林德福 , 牟宇 , 常超 , 等 . 激光半主动末制导炮弹捕获概率研究 [J ] . 北京理工大学学报 , 2010 , 30 ( 6 ): 698 - 701 ,706.

LIN D F , MOU Y , CHANG C , et al . A study of target acquisition probability for laser semi-active terminal guided projectile [J ] . Transactions of Beijing Institute of Technology , 2010 , 30 ( 6 ): 698 - 701 ,706. (in Chinese)

温求遒 , 崔莹莹 , 夏群利 , 等 . 基于导引头地面捕获域的激光制导炸弹射表修正技术 [J ] . 红外与激光工程 , 2012 , 41 ( 8 ): 2053 - 2057 .

WEN Q Q , CUI Y Y , XIA Q L , et al . Firing table modifying based on acquisition ground zone of seeker for laser guidance bomb [J ] . Infrared and Laser Engineering , 2012 , 41 ( 8 ): 2053 - 2057 . (in Chinese)

樊会涛 . 复合制导空空导弹截获目标概率研究 [J ] . 航空学报 , 2010 , 31 ( 6 ): 1225 - 1229 . 中远程空空导弹普遍采用中制导加末制导的复合制导体制，在中末制导交接段，导弹截获目标的概率（TAP）是一个重要的设计指标。建立了一种工程上实用的截获概率计算数学模型，研究了影响截获概率的5种主要误差源及其计算公式，并给出了一条典型弹道的截获概率计算结果。该方法特别适用于研究不同误差源对截获概率的影响，可以在一次弹道计算中得到该条弹道的截获概率。

FAN H T . Study on target acquisition probability of air-to-air missiles with combined guidance [J ] . Acta Aeronautica et Astronautica Sinica , 2010 , 31 ( 6 ): 1225 - 1229 . (in Chinese) <FONT face=Verdana>Medium/long range air-to-air missiles usually adopt a combined guidance of midcourse and terminal. The target acquisition probability (TAP) for a missile in the takeover stage from midcourse to terminal phase is a key design parameter. In this article, a practical mathematical model for calculation of the target acquisition probability is built up, five main error sources which may have an impact on the TAP and their calculating formulas are studied, and the TAP calculation result for a typical missile trajectory is given. This method, by which the TAP can be obtained from a single trajectory calculation, is especially suitable to estimate impacts of various error sources on the TAP.</FONT>

卢晓 , 梁晓庚 , 贾晓洪 . 红外型空空导弹发射后截获概率研究 [J ] . 航空兵器 , 2020 , 27 ( 5 ): 51 - 57 .

LU X , LIANG X G , JIA X H . Research on acquisition probability of lock-on-after-launch infrared air-to-air missiles [J ] . Aero Weaponry , 2020 , 27 ( 5 ): 51 - 57 . (in Chinese)

韩宇萌 , 贾晓洪 , 梁晓庚 . 红外成像导弹目标截获概率 [J ] . 航空学报 , 2016 , 37 ( 10 ): 3101 - 3109 . DOI: 10.7527/S1000-6893.2015.0359 http://doi.org/10.7527/S1000-6893.2015.0359 导弹截获目标的概率是红外成像导弹的一项重要的设计指标。传统的目标截获概率通常通过统计方法得到，该方法需要建立导弹制导控制系统的详细数学模型，因此不适合在导弹总体方案设计阶段使用。针对传统方法的缺陷，通过分析影响红外成像导弹截获概率的主要误差源，从而建立了截获概率的数学模型，从理论分析角度给出了导弹截获概率的计算方法。仿真结果表明，建立的截获概率数学模型正确可信，计算的目标截获概率与传统统计方法结果相当，可以辅助进行各项误差的精度分配以及系统指标的设计，具有重要的理论意义和实际应用价值。

HAN Y M , JIA X H , LIANG X G . Target acquisition probability of infrared imaging missile [J ] . Acta Aeronautica et Astronautica Sinica , 2016 , 37 ( 10 ): 3101 - 3109 . (in Chinese) DOI: 10.7527/S1000-6893.2015.0359 http://doi.org/10.7527/S1000-6893.2015.0359 The target acquisition probability is a key design parameter for the infrared imaging missile. The traditional target acquisition probability calculation method depends on the statistical theory which requires a detailed mathematical model of the missile guidance and control system, so it is not suitable for the stage of missile overall design. According to these disadvantages, on the basis of analyzing the main error sources who affect the calculation of missile target acquisition probability, a mathematical model of target acquisition probability was designed; through this model, we can get the missile target acquisition probability at the stage of missile overall design. A comparative simulation was made between the calculation method in this paper and the traditional statistical method. The simulation results show that the calculation method is correct and credible, and can help missile designers to complete the precision distribution of those error sources and the design of system index, which is of important theoretical significance and practical value.

