焦平面图像制导导弹对地面目标截获概率计算

doi:10.12382/bgxb.2023.1107

摘要/Abstract

摘要：

针对图像制导导弹的目标探测和精确制导的需求,研究基于矩形焦平面探测器的图像制导导弹转入末制导时对地面目标的截获概率。根据导弹的高度姿态和探测器参数推导对地面探测的不规则四边形视场(Irregular Quadrilateral Detection Field,IQDF)的解析解和简化的矩形探测视场(Simplified Rectangular Detection Field,SRDF)模型,确定影响目标截获概率的主要误差源。利用条件概率思想,将目标截获概率分解为导弹状态概率和当前状态下目标落入地面视场概率,并利用有限元分割算法推导出目标落入地面视场概率,从而建立多源误差下的目标截获概率模型。通过仿真分析在IQDF和SRDF下主要误差源对目标落入地面视场概率的影响,并在多源误差下将推导的目标截获概率与蒙特卡洛方法仿真结果进行对比,验证了目标截获概率计算方法的有效性。

关键词: 图像制导导弹, 焦平面探测器, 截获概率, 多源误差, 探测视场模型

Abstract:

For the needs of target detection and precision guidance of image guided missile,the ground target intercept probability of image guided missile when it is transferred to terminal guidance based on a rectangular focal plane detector is investigated.The analytical solution of irregular quadrilateral detection field(IQDF) and the simplified rectangular detection field(SRDF) model for ground detection are derived from the altitude,attitude and detector parameters of missile.The main error sources affecting the target intercept probability are identified.The target intercept probability is decomposed into the missile state probability andthe probability of a target falling into the ground field-of-view in the current state by using the conditional probability idea,and the finite element segmentation algorithm is utilized to derive the probability of the target falling into the ground field of view(FOV),so as to establish a model of target intercept probability in the case of multi-source error.The effects of the main error sources on the probability of the target falling into the ground FOV in IQDF and SRDF are analyzed by simulation,and the derived target intercept probability is compared with the Monte Carlo simulation results in the case of multi-source errors,which verifies the effectiveness of the target intercept probability calculation method.

Key words: image guided missile, focal plane detector, intercept probability, multi-source error, detection field-of-view model

中图分类号:

TJ765.3

赵洁, 徐子钰, 莫波, 石忠佼. 焦平面图像制导导弹对地面目标截获概率计算[J]. 兵工学报, 2025, 46(1): 231107-.

ZHAO Jie, XU Ziyu, MO Bo, SHI Zhongjiao. Ground Target Intercept Probability of Focal Plane Image Guided Missiles[J]. Acta Armamentarii, 2025, 46(1): 231107-.

图/表 15

图1 导引头探测器等效视场角示意图

Fig.1 Equivalent field of view of seeker detector

图2 一般情况下导弹对地面的探测视场

Fig.2 Missile’s field of view for ground detection(typically)

图3 探测视场范围平面示意图

Fig.3 Field of view for detection on ground

图4 简化的SRDF探测视场示意图

Fig.4 Schematic diagram of SRDF

图5 SRDF与IQDF对比(γ=0rad)

Fig.5 Comparison of SRDF with IQDF(γ=0rad)

表1 目标截获的主要误差源

Table 1 The main error sources for target intercept

误差源	方向	分布类型	均值	标准差
导弹位置误差	x	正态分布	0	σ_M_x
	y		h_s	σ_M_y
	z		0	σ_M_z
导弹角度误差	滚转	正态分布	γ_s	σ_γ
导弹角度误差	俯仰	正态分布	ϑ_m₀	σ_ϑm
导引头框架角误差		正态分布	ϑ_k₀	σ_ϑk
目标位置误差	x	正态分布	x_T	σ_T_x
目标位置误差	z	正态分布	z_T	σ_T_z

图6 有限元分割探测视场示意图

Fig.6 Finite element segmentation of detection field of view

图7 不同滚转角情况下的IQDF地面探测视场

Fig.7 IQDFs at different roll angles

图8 Ps0,Ps1,Ps2随滚转角变化曲线

Fig.8 Variations of Ps0,Ps1 and Ps2 with roll angle

图9 Ps0,Ps1,Ps2随导弹高度变化

Fig.9 Variations of Ps0,Ps1 and Ps2 with altitude

图10 Ps0,Ps1,Ps2随导引头下视角变化曲线

Fig.10 Variations of Ps0,Ps1 and Ps2 with seeker downview

图11 满足匹配条件下Ps0,Ps1,Ps2变化

Fig.11 Variations of Ps0,Ps1 and Ps2 under satisfying matching conditions

图12 Ps0,Ps1,Ps2随T-C误差标准差变化

Fig.12 Variations of Ps0,Ps1 and Ps2 with standard deviation of T-C error

表2 多源误差下目标截获概率(较小误差)

Table 2 Target intercept probability under multi-source error(smaller error)

误差源	均值	标准差	误差源	均值	标准差	误差源	均值	标准差	误差源	均值	标准差	P_s	P_t	P_t0
高度	1100	30	下视角	-50°	0.6°	滚转角	0°	0.6°	T-C 误差	0	60	0.8186	0.7578	0.7657
		45			0.6°			0.6°			60	0.8186	0.6854	0.6911
		30			1.0°			0.6°			60	0.8186	0.7477	0.7498
		30			0.6°			1.0°			60	0.8186	0.7578	0.7621
		30			0.6°			0.6°			80	0.6237	0.5765	0.5804

表3 多源误差下目标截获概率(较大误差)

Table 3 Target intercept probability under multi-source error(larger error)

误差源	均值	标准差	误差源	均值	标准差	误差源	均值	标准差	误差源	均值	标准差	P_s	P_t	P_t0
高度	1100	70	下视角	-50°	3°	滚转角	0°	0.6°	T-C 误差	0	60	0.8186	0.5570	0.5594
		110			3°			0.6°			60	0.8186	0.4838	0.5030
		70			5°			0.6°			60	0.8186	0.5193	0.5165
		70			3°			1.0°			60	0.8186	0.5570	0.5597
		70			3°			0.6°			100	0.4680	0.3107	0.3123

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