Three-Dimensional Guidance Accuracy Evaluation of Air-to-Air Missiles under Small Sample Conditions Based on Bayesian Theory

NING Xiao-lei

doi:10.12382/bgxb.2025.0824

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Three-Dimensional Guidance Accuracy Evaluation of Air-to-Air Missiles under Small Sample Conditions Based on Bayesian Theory

更新时间：2026-06-15

- Three-Dimensional Guidance Accuracy Evaluation of Air-to-Air Missiles under Small Sample Conditions Based on Bayesian Theory
- Acta Armamentarii (2026)
- 作者机构：
  
  部队，陕西华阴,714200
- 作者简介：
- 基金信息：
- DOI：10.12382/bgxb.2025.0824
  CLC： TJ760
- Received：08 September 2025，
  
  Online First：15 June 2026，
- 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

references

孙毓凯,孙斐,任宏光,等.直升机载空空导弹工程验证试验与鉴定技术研究[J]. 弹箭与制导学报, 2020, 40(3): 60-64.

SUN Y K, SUN F, REN H G, et al. Research on engineering verification test and evaluation technology of air-to-air missile for helicopter[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2020, 40(3): 60-64 .(in Chinese)

宁小磊,王晨辉,刘艳云,等.导弹武器三维射击精度小样本序贯概率比检验方法[J].中国惯性技术学报, 2026, 34(5): 521-530.

NING X L, WANG C H, LIU Y Y, et al. A small-sample sequential probability ratio test method for three-dimensional missile weapon firing accuracy[J]. Journal of Chinese Inertial Technology, 2026, 34(5): 521-530. (in Chinese).

豆建斌,王小兵,杨红坚,等. 成像制导导弹试验鉴定半实物仿真系统设计与应用[J]. 系统仿真学报, 2024, 36(2): 522-532.

DOU J B, WANG X B, YANG H J, et al. Design and application of Hardware-in-the-loop Simulation System for infrared imaging guide missile test and evaluation[J]. Journal of System Simulation, 2024, 36(2): 522-532. (in Chinese)

宋天莉, 安维廉, 王书宁. 三维射击精度的一阶逼近评估方法[J]. 宇航学报, 2007, 28(5): 1411-1414.

SONG T L, AN W L, WANG S N. First-order approximation evaluation method for three-dimensional firing accuracy[J]. Journal of Astronautics, 2007, 28(5): 1411-1414. (in Chinese)

宁小磊,曾伟,赵新,等.导弹对空射击精度的小子样球概率误差检验方法[J].中国惯性技术学报,2025,33(11): 1156-1166.

NING X L, ZENG W, ZHAO X, et al. Small-sample spherical probabilistic error test method for missile anti-air firing accuracy[J]. Journal of Chinese Inertial Technology, 2025, 33(11): 1156-1166. (in Chinese)

MIAO Y F, WANG G, TIAN W. A new method for evaluating the firing precision of multiple launch rocket system based on Bayesian theory[J]. Defence Technology, 2024, 32(2): 232-241.

TRZUN Z, VRDOLJAK M. Probability of hitting the target with an imperfectly manufactured projectile[J]. Proceedings in Applied Mathematics and Mechanics, 2021, 21(1): 321-334.

宁小磊, 吴颖霞, 赵新. 融合仿真数据的小子样圆概率误差评估[J]. 兵工学报, 2021, 42(2): 388-398.

NING X L, WU Y X, ZHAO X. Small Sample Circular Error Probable Estimation Based on Fusing Simulation and Flight Test Data[J]. Acta Armamentarii, 2021, 42(2): 388-398. (in Chinese)

井沛良, 段宇, 韩超, 等. 基于高斯混合模型和期望最大化算法的非高斯分布圆概率误差估计方法研究[J]. 兵工学报, 2019, 40(2): 369-376.

JING P L, DUAN Y, HAN C, et al. Circular error probable estimation method based on Gaussian mixture model and expectation maximum algorithm for non-Gaussian distribution[J]. Acta Armamentarii, 2019, 40(2): 369-376. (in Chinese)

杨华波, 张士峰.导弹命中精度的序贯截尾概率圆检验方法[J].国防科技大学学报, 2024, 46(2):62-69.

YANG H B, ZHANG S F. Sequential truncated probability circle test for hit accuracy of missile[J]. Journal of National University of Defense Technology, 2024, 46(2):62-69. (in Chinese)

李艳, 濮晓龙. 基于Koopman-Darmois分布族的序贯网图检验方法[J]. 中国科学, 2009, 39(5): 614-624.

LI Y, PU X L.Sequential network graph verification method based on Koopman-Darmois distribution family[J]. Science in China, 2009, 39(5): 614-624. (in Chinese)

闫章更, 濮晓龙.现代军事抽样检验方法及应用[M].北京:国防工业出版社, 2008.