张大元 , 雷虎民 , 李海宁 , 等 . 复合制导导引头开机截获概率估算 [J ] . 固体火箭技术 , 2014 , 37 ( 2 ): 150 - 155 .

ZHANG D Y , LEI H M , LI H N , et al . Estimate of startup target acquisition probability of seeker for missiles with composite guidance [J ] . Journal of Solid Rocket Technology , 2014 , 37 ( 2 ): 150 - 155 . (in Chinese)

LIU X , TANG S J , GUO J , et al . Midcourse guidance law based on high target acquisition probability considering angular constraint and line-of-sight angle rate control [J ] . International Journal of Aerospace Engineering , 2016 , 2016 : 1 - 20 .

刘骁 , 唐胜景 , 朱大林 , 等 . 制导弹药末段目标截获概率研究 [J ] . 兵工学报 , 2015 , 36 ( 2 ): 287 - 293 . DOI: 10.3969/j.issn.1000-1093.2015.02.014 http://doi.org/10.3969/j.issn.1000-1093.2015.02.014 针对末制导弹药对地面目标攻击时是否加入中制导环节，研究其末段飞行过程中与目标的几何位置关系，采用快速计算与解析方法分析其打击地面固定目标时导引头对目标的角度截获。通过空中散布椭球和地面散布椭圆的近似计算得到视场角计算公式，进而建立一般的数学模型，并从统计概率角度，得到末制导目标截获概率，根据3σ原则判断是否加入中制导环节。同时研究了零控脱靶量与末制导修正距离，结果表明末制导修正能力满足零控脱靶量。仿真发现导引头开机位置距离目标逐渐变小时，视场角的置信区间先减小、后增大。计算了不同干扰因素对视场角置信区间的影响，结果表明水平风对视场角分布的影响比侧风的影响要大。

LIU X , TANG S J , ZHU D L , et al . Research on target acquisition probability in the terminal guidance of guided munition [J ] . Acta Armamentarii , 2015 , 36 ( 2 ): 287 - 293 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2015.02.014 http://doi.org/10.3969/j.issn.1000-1093.2015.02.014 The addition of the midcourse guidance in the guided munition attack and the geometrical position between the missile and the target during the missile flight are studied. The key analysis focuses on the angle of the target intercepted from the seeker when the missile attacks the ground fixed target. The fast calculation method and the analytic method are put forward. In the result of the approximate calculation which is from the space distribution ellipsoid and the ground distribution ellipse, the view angle calculation formula is derived. Furthermore, a general mathematical model to get the target acquisition probability from the view of statistical probability is created. According to the 3σ principle, whether to add the midcourse guidance is decided. The zero-effect miss and the maneuvering ability of the guided munition are researched. The results show that the maneuvering ability of the guided munition covers the zero-effort miss. The confidence interval of the view angle first decreases and then increases when the distance between the seeker and the target decreases. Finally, the influences of different disturbance factors on the view angle's confidence interval are calculated. The calculated results show that the wind in x direction has more influence on the view angle than the wind in z direction.

赵博博 , 刘荣忠 , 郭锐 , 等 . 新型掠飞末敏弹的捕获概率分析 [J ] . 兵工学报 , 2016 , 37 ( 2 ): 232 - 238 . DOI: 10.3969/j.issn.1000-1093.2016.02.006 http://doi.org/10.3969/j.issn.1000-1093.2016.02.006 针对掠飞末敏弹新型扫描机理的作战效能进行评估，研究末敏弹在弹道末段的捕获特性。通过坐标变换的方法得到掠飞末敏弹的扫描线方程，耦合求解其六自由度弹道方程组，得到了弹丸的稳态扫描区域，通过证明扫描依赖区结论，进一步推导求解了捕获概率的解析公式。结果表明：掠飞末敏弹的空间扫描轨迹为螺旋线、扫描区域为圆柱体，平面上的扫描区域为左半椭圆；增加弹丸初速、降低弹丸射角、准确预估目标运动，能有效提升掠飞末敏弹的捕获概率，其中初速的影响更胜一筹；解析公式求得捕获概率与蒙特卡洛打靶法计算结果吻合较好，验证了公式的正确性。

ZHAO B B , LIU R Z , GUO R , et al . Research on acquisition probability of a novel hedgehopping terminal sensitive projectile [J ] . Acta Armamentarii , 2016 , 37 ( 2 ): 232 - 238 . (in Chinese)

刘少波 , 赵良玉 . 超视距防空导弹中末制导交接班时的目标捕获概率研究 [J ] . 固体火箭技术 , 2016 , 39 ( 5 ): 723 - 728 .

