基于高斯混合模型的光纤罗经误差概率分布建模

doi:10.12305/j.issn.1001-506X.2021.06.22

摘要/Abstract

摘要：

针对船用光纤罗经误差的概率分布不完全符合高斯分布的情况, 提出了一种基于高斯混合模型(Gaussian mixture model, GMM)的光纤罗经误差概率分布函数(probability distribution function, PDF)建模方法。该方法使用多个高斯分布的线性叠加来拟合光纤罗经误差的概率分布, 并结合一种鲁棒性的期望最大化(expectation maximization, EM)算法来估计GMM中的参数。仿真分析和实测数据验证, 相比于使用单一的高斯分布, 基于所提方法建立的光纤罗经误差概率分布更加符合该导航设备误差的实际概率分布。

关键词: 高斯混合模型, 期望最大化, 光纤罗经, 概率分布函数

Abstract:

Aiming at the situation that the probability distribution of the fiber-optical gyrocompass error does not conform to the Gaussian distribution, a modeling method of the fiber-optical gyrocompass error probability distribution function (PDF) based on the Gaussian mixture models (GMM) is proposed. The method uses linear superposition of the multiple Gaussian distributions to fit the probability distribution of fiber-optical gyrocompass errors, and combines a robust expectation maximization (EM) algorithm to estimate the parameters in the GMM. Through simulation analysis and verification of the test data, compared with using a single Gaussian distribution, the error probability distribution based on the proposed method is more consistent with the actual probability distribution of the navigation equipment error.

Key words: Gaussian mixture model (GMM), expectation maximization (EM), fiber-optic gyrocompass, probability distribution function (PDF)

中图分类号:

U666.1

胡耀金, 卞鸿巍, 王荣颖, 马恒. 基于高斯混合模型的光纤罗经误差概率分布建模[J]. 系统工程与电子技术, 2021, 43(6): 1644-1650.

Yaojin HU, Hongwei BIAN, Rongying WANG, Heng MA. Modeling of error probability distribution of fiber-optic gyrocompass based on Gaussian mixture model[J]. Systems Engineering and Electronics, 2021, 43(6): 1644-1650.

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类型	参数取值
类型	α	μ	σ
真实参数	0.20	-5.00	1.50
	0.15	13.00	5.00
	0.65	0.00	2.00
传统EM算法	0.16	-3.40	1.78
	0.35	12.90	5.18
	0.49	-0.14	2.22
Robust-EM算法	0.17	-5.10	1.37
	0.15	13.30	4.73
	0.68	-0.14	2.03

设备序号	1	2	3	4
RMSE	0.047 039	0.074 171	0.080 862	0.072 617

分模型序号	参数取值
分模型序号	α	μ	σ
1	0.088 14	-1.873 34	0.172 44
2	0.103 62	2.079 27	0.186 38
3	0.115 63	1.431 74	0.417 17
4	0.345 86	0.126 94	0.389 07
5	0.346 75	-1.097 89	0.243 74

分模型序号	参数取值
分模型序号	α	μ	σ
1	0.057 65	0.970 74	0.123 22
2	0.073 24	-3.270 37	0.167 04
3	0.217 99	0.292 09	0.196 89
4	0.299 22	-0.112 53	0.472 97
5	0.351 91	-1.771 78	0.632 93

分模型序号	参数取值
分模型序号	α	μ	σ
1	0.035 16	0.460 58	0.095 89
2	0.181 49	1.212 21	0.668 04
3	0.170 72	-1.692 60	0.266 11
4	0.171 56	-0.715 14	0.221 72
5	0.441 07	-0.337 65	0.435 60