基于贝叶斯理论的小样本空空导弹三维制导精度评估

宁小磊

doi:10.12382/bgxb.2025.0824

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基于贝叶斯理论的小样本空空导弹三维制导精度评估

更新时间：2026-06-15

- 基于贝叶斯理论的小样本空空导弹三维制导精度评估
- Three-Dimensional Guidance Accuracy Evaluation of Air-to-Air Missiles under Small Sample Conditions Based on Bayesian Theory
- 兵工学报 2026年
- 作者机构：
  
  部队，陕西华阴,714200
- 作者简介：
- 基金信息：
  
  基础加强计划重点基础研究项目(2020-JCJQ-ZD-076-00)
- DOI：10.12382/bgxb.2025.0824
  中图分类号： TJ760
- 收稿：2025-09-08，
  
  网络首发：2026-06-15，
- 稿件说明：
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宁小磊. 基于贝叶斯理论的小样本空空导弹三维制导精度评估[J/OL]. 兵工学报, 2026(2026-06-15). https://doi.org/10.12382/bgxb.2025.0824.

NING X L. Three-dimensional guidance accuracy evaluation of air-to-air missiles under small sample conditions based on bayesian theory[J/OL]. Acta Armamentarii, 2026(2026-06-15). https://doi.org/10.12382/bgxb.2025.0824. (in Chinese)
宁小磊. 基于贝叶斯理论的小样本空空导弹三维制导精度评估[J/OL]. 兵工学报, 2026(2026-06-15). https://doi.org/10.12382/bgxb.2025.0824. DOI：

NING X L. Three-dimensional guidance accuracy evaluation of air-to-air missiles under small sample conditions based on bayesian theory[J/OL]. Acta Armamentarii, 2026(2026-06-15). https://doi.org/10.12382/bgxb.2025.0824. (in Chinese) DOI：

摘要

导弹精度鉴定试验受成本限制，实弹射击样本量较小，导致经典统计方法估计精度偏低，且现有研究多局限于二维平面，难以满足武装直升机载空空导弹三维精度实战化考核评估的实际需求。为此，从三维位置误差分量独立同正态分布的一般性假设出发，提出一种基于贝叶斯理论的小样本空空导弹三维制导精度评估方法。首先定义反映空空导弹空间作战实际脱靶特性的三维脱靶量，并在理论上确认其统计分布模型的基础上，建立了三维脱靶量

与位置散布参数

的函数关系；然后选取逆伽马分布作为精度特征参数的共轭先验，通过融合先验信息与现场实弹脱靶量实测试验数据，求解导弹三维误差分量散布参数的后验分布，从而实现导弹三维制导精度的贝叶斯点估计与区间估计。实例验证结果表明，该方法能够显著提升制导精度估计结果的准确性与稳健性，为计算小样本条件下的直升机载空空导弹三维制导精度提供了参考依据。

Abstract

Missile accuracy qualification tests are often constrained by high costs

resulting in small sample sizes of live-fire tests and low estimation accuracy of classical statistical methods. Moreover

existing studies are mostly confined to two-dimensional plane analysis

which fails to meet the practical requirements of three-dimensional combat evaluation for helicopter-borne air-to-air missiles. To address this issue

based on the general assumption that the three-dimensional position error components are independent and identically normally distributed

a Bayesian method for evaluating the three-dimensional guidance accuracy of air-to-air missiles under small sample conditions is propose

d. First

the three-dimensional miss distance

which reflects the actual spatial miss characteristics in air-to-air combat

is defined

and its statistical distribution model is theoretically confirmed; on this basis

the functional relationship between the three-dimensional miss distance

and the position dispersion parameter

is established. Then

the inverse gamma distribution is selected as the conjugate prior for the accuracy characteristic parameters. By integrating prior information with field live-fire miss distance test data

the posterior distribution of the dispersion parameter is obtained

thereby achieving Bayesian point estimation and interval estimation of the three-dimensional guidance accuracyof missiles. The example verification results show that the proposed method significantly improves the accuracy and robustness of guidance accuracy estimation

providing a reference for calculating the three-dimensional guidance accuracy of helicopter-borne air-to-air missiles under small sample conditions.

关键词

Keywords

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