LIU S B , ZHAO L Y . Target acquisition probability at hand-off from midcourse to terminal guidance of a BVR air defense missile [J ] . Journal of Solid Rocket Technology , 2016 , 39 ( 5 ): 723 - 728 . (in Chinese)

李斌 , 强艳辉 . 基于相对坐标的空空导弹截获概率计算模型 [J ] . 弹箭与制导学报 , 2022 , 42 ( 6 ): 107 - 110 ,136. DOI: 10.15892/j.cnki.djzdxb.2022.06.016 http://doi.org/10.15892/j.cnki.djzdxb.2022.06.016 中远距空空导弹通常采用捷联惯导/GPS+双向数据链+末制导的复合制导体制,机弹惯导对准误差和机载雷达测角误差是目标指示误差的主要误差源。在攻击隐身目标时,由于导引头探测距离减少,对准误差和测角误差对目标指示误差影响更加显著,降低了截获概率约束的攻击距离。针对中远距空空导弹中末制导交接班,提出了一种基于相对坐标计算目标指示误差方法,推导了计算公式,并与采用绝对坐标计算目标指示误差方法对比,结果表明采用相对坐标的目标截获概率模型显著提高了中末制导交接班时的目标截获概率。

LI B , QIANG Y H . Computational model of the target acquisition probability of air-to-air missile based on relative coordinate [J ] . Journal of Projectiles,Rockets,Missiles and Guidance , 2022 , 42 ( 6 ): 107 - 110 ,136. (in Chinese)

袁俊超 , 张小宽 , 刘铭 , 等 . 目标机动对导引头中末制导交班影响研究 [J ] . 现代雷达 , 2017 ( 7 ): 7 - 11 .

YUAN J C , ZHANG X K , LIU M , et al . The effects of maneuvering target on midcourse and terminal guidance handover of the seeker [J ] . Modem Radar , 2017 ( 7 ): 7 - 11 . (in Chinese)

刘洪全 , 杨国胜 , 同志强 . 协同制导空空导弹目标截获概率研究 [J ] . 航空兵器 , 2020 , 27 ( 6 ): 49 - 54 .

LIU H Q , YANG G S , TONG Z Q . Research on target acquisition probability of air-to-air missiles in cooperative guidance scenarios [J ] . Aero Weaponry , 2020 , 27 ( 6 ): 49 - 54 . (in Chinese)

房施东 , 陈栋 , 马翰宇 , 等 . 图像自寻的火箭弹目标捕获概率计算与分析 [J ] . 弹箭与制导学报 , 2018 , 38 ( 6 ): 51 - 54 . DOI: 10.15892/j.cnki.djzdxb.2018.06.012 http://doi.org/10.15892/j.cnki.djzdxb.2018.06.012 图像自寻的火箭弹目标捕获概率的计算与分析是其作战效能分析的重要内容。为了准确计算捕获概率,结合火箭弹弹道特点及探测设备性能,依据命中误差理论和约翰斯顿(Johnson)准则等,建立了基于火箭弹落入有效可导幅员的概率与导引头对目标识别概率的导引头捕获概率数学模型;根据模型分析了探测高度、诸元误差、目标幅员及目标运动速度等因素对捕获概率的影响,取得了一些有意义的结论,为该弹种作战使用提供了重要参考。

FANG S D , CHEN D , MA H Y , et al . Calculation and analysis on target acquisition probability of image homing rocket [J ] . Journal of Projectiles,Rockets,Missiles and Guidance , 2018 , 38 ( 6 ): 51 - 54 . (in Chinese)

ZHOU J , LEI H M . Coverage-based cooperative target acquisition for hypersonic interceptions [J ] . Science China Technological Sciences , 2018 , 61 ( 10 ): 1575 - 1587 .

