	10.00	10.00	10.00	10.00	10.00
z_M/km	-18.87	6.55	27.63	9.19	-27.73

中制导导引点	弹数	打靶仿真命中概率/%
目标误差区域五等分点目标误差区域六等分点协同覆盖优化分配点	5 6 5	71.65 92.95 93.85