基于多批次增长试验的舰空导弹命中概率贝叶斯估计

doi:10.12305/j.issn.1001-506X.2025.03.19

Abstract

Abstract:

The existing ship-to-air missile hit probability estimation methods are mainly studied from the perspective of single batch tests, but fail to consider the characteristics of multiple batches growth tests, which makes it difficult to accurately estimate the hit probability. In this paper, the two-dimensional normal projectile dispersion phenomenon of ship-to-air missile is taken as the entry point, the normal-inverse Gamma distribution is selected as the prior distribution of projectile dispersion parameters based on Bayesian method, and the prior information is merged to make up for the insufficient data in the small sample tests. The sequential constraint relationship is established between the projectile dispersion parameter values of each batch of tests, and the Markov chain-Monte Carlo (MCMC) method is combined with Gibbs sampling for Bayesian solution, so as to achieve the purpose of fusing multiple batches growth tests information. The research results show that this method can consider the characteristics of multiple batches growth tests compared with the existing single batch tests hit probability estimation method, and provide reference for ship-to-air missile hit probability estimation.

Key words: ship-to-air missile, hit probability, multiple batches growth tests, projectile dispersion, Bayesian, Markov chain-Monte Carlo (MCMC)

CLC Number:

E917

Haobang LIU, Tong CHEN, Tao HU, Minggui LI, Kai DU. Bayesian estimation of ship-to-air missile hit probability based on multiple batches growth tests[J]. Systems Engineering and Electronics, 2025, 47(3): 871-882.

Figures/Tables 11

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试验批次	舰空导弹射弹散布外场发射试验数据	舰空导弹射弹散布先验信息数据
	(y_i, z_i)	h(u_yj, σ_yj²)	h(u_zj, σ_zj²)
	(y_i, z_i)	N(u_y0, σ_y²/k_y0)· IGa(v_y0/2, v_y0σ_y0²/2)	N(u_z0, σ_z²/k_z0)· IGa(v_z0/2, v_z0σ_z0²/2)
初始批次试验	(8.869, 7.447), (6.338, 4.557), (8.377, 8.556) (10.155, 8.134), (8.773, 7.334), (4.508, 5.667) (8.446, 7.421), (9.883, 6.233), (7.722, 4.584) (9.362, 5.663)	N(8.488, σ_y²/2.135)· IGa(12.247, 40.414)	N(6.363, σ_z²/2.073)· IGa(9.078, 21.812)
第2批次试验	(4.776, 3.586), (6.527, 4.832), (5.324, 4.432) (4.337, 5.253), (3.882, 3.237), (4.118, 5.229) (7.553, 3.793), (5.753, 2.507), (7.133, 1.891) (5.975, 2.736)	N(5.915, σ_y²/1.783)· IGa(8.523, 17.284)	N(3.938, σ_z²/1.926)· IGa(7.883, 13.971)
第3批次试验	(2.569, 2.667), (2.477, 1.556), (3.435, 1.137) (4.932, 3.016), (1.893, 2.669), (2.223, 2.891) (2.464, 1.667), (2.662, 2.349), (3.255, 0.951) (1.875, 1.533)	N(2.753, σ_y²/1.385)· IGa(4.444, 3.548)	N(1.917, σ_z²/1.471)· IGa(4.381, 2.965)

参数	样本数	均值	方差	蒙特卡罗误差	置信区间下限2.5%	中位数	置信区间上限97.5%
u_y1	3 000	8.324	1.763	3.125E-4	5.825	8.346	10.866
σ_y1²	3 000	3.567	1.232	2.306E-4	2.084	3.396	6.155
u_z1	3 000	6.453	1.288	2.663E-4	4.126	6.404	8.631
σ_z1²	3 000	2.663	1.017	2.137E-4	1.643	2.548	5.284
u_y2	3 000	5.783	1.256	2.442E-4	3.675	5.698	8.012
σ_y2²	3 000	2.216	0.812	1.885E-4	0.963	2.032	4.086
u_z2	3 000	3.887	1.013	2.255E-4	2.056	3.882	5.892
σ_z2²	3 000	1.974	0.663	1.866E-4	0.843	1.906	4.175
u_y3	3 000	2.768	0.746	1.623E-4	1.276	2.811	4.453
σ_y3²	3 000	1.027	0.434	1.114E-4	0.127	0.985	2.336
u_z3	3 000	1.973	0.588	1.339E-4	0.878	1.986	3.240
σ_z3²	3 000	0.864	0.323	1.003E-4	0.086	0.873	2.255

参数	样本数	均值	方差	蒙特卡罗误差	置信区间下限2.5%	中位数	置信区间上限97.5%
u_y	3 000	2.953	0.833	1.771E-4	1.355	2.887	4.558
σ_y²	3 000	1.066	0.448	1.157E-4	0.132	0.992	2.388
u_z	3 000	2.008	0.672	1.557E-4	0.922	2.018	3.378
σ_z²	3 000	0.897	0.374	1.083E-4	0.086	0.912	2.305

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Bayesian estimation of ship-to-air missile hit probability based on multiple batches growth tests

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