田恒斗 , 曹庆刚 , 侯代文 , 等 . 火箭助飞鱼雷捕获概率的解析模型 [J ] . 兵工学报 , 2013 , 34 ( 7 ): 916 - 921 . DOI: 10. 3969/ j. issn. 1000-1093. 2013. 07. 019 http://doi.org/10. 3969/ j. issn. 1000-1093. 2013. 07. 019 针对火箭助飞鱼雷作战方式及弹道形式与传统声自导鱼雷的不同,深入分析了搜索区域、落点散布和目标散布等影响火箭助飞鱼雷捕获概率的关键因素,得出了各要素的数学描述。进而综合考虑3 个要素的相互关系,并根据不同射击方式下目标散布模型的本质区别,分别采用“误差综合冶与“全概率冶的思想,构建了前置点和现在点2 种典型射击方式下火箭助飞鱼雷捕获概率的解析模型。且其计算值与仿真实验结果吻合良好。

TIAN H D , CAO Q G , HOU D W , et al . Analytical model of rocket-assisted torpedo’s acquisition probability [J ] . Acta Armamentarii , 2013 , 34 ( 7 ): 916 - 921 . (in Chinese)

田恒斗 , 侯代文 , 房毅 , 等 . 火箭助飞鱼雷不同齐射方式下的捕获概率分析 [J ] . 兵工学报 , 2015 , 36 ( 7 ): 1370 - 1376 . DOI: 10.3969/j.issn.1000-1093.2015.07.029 http://doi.org/10.3969/j.issn.1000-1093.2015.07.029 针对火箭助飞鱼雷打击远距离目标时捕获概率大幅下降的问题，依据其对目标搜索方式及反潜作战的特点，提出了一种与传统“同一点齐射”不同的“人工散布齐射”方式；并基于全概率的基本思想，构建了描述两种齐射方式捕获概率的数学解析模型；计算了打击目标前置点和现在点两种典型作战样式下，二者在不同射击距离上的捕获概率。计算值与仿真实验结果吻合良好，表明在远距离上打击目标现在点时，人工散布齐射的捕获概率优于同一点齐射。

TIAN H D , HOU D W , FENG Y , et al . Analysis of acquisition probability of rocket-assisted torpedo in different salvo modes [J ] . Acta Armamentarii , 2015 , 36 ( 7 ): 1370 - 1376 . (in Chinese)

袁富宇 , 代志恒 , 肖碧琴 . 基于误差折算的鱼雷一次转角射击命中/发现概率解析计算方法 [J ] . 水下无人系统学报 , 2020 , 28 ( 3 ): 303 - 308 .

YUAN F Y , DAI Z H , XIAO B Q . An analytical calculation method of the hitting/finding probability of torpedo one-time turning-angle shooting based on error conversion [J ] . Journal of Unmanned Undersea Systems , 2020 , 28 ( 3 ): 303 - 308 . (in Chinese)

孙希彤 , 罗兴柏 , 高敏 , 等 . 中末制导交班空间边界建立及影响因素分析 [J ] . 北京理工大学学报 , 2020 , 40 ( 12 ): 1321 - 1331 ,1355.

SUN X T , LUO X B , GAO M , et al . Boundary establishment and analysis of influencing factors in the mid-end guidance transfer space [J ] . Transactions of Beijing Institute of Technology , 2020 , 40 ( 12 ): 1321 - 1331 ,1355. (in Chinese)

WU B Q , GUAN X C , GUAN S H , et al . A capture probability analytic model for the electromagnetic launched anti-torpedo torpedo [J ] . Defence Technology , 2022 , 18 ( 2 ): 261 - 270 . DOI: 10.1016/j.dt.2020.12.006 http://doi.org/10.1016/j.dt.2020.12.006 With the unique characteristics, electromagnetic launch technology is applicable to launch shipborne anti-torpedo torpedo(ATT). This paper aims to establish an analytic model to pre-evaluate the capture probability of the electromagnetic launched ATT. The mathematics model of the multi-stage coilgun and the trajectory of the ATT is established for analysis. The influence factors of the capture probability are analyzed respectively, including the entry point dispersion of the ATT and the position dispersion of the incoming torpedo. Adopting the advanced angle interception mode, the ATT search model is obtained according to the positional relationship, and the course error is synthetically calculated according to the differentiation of implicit function. A geometric method to calculate the integral boundaries of the probability density function is proposed, based on the relative motion of the ATT and the incoming target. To verify the proposed integral model, the digital simulation and comparison is conducted. The results reveal that the variation trends and the calculation value of the proposed analytic model are coincident with the statistic results from Monte Carlo method. And implications of the results regarding the analytic model are discussed. © 2021 The Authors

赵洁 , 徐子钰 , 莫波 , 等 . 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 . DOI: 10.12382/bgxb.2023.1107 http://doi.org/10.12382/bgxb.2023.1107 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。

ZHAO J , XU Z Y , MO B , et al . Intercept probability of ground targets for focal plane image-guided missiles [J ] . Acta Armamentarii , 2025 , 46 ( 1 ): 231107 . (in Chinese) DOI: 10.12382/bgxb.2023.1107 http://doi.org/10.12382/bgxb.2023.1107 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.

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