基于正态-逆威沙特分布的地空导弹命中概率贝叶斯估计  

Bayesian Estimation of Surface-to-Air Missile Hit Probability Based on Normal-inverse Wishart Distribution

作　　者：刘昊邦 史宪铭 赵美 张建军 LIU Haobang;SHI Xianming;ZHAO Mei;ZHANG Jianjun(Department of Equipment Command and Management,Shijiazhuang Campus of Army Engineering University,Shijiazhuang 050003,Hebei,China;Unit 32140 of PLA,Shijiazhuang 050061,Hebei,China)

机构地区：[1]陆军工程大学石家庄校区装备指挥与管理系,河北石家庄050003 [2]32140部队,河北石家庄050061

出　　处：《兵工学报》2024年第1期339-348,共10页Acta Armamentarii

摘　　要：针对现有导弹命中概率贝叶斯估计中主要采用二维正态射弹散布但未考虑X轴、Y轴两向相关导致估计精度不高的问题,采用正态-逆威沙特分布作为射弹散布参数先验分布,对地空导弹命中概率估计方法展开研究。在描述地空导弹脱靶量定义的基础上,以两向相关特点确定相关系数。针对地空导弹外场试验成本高、数据少,经典统计学方法估计命中概率困难问题,采用贝叶斯方法融合先验信息进行研究。基于正态-逆威沙特分布,利用先验信息对先验分布超参数进行求解,并利用贝叶斯公式融合外场实测试验数据,求出射弹散布参数后验分布,最终完成地空导弹命中概率估计。试验结果表明,该方法相比现有正态-逆伽马分布方法,能够考虑地空导弹射弹散布两向相关的实际情况,并充分利用命中概率信息,有利于提升估计准确性,为地空导弹命中概率估计提供理论方法。The two-dimensional normal projectile dispersion is mainly used in the existing Bayesian estimation of missile hit probability,but the accuracy of estimation is not high enough due to the failure of considering the two-direction correlation of X and Y axes.The normal-inverse Wishart distribution is used as the prior distribution of projectile dispersion parameters,and the hit probability estimation method of surface-to-air missile is studied.Firstly,on the basis of describing the definition of miss distance of surface-to-air missile,the correlation coefficientρis determined by two related characteristics.Secondly,in view of the problems of high cost,little dataof the surface-to-air missile field test,and the difficulty of estimating hit probability by classical statistical methods,the Bayesian method is used to integrate the prior informationfor research.Then,based on the normal-inverse Wishart distribution,the prior information is used to solve the hyperparameters of the prior distribution,and the posterior distribution of projectile dispersion parameters are obtained by integrating the field test data with the Bayesian formula,and finally the hit probability of surface-to-air missile is estimated.The results show that,compared with the existing normal-inverse gamma distribution method,the proposed method take into account the actual situation of the projectile dispersion two-direction correlation of surface-to-air missile,and makes full use of the hit probability information,which is conducive to improving the accuracy of estimation,and provide a theoretical method for the estimation of surface-to-air missile hit probability.

关 键 词：地空导弹 命中概率 射弹散布 两向相关 正态-逆威沙特分布 贝叶斯 

分 类 号：E917[军事]