基于正态-逆威沙特分布的地空导弹命中概率贝叶斯估计

刘昊邦; 史宪铭; 赵美; 张建军

doi:10.12382/bgxb.2022.0547

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基于正态-逆威沙特分布的地空导弹命中概率贝叶斯估计

更新时间：2025-08-18

- 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
- 兵工学报 2024年45卷第1期页码：339-348
- 作者机构：
  
  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
- 作者简介：
  
  * 邮箱: sxm@nudt.edu.cn
- 基金信息：
- DOI：10.12382/bgxb.2022.0547
  中图分类号：
- 收稿：2022-06-19，
  
  网络出版：2024-02-06，
  
  纸质出版：2024-01-30
- 稿件说明：
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刘昊邦, 史宪铭, 赵美, 等. 基于正态-逆威沙特分布的地空导弹命中概率贝叶斯估计[J]. 兵工学报, 2024,45(1):339-348.

Haobang LIU, Xianming SHI, Mei ZHAO, et al. Bayesian Estimation of Surface-to-Air Missile Hit Probability Based on Normal-inverse Wishart Distribution[J]. Acta Armamentarii, 2024, 45(1): 339-348.
刘昊邦, 史宪铭, 赵美, 等. 基于正态-逆威沙特分布的地空导弹命中概率贝叶斯估计[J]. 兵工学报, 2024,45(1):339-348. DOI： 10.12382/bgxb.2022.0547.

Haobang LIU, Xianming SHI, Mei ZHAO, et al. Bayesian Estimation of Surface-to-Air Missile Hit Probability Based on Normal-inverse Wishart Distribution[J]. Acta Armamentarii, 2024, 45(1): 339-348. DOI： 10.12382/bgxb.2022.0547.

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

轴、

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。

Abstract

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

and

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 coefficient

is 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

Keywords

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