Prediction of Exterior Ballistics and Impact Point of Mortar Based on Transformer-LSTM Hybrid Neural Network

doi:10.12382/bgxb.2025.0123

Abstract

Abstract:

It is required to fastly and accurately predict the exterior ballistics and impact points of mortars on the modern battlefield.A mortar exterior ballistics prediction method based on Transformer-long short-term memory (Transformer-LSTM) hybrid neural network is proposed.The Transformer network is utilized to extract the intrinsic joint features of mortar’s velocity and three-dimensional coordinates at the moments from T to T+K,and the LSTM network takes these time series features as an input to map the three-dimensional coordinate information at the moment of T+K+1.In order to optimize the network model,the effects of different sliding window step sizes on the convergence performance of the exterior ballistics prediction model are investigated and analyzed.The proposed hybrid network is compared with GRU and LSTM networks in terms of single-step,multi-step and impact-point prediction.It is found that the prediction accuracies of the proposed hybrid network for the three-dimensional coordinates of exterior ballistics can reach up to 99.78%,99.72% and 99.81%,which are better than those of GRU and LSTM networks; and the single-step prediction of the exterior ballistics of the proposed hybrid network consumes only 1.2ms,which significantly improves the prediction accuracy and efficiency.The method enables accurate and fast prediction of exterior ballistics and impact point,providing more response time for mortar interception missions.

Key words: exterior ballistics prediction, deep learning, Transformer-LSTM hybrid neural network, sliding window

CLC Number:

TJ31

YANG Shouhuai, HUANG Jiangliu, CHEN Zhihua, HUANG Zhengui, WU Mingyu, QIU Rongxian, ZHENG Chun. Prediction of Exterior Ballistics and Impact Point of Mortar Based on Transformer-LSTM Hybrid Neural Network[J]. Acta Armamentarii, 2025, 46(11): 250123-.

