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

doi:10.3969/j.issn.1000-1093.2019.02.017

兵工学报 ›› 2019, Vol. 40 ›› Issue (2): 369-376.doi: 10.3969/j.issn.1000-1093.2019.02.017

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

井沛良¹，段宇²，韩超¹，郭荣化¹，宁小磊¹，刘瑜³

（1.中国华阴兵器试验中心，陕西华阴 714200； 2.空军军医大学，陕西西安 714299； 3.海军航空大学，山东烟台 264001）

收稿日期:2018-04-27 修回日期:2018-04-27 上线日期:2019-04-08
作者简介:井沛良（1987—），男，工程师。E-mail：jingpeiliang@nudt.edu.cn

Circular Error Probable Estimation Method Based on Gaussian Mixture Model and Expectation Maximum Algorithm for Non-GaussianDistribution

JING Peiliang¹， DUAN Yu²， HAN Chao¹， GUO Ronghua¹， NING Xiaolei¹， LIU Yu³

(1.Huayin Ordnance Test Center， Huayin 714200， Shaanxi， China； 2.The Fourth Military Medical University， Xi'an 714299， Shaanxi， China； 3.Naval Aviation University， Yantai 264001， Shandong， China)

Received:2018-04-27 Revised:2018-04-27 Online:2019-04-08

摘要/Abstract

摘要： 传统圆概率误差（CEP）估计方法无法处理兵器攻击点/观测点数据服从非高斯分布的情况。为了解决这一问题，提出了一种基于高斯混合模型（GMM）和期望最大化（EM）算法的CEP估计新方法。该方法利用 GMM对兵器攻击点/观测点非高斯分布概率密度函数（PDF）进行建模，通过EM算法迭代估计GMM参数得到兵器攻击点/观测点PDF，并依据所得到的兵器攻击点/观测点PDF，使用二分法得到兵器攻击点/观测点的CEP指标值。采用大量非高斯分布场景生成兵器攻击点/观测点数据，应用所提方法和传统方法进行CEP估计实验。实验结果表明：所提方法估计的CEP均方误差约为传统方法的1/10，由此说明所提方法性能显著好于传统方法，可以有效解决兵器攻击点/观测点数据服从非高斯分布时的CEP估计问题。

关键词: 圆概率误差, 非高斯分布, 高斯混合模型, 期望最大化算法

Abstract: For the situation when the ordnance attacking and/or observing points do not obey the Gaussian distribution, the traditional circular error probability (CEP) computation method could not effectively deal with the experimental data. In order to resolve this problem, one new CEP estimation method based on Gaussian mixture model (GMM) and expectation maximum (EM) algorithm is proposed. In the proposed method, GMM is used to depict the ordnance attacking and/or observing points probability density function（PDF）, the EM algorithm is used to solve the model parameters, and the bisection method is used to compute CEP. A lot of scenes are used to generate the ordnance attacking and/or observing points, and the traditional method and the proposed method are used to estimate the CEP. Experimental results show that the mean square error of CEP computed by the proposed method is about 1/10 of that computed by the traditional method. This illustrates that the performance of the proposed method is better than that of the traditional method. The proposed method could be used effectively to estimate CEP when the ordnance attacking and/or observing points do not obey the Gaussian distribution. Key

Key words: circularerrorprobability, non-Gaussiandistribution, Gaussianmixturemodel, expectationmaximumalgorithm

中图分类号:

E920.8

井沛良，段宇，韩超，郭荣化，宁小磊，刘瑜. 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 Peiliang， DUAN Yu， HAN Chao， GUO Ronghua， NING Xiaolei， LIU Yu. Circular Error Probable Estimation Method Based on Gaussian Mixture Model and Expectation Maximum Algorithm for Non-GaussianDistribution[J]. Acta Armamentarii, 2019, 40(2): 369-376.

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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

Circular Error Probable Estimation Method Based on Gaussian Mixture Model and Expectation Maximum Algorithm for Non-GaussianDistribution

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