YAN Z G, PU X L. Modern Military Sampling Inspection Methods and Their Applications[M]. Beijing: National Defense Industry Press, 2008. (in Chinese)

刘昊邦, 史宪铭, 屈金标, 等. 基于多项分布的导弹命中精度贝叶斯验收方案设计[J]. 北京航空航天大学学报, 2024, 50(6):1991-2000.

LIU H B, SHI X M, QU J B, et al. Design of Bayesian acceptance scheme for missile hit accuracy based on multinomial distribution[J]. Journal of Beijing University of Aeronautics and Astronautics, 2024, 50(6):1991-2000. (in Chinese)

王康, 史贤俊, 秦亮, 等. 基于Bayes小子样理论和序贯网图检验的武器装备测试性验证试验方案设计[J]. 兵工学报, 2019, 40(11): 2319-2328.

WANG K, SHI X J, QIN L, et al. Design of BSST-SMT-based weaponry testability verification test scheme[J]. Acta Armamentarii, 2019, 40(11): 2319-2328. (in Chinese)

刘昊邦, 史宪铭, 郝冰, 等. 基于多项分布的弹药多批次试验命中概率估计[J]. 兵工学报, 2023, 44(10): 3156-3164.

LIU H B, SHI X M, HAO B, et al. Estimation of ammunition hit probability in multiple-batch tests using multinomial distribution[J]. Acta Armamentarii, 2023, 44(10): 3156-3164. (in Chinese)

宁小磊, 吴颖霞, 赵新, 等.小样本概率关联度模型研究[J]. 西北工业大学学报, 2022, 40(5): 1164-1171.

NING X L, WU Y X, ZHAO X, et al. Research on small sample probability relational degree model[J]. Journal of Northwestern Polytechnical University, 2022, 40(5): 1164-1171. (in Chinese)

GUO J Y, LI Y F, PENG W W, et al. Bayesian information fusion method for reliability analysis with failure-time data and degradation data[J]. Quality and Reliability Engineering International, 2022, 38(4): 99-117.

PAPANANIAS M, MCLEAY T E, MAHFOUF M, et al. A Bayesian information fusion approach for end product quality estimation using machine learning and on-machine probing[J]. Journal of Manufacturing Processes, 2022, 76: 475-485.

李康, 史宪铭, 李广宁, 等. 基于正态-逆伽马分布的反巡航导弹命中概率估计方法[J]. 系统工程与电子技术, 2022, 44(8): 2621-2627.

LI K, SHI X M, LI G N, et al. Anti-cruise missile hit probability estimation method based on normal-inverse gamma distribution[J]. Systems Engineering and Electronics, 2022, 44(8):2621-2627. (in Chinese)

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.

LIU H B, SHI X M, ZHAO M, 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. (in Chinese)

宁小磊, 吴颖霞. 基于等效样本和实仿融合的现场小子样试验制导精度评估方法[J]. 中国惯性技术学报, 2021, 29(2): 264-272.

NING X L, WU Y X. Guidance accuracy evaluation method of field small sample test based on equivalent sample and real simulation fusion[J]. Journal of Chinese Inertial Technology, 2021, 29(2): 264-272. (in Chinese)

孙锦, 李国林, 许诚. 基于仿真信息的反舰导弹小子样靶场试验综合评定方法. 系统工程理论与实践, 2014, 34(4): 1077-1088

SUN J, LI G L, XU C. Synthetical evaluation method of anti-ship missile in range trial in condition of small sample based on simulation information[J]. Systems Engineering Theory & Practice, 2014, 34(4): 1077-1088 (in Chinese)

王亚龙, 史宪铭, 刘昭, 等.基于特小子样下弹药命中概率的贝叶斯改进算法[J]. 系统工程与电子技术, 2026, 48(4): 1322-1330.

WANG Y L, SHI X M, LIU Z, et al. Bayesian improved algorithm for estimating ammunition hit probability under ultra-small subsample[J]. Systems Engineering and Electronics, 2026, 48(4): 1322-1330.

宁小磊. 基于麦克斯韦-玻尔兹曼分布的空间脱靶量试验评估[J]. 兵工学报, 2026,47(5):250776.

NING X L. Test Evaluation of Spatial Miss Distance Based on Maxwell-Boltzmann Distribution[J]. Acta Armamentarii, 2026, 47(5): 250776.（in Chinese）

李树. 光子与相对论麦克斯韦分布电子散射截面的蒙特卡罗计算方法[J]. 物理学报, 2018, 67(21): 215201.

L S. Monte Carlo method for computing relativistic photon-Maxwellian electron scattering cross sections[J]. Acta Physica Sinica, 2018, 67(21): 215201. (in Chinese)

马妍,汪建均,冯泽彪.非正态响应稳健参数设计的贝叶斯建模与优化[J]. 系统工程与电子技术, 2023, 45(3): 921-930.

MA Y, WANG J J, FENG Z B. Bayesian modeling and optimization of robust parametric design with non-normal response[J]. Systems Engineering and Electronics, 2023, 45(3): 921-930. (in Chinese)

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China Huayin Ordnance Test Center，Huayin

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