Figures/Tables 15

References 23

[1]	梁桐嘉, 孙康, 范继, 等. 基于BiLSTM-AM的迫弹外弹道轨迹及落点预测[J/OL]. 火炮发射与控制学报, 2024(2024-09-25)[2025-02-25].https://doi.org/10.19323/j.issn.1673-6524.202405016.
	LIANG T J, SUN K, FAN J, et al. Prediction of external ballistic trajectory and landing point of mortar based on BiLSTM-AM[J/OL]. Journal of Gun Launch & Control, 2024(2024-09-25)[2025-02-25].https://doi.org/10.19323/j.issn.1673-6524.202405016. (in Chinese)
[2]	李兴隆, 贾方秀, 王晓鸣, 等. 基于线性弹道模型的末段修正弹落点预测[J]. 兵工学报, 2015, 36(7):1188-1194. doi: 10.3969/j.issn.1000-1093.2015.07.006
	LI X L, JIA F X, WANG X M, et al. Impact point prediction of terminal correction projectile based on linear trajectory model[J]. Acta Armamentarii, 2015, 36(7):1188-1194. (in Chinese)
[3]	RAMEZANI A, ROTHE H. Simulation-based early prediction of rocket,artillery,and mortar trajectories and real-time optimization for counter-ram systems[J]. Mathematical Problems in Engineering, 2017, 2017(1):8157319. doi: 10.1155/mpe.v2017.1 URL
[4]	魏五洲, 霍李, 李军明, 等. 基于无迹卡尔曼滤波算法的弹道落点预测方法[J]. 兵工自动化, 2022, 41(2):70-74.
	WEI W Z, HUO L, LI J M, et al. Ballistic impact point prediction method based on UKF algorithm[J]. Ordnance Industry Automation, 2022, 41(2):70-74. (in Chinese)
[5]	HAN P, YUE J C, FANG C, et al. Short-term 4D trajectory prediction based on LSTM neural network[J]. Proceedings of SPIE, 2020, 11427(21):2550425.
[6]	XIE Y F, ZHUANG X B, XI Z P, et al. Dual-channel and bidirectional neural network for hypersonic glide vehicle trajectory prediction[J]. IEEE Access, 2021, 9:92913-92924. doi: 10.1109/ACCESS.2021.3092515 URL
[7]	卢新月, 祁克玉, 钱荣朝, 等. 基于长短期记忆神经网络的弹丸落点预测[J]. 探测与控制学报, 2023, 45(1):73-77.
	LU X Y, QI K Y, QIAN R Z, et al. A LSTM neural network based projectile impact-point prediction method[J]. Journal of Detection & Control, 2023, 45(1):73-77. (in Chinese)
[8]	LUI D G, TARTAGLIONE G, CONTI F, et al. Long short-term memory-based neural networks for missile maneuvers trajectories prediction[J]. IEEE Access, 2023, 11:30819-30831. doi: 10.1109/ACCESS.2023.3262023 URL
[9]	SUN L H, YANG B Q, MA J. Trajectory prediction in pipeline form for intercepting hypersonic gliding vehicles based on LSTM[J]. Chinese Journal of Aeronautics, 2023, 36(5):421-433.
[10]	任济寰, 吴祥, 薄煜明, 等. 基于增强上下文信息长短期记忆网络的弹道轨迹预测[J]. 兵工学报, 2023, 44(2):462-471. doi: 10.12382/bgxb.2021.0489
	REN J H, WU X, BO Y M, et al. Ballistic trajectory prediction based on context-enhanced long short-term memory network[J]. Acta Armamentarii, 2023, 44(2):462-471. (in Chinese) doi: 10.12382/bgxb.2021.0489
[11]	郑志伟, 管雪元, 傅健, 等. 基于卷积神经网络与长短期记忆神经网络的弹丸轨迹预测[J]. 兵工学报, 2023, 44(10):2975-2983. doi: 10.12382/bgxb.2022.0511
	ZHENG Z W, GUAN X Y, FU J, et al. Projectile trajectory prediction based on CNN-LSTM model[J]. Acta Armamentarii, 2023, 44(10):2975-2983. (in Chinese) doi: 10.12382/bgxb.2022.0511
[12]	MNIH V, HEESS N, GRAVES A. Recurrent models of visual attention[J]. Advances in Neural Information Processing Systems, 2014, 27:2204-2212.
[13]	孙溪晨, 李伟兵, 黄昌伟, 等. 基于自注意力机制增强的CNN-LSTM的榴弹轨迹多步超前预测[J]. 兵工学报, 2024, 45(增刊1):51-59.
	SUN X C, LI W B, HUANG C W, et al. Multi-step-ahead prediction of grenade trajectory based on cnn-lstm enhanced by deep learning and self-attention mechanism[J]. Acta Armamentarii, 2024, 45(S1):51-59. (in Chinese) doi: 10.12382/bgxb.2024.0659
[14]	赵蒙, 王明宇, 王健, 等. 基于运动方程的弹道导弹建模仿真方法[J]. 兵器装备工程学报, 2022, 43(12):118-124.
	ZHAO M, WANG M Y, WANG J, et al. Modeling and simulation of ballistic missiles based on motion equation[J]. Journal of Ordnance Equipment Engineering, 2022, 43(12):118-124. (in Chinese)
[15]	MCCOY R. Modern exterior ballistics:the launch and flight dynamics of symmetric projectiles[M]. Atglen,PA,US: Schiffer Pub Ltd., 1999:220.
[16]	VASWANI A, SHAZEER N, PARMAR N, et al. Attention is all you need[J]. Advances in Neural Information Processing Systems, 2017, 30:5998-6008.
[17]	张圆梦, 李少波, 周鹏, 等. 基于多头注意力机制的残差网络深度学习推荐模型[J]. 计算机与数字工程, 2024, 52(7):1955-1958,1965.
	ZHANG Y M, LI S B, ZHOU P, et al. Residual network deep learning recommendation model based on multi-head attention mechanism[J]. Computer & Digital Engineering, 2024, 52(7):1955-1958,1965. (in Chinese)
[18]	余力, 李慧媛, 焦晨璐, 等. 基于多头注意力对抗机制的复杂场景行人轨迹预测[J]. 计算机学报, 2022, 45(6):1133-1146.
	YU L, LI H Y, JIAO C L, et al. Trajectory prediction in complex scenes based on multi-head attention adversarial mechanism[J]. Chinese Journal of Computers, 2022, 45(6):1133-1146. (in Chinese)
[19]	BALDERAS L, LASTRA M, BENÍTEZ J M. Optimizing dense feed-forward neural networks[J]. Neural Networks, 2024, 171(3):229-241. doi: 10.1016/j.neunet.2023.12.015 URL
[20]	LIPTON Z C, BERKOWITZ J, ELKAN C. A critical review of recurrent neural networks for sequence learning[J]. Computer Science, 2015, 1506:00019.
[21]	JI R P, ZHANG C Y, LIANG Y, et al. Trajectory prediction of boost-phase ballistic missile based on LSTM[J]. Systems Engineering & Electronics, 2022, 44(6):1969-1976.
[22]	宋波涛, 许广亮. 基于LSTM与1DCNN的导弹轨迹预测方法[J]. 系统工程与电子技术, 2023, 45(2):504-512. doi: 10.12305/j.issn.1001-506X.2023.02.22
	SONG B T, XU G L. Missile trajectory prediction method based on LSTM and 1DCNN[J]. Systems Engineering and Electronics, 2023, 45(2):504-512. (in Chinese) doi: 10.12305/j.issn.1001-506X.2023.02.22
[23]	王余宽, 谢新连, 马昊, 等. 基于滑动窗口LSTM网络的船舶航迹预测[J]. 上海海事大学学报, 2022, 43(1):14-22.
	WANG Y K, XIE X L, MA H, et al. Ship trajectory prediction based on sliding window LSTM network[J]. Journal of Shanghai Maritime University, 2022, 43(1):14-22. (in Chinese)

