基于LSTM的弹道导弹主动段轨迹预报

doi:10.12305/j.issn.1001-506X.2022.06.24

摘要/Abstract

摘要：

弹道导弹主动段长周期轨迹预报能够为导弹防御系统提供早期预警信息。传统的轨迹预报方法大多集中在导弹的自由段与再入段, 通过解析法、数值积分法或函数逼近法推断未来时刻目标的状态。由于弹道导弹在主动段会受到多个未知作用力的影响, 其轨迹预报相比自由段与再入段更具挑战性。为此, 本文提出了一种基于长短时记忆(long short-term memeory, LSTM)网络的弹道导弹主动段轨迹预报方法。首先, 根据导弹主动段动力学模型与弹道参数典型取值生成用于网络训练的大规模轨迹样本; 其次, 设计了基于深度LSTM网络的弹道导弹主动段轨迹递归预报方法; 最后, 与基于数值积分法、多项式拟合及反向传播神经网络的轨迹预报方法的实验对比, 表明了所提方法在主动段轨迹预报上的优越性。

关键词: 弹道导弹, 轨迹预报, 长短时记忆网络, 主动段弹道

Abstract:

Long term trajectory prediction for boost-phase ballistic missile (BM) can provide early warning information for the missile defense system. Traditional trajectory prediction methods mostly focus on the BM's coast and reentry phases, inferring the target state at future time through analytical, numerical integration or function approximation methods. In contrast, the boost-phase trajectory prediction is more challenging because there are many unknown forces acting on the BM during this stage. To this end, a long short-term memory (LSTM) network based boost-phase BM trajectory prediction method is proposed in this paper. Specifically, large-scale trajectory samples for the network training are generated first according to the dynamic model of the boost-phase BM and the typical ballistic parameters. Next, a recursive trajectory prediction method for the boost-phase BM based on deep LSTM network is designed. Finally, simulation results compared with the numerical integration, polynomial fitting and back propagation neural network based trajectory prediction methods show the superiority of the proposed method in long term boost-phase BM trajectory prediction.

Key words: ballistic missile, trajectory prediction, long short-term memory (LSTM) network, boost-phase trajectory

中图分类号:

吉瑞萍, 张程祎, 梁彦, 王跃东. 基于LSTM的弹道导弹主动段轨迹预报[J]. 系统工程与电子技术, 2022, 44(6): 1968-1976.

Ruiping JI, Chengyi ZHANG, Yan LIANG, Yuedong WANG. Trajectory prediction of boost-phase ballistic missile based on LSTM[J]. Systems Engineering and Electronics, 2022, 44(6): 1968-1976.

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参数名称		取值
环境参数	地球半径R/km	6 378
	地球自转角速度ω/(rad·s^－1)	7.29×10^－5
	空气密度常数ρ₀/(kg·m^-3)	1.22
	空气密度常数d/m^－1	0.14×10^－3
	地球重力常数μ/(Nm²·kg^－1)	3.99×10¹⁴
弹道参数	火箭排气速度U/(m·s^－1)	2 700
	归一化质量燃烧率q	0.01
	弹道系数c/(kg·N^－1)	4 000
	主动段飞行时间/s	70~110
	主动段飞行高度/km	70~90

网络层	神经元节点数
LSTM 1	128
LSTM 2	256
LSTM 3	256
Maxout	64
FC	6

参数名称	参数值
小批量样本	64
训练迭代步数	50 000
初始学习率	10^-3
惩罚系数	0.003

数据集	轨迹条数
训练集	7 000
验证集	2 000
测试集	1 000

变量名称		变量值
网络参数	LSTM 1节点数	128	64	256	128	128	128	128
	LSTM 2节点数	256	128	512	256	256	256	256
	LSTM 3节点数	256	128	512	256	256	256	256
	Maxout节点数	64	32	128	64	64	64	64
	小批量样本数	64	64	64	32	128	64	64
	训练迭代步数	50 000	50 000	50 000	50 000	50 000	25 000	100 000
预报性能	APRMSE_x/m	124.8	1 273.9	366.2	286.8	846.1	427.6	131 581.1
	APRMSE_y/m	1 780.3	8 844.5	2 915.2	1 920.5	6 647.5	3 099.2	42 442.8
	APRMSE_z/m	846.8	6 599.5	1 348.2	3 691.6	3 302.2	1 535.8	8 494.9
	APRMSE_{v_x}/(m·s^-1)	4	29.1	12.4	12.1	19.1	24.3	56.8
	APRMSE_{v_y}/(m·s^-1)	24.5	126.8	96.3	57	81.2	70.1	471
	APRMSE_{v_z}/(m·s^-1)	16.2	90.7	41.1	29.5	47.1	59.6	207
	平均运行时间/s	0.4	0.3	0.5	0.4	0.4	0.4	0.4