Bayesian estimation of missile hit accuracy for Dirichlet distribution based on multiple stages growth tests

doi:10.23919/JSEE.2026.000137

Abstract

Abstract:

The missiles typically require multiple stages tests to improve hit accuracy. The existing estimation methods seldom consider the tests characteristics of multiple stages growth of missile hit accuracy, which bring difficulties to accurately estimate the missile hit accuracy. Considering the different degrees of damage caused by missile hitting the target in different areas, the Dirichlet distribution is selected as the prior distribution of hit accuracy parameters based on the Bayesian method. The sequence constraint relationship between the hit accuracy parameters of each stage test is established, and the Bayesian estimation model of hit accuracy based on multiple stages growth tests is constructed. The Markov chain-Monte Carlo method combined with Gibbs sampling is used to overcome the problem of solving the posterior high-dimensional integral of the model to complete the model solution. The example shows that this method can fuse multiple stages growth tests information compared with the existing single stage test method, which can provide reference for the estimation of missile hit accuracy during the period of research and development.

Key words: missile hit accuracy, multiple stages growth test, Bayesian estimation, Dirichlet distribution, Markov chain-Monte Carlo

Haobang Liu, Xianming Shi, Tao Hu, Tong Chen. Bayesian estimation of missile hit accuracy for Dirichlet distribution based on multiple stages growth tests[J]. Journal of Systems Engineering and Electronics, 2026, 37(4): 1325-1340.

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Stage	Hit result information of the missile outfield firing test	Prior information of missile hit accuracy
Initial stage test	$ (5,4,4,2) $	$ (6.8,5.7,5.3,3.6) $
The second stage test	$ (3,4,5,3) $	$ (5.3,5.8,6.3,4.8) $
The third stage test	$ (2,3,6,4) $	$ (2.5,3.4,6.6,5.2) $

Node	Sample	Mean	sd	MC error	2.5%	Median	97.5%
$ {\theta }_{11} $	1500	0.3255	0.2763	5.125E-4	0.0165	0.2846	0.8367
$ {{{\theta }^{\prime}}}_{11} $	1500	0.3242	0.2735	4.993E-4	0.0158	0.2792	0.8355
$ {\theta }_{21} $	1500	0.2673	0.2322	4.522E-4	0.0142	0.2306	0.7523
$ {{{\theta }^{\prime}}}_{21} $	1500	0.2665	0.2311	4.355E-4	0.0134	0.2292	0.7388
$ {\theta }_{31} $	1500	0.2534	0.2288	4.497E-4	0.0137	0.2115	0.7212
$ {{{\theta }^{\prime}}}_{31} $	1500	0.2555	0.2283	4.513E-4	0.0129	0.2120	0.7183
$ {\theta }_{41} $	1500	0.1568	0.1517	3.143E-4	0.0043	0.1312	0.4784
$ {{{\theta }^{\prime}}}_{41} $	1500	0.1538	0.1504	3.097E-4	0.0048	0.1317	0.4811
$ {\theta }_{12} $	1500	0.2107	0.1756	3.873E-4	0.0058	0.1723	0.6032
$ {{{\theta }^{\prime}}}_{12} $	1500	0.2231	0.2088	4.308E-4	0.0076	0.1818	0.6723
$ {\theta }_{22} $	1500	0.2446	0.1559	3.327E-4	0.0333	0.2172	0.5788
$ {{{\theta }^{\prime}}}_{22} $	1500	0.2634	0.1928	2.663E-4	4.126	6.504	8.231
$ {\theta }_{32} $	1500	0.2812	0.1477	3.255E-4	0.0596	0.2523	0.6315
$ {{{\theta }^{\prime}}}_{32} $	1500	0.3038	0.2685	4.736E-4	0.0148	0.2714	0.7755
$ {\theta }_{42} $	1500	0.2635	0.2363	4.178E-4	0.0055	0.2116	0.7272
$ {{{\theta }^{\prime}}}_{42} $	1500	0.2097	0.1915	3.377E-4	0.0068	0.1723	0.6258
$ {\theta }_{13} $	1500	0.1264	0.0936	2.643E-4	0.0071	0.0983	0.3783
$ {{{\theta }^{\prime}}}_{13} $	1500	0.1364	0.1327	2.652E-4	0.0045	0.1173	0.4194
$ {\theta }_{23} $	1500	0.1639	0.0877	2.174E-4	0.0277	0.1687	0.3613
$ {{{\theta }^{\prime}}}_{23} $	1500	0.1939	0.1883	3.005E-4	0.0065	0.1622	0.5993
$ {\theta }_{33} $	1500	0.3518	0.1618	4.339E-4	0.0962	0.3407	0.6862
$ {{{\theta }^{\prime}}}_{33} $	1500	0.3818	0.3035	5.232E-4	0.0453	0.3565	0.8713
$ {\theta }_{43} $	1500	0.3579	0.2922	5.523E-4	0.0136	0.3243	0.8815
$ {{{\theta }^{\prime}}}_{43} $	1500	0.2879	0.2473	4.532E-4	0.0279	0.2312	0.7627

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