选取对象	选取区间	选取步长
弹道倾角θ/(°)	[40,80]	2
迫弹初始射速v₀/(m·s^-1)	[100,400]	10

选取对象	选取区间	选取步长
弹道倾角θ/(°)	[40,80]	2
迫弹初始射速v₀/(m·s^-1)	[100,400]	10

块名称	层名称	参数	输出尺寸
Transformer	输入层		(128,10,4)
	嵌入层	神经元数64	(128,10,64)
	多头注意力层	注意力头数8	(128,10,64)
	归一化层1	输入形状64	(128,10,64)
	Dropout层1	dropout率0.1	(128,10,64)
	前馈神经网络	神经元数128	(128,10,128)
	归一化层2	神经元数64	(128,10,64)
	Dropout层2	输入形状64	(128,10,64)
		dropout率0.1	(128,10,64)
链接块	全局平均池化层	池化窗口为10	(128,1,64)
LSTM	LSTM层1	神经元数32	(128,1,32)
	Dropout层3	dropout率0.1	(128,1,32)
	LSTM层2	神经元数32	(128,32)
	Dropout层4	dropout率0.1	(128,32)
	全连接层(输出层)	神经元数3	(128,3)

块名称	层名称	参数	输出尺寸
Transformer	输入层		(128,10,4)
	嵌入层	神经元数64	(128,10,64)
	多头注意力层	注意力头数8	(128,10,64)
	归一化层1	输入形状64	(128,10,64)
	Dropout层1	dropout率0.1	(128,10,64)
	前馈神经网络	神经元数128	(128,10,128)
	归一化层2	神经元数64	(128,10,64)
	Dropout层2	输入形状64	(128,10,64)
		dropout率0.1	(128,10,64)
链接块	全局平均池化层	池化窗口为10	(128,1,64)
LSTM	LSTM层1	神经元数32	(128,1,32)
	Dropout层3	dropout率0.1	(128,1,32)
	LSTM层2	神经元数32	(128,32)
	Dropout层4	dropout率0.1	(128,32)
	全连接层(输出层)	神经元数3	(128,3)

模型名称	层内容
LSTM	LSTM层1	神经元数量32
	Dropout层1	dropout率为0.1
	LSTM层2	神经元数量32
	Dropout层2	dropout率为0.1
	全连接层	神经元数量3
GRU	GRU层1	神经元数量32
	Dropout层1	dropout率为0.1
	GRU层2	神经元数量32
	Dropout层2	dropout率为0.1
	全连接层	神经元数量3