参数优化变分模态分解的GNSS坐标时间序列降噪方法

鲁铁定; 何锦亮; 贺小星; 陶蕊

doi:10.13203/j.whugis20220363

参数优化变分模态分解的GNSS坐标时间序列降噪方法

鲁铁定^{1, 2,},
何锦亮^1, ,,
贺小星³,
陶蕊¹

1.
东华理工大学测绘与空间信息工程学院,江西南昌,330013
2.
自然资源部环鄱阳湖区域矿山环境监测与治理重点实验室,江西南昌,330013
3.
江西理工大学土木与测绘工程学院,江西赣州,341000

基金项目:

国家自然科学基金 42061077

国家自然科学基金 42374040

国家自然科学基金 42064001

国家自然科学基金 42104023

江西省自然科学基金 20202BABL213033

江西省自然科学基金 20202BAB212010

2022年度中国科协科技智库青年人才计划

详细信息

作者简介:
鲁铁定,博士,教授,主要从事测绘数据处理研究。tdlu@whu.edu.cn

通讯作者:
何锦亮,硕士。hejjlxin@163.com

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出版历程
- 收稿日期: 2022-10-24
- 网络出版日期: 2023-04-12
- 刊出日期: 2024-10-04

GNSS Coordinate Time Series Denoising Method Based on Parameter-Optimized Variational Mode Decomposition

LU Tieding^{1, 2,},
HE Jinliang^1, ,,
HE Xiaoxing³,
TAO Rui¹

1.
School of Surveying and Geoinformation Engineering, East China University of Technology, Nanchang330013, China
2.
Key Laboratory of Mine Environmental Monitoring and Improving Around Poyang Lake, Ministry of Natural Resources,Nanchang330013, China
3.
School of Civil and Surveying and Mapping Engineering, Jiangxi University of Science and Technology, Ganzhou341000, China

摘要

摘要:
针对全球导航卫星系统（global navigation satellite system,GNSS）坐标时间序列中噪声成分难以有效滤除的问题,构建一种基于参数优化变分模态分解（variational mode decomposition,VMD）的降噪方法。该方法首先以排列熵结合互信息为适应度函数,利用灰狼优化（grey wolf optimization,GWO）算法自适应获取VMD的模态分解个数 $K$ 和二次惩罚因子 $α$ 的最优参数组合；然后将GNSS坐标时间序列分解为 $K$ 个本征模态函数分量,并利用样本熵确定有效模态分量,将其重构为有效信号,从而实现信号与噪声的有效分离；最后,利用仿真信号和中国地壳运动观测网络的20个基准站的实测数据进行实验,将GWO-VMD方法与经验模态分解、小波降噪和基于VMD的降噪方法进行对比分析。结果表明,GWO-VMD方法能够更为有效地去除GNSS坐标时间序列中的噪声,且能较好地保留信号的原始特征,为后续的分析处理提供可靠数据。
- GNSS坐标时间序列 /
- VMD /
- GWO /
- 排列熵 /
- 互信息 /
- 样本熵 /
- 信号降噪
Abstract:
Objectives
In order to effectively filter out complex noise components in GNSS coordinate time series and extract effective signals, we construct a denoising method based on parameter-optimized variational modal decomposition (VMD).
Methods
First, the combination of permutation entropy and mutual information is used as fitness function, and the optimal parameter combination of the mode decomposition number $K$ and the quadratic penalty factor $α$ of VMD is obtained by using grey wolf optimization algorithm(GWO). Then the GNSS coordinate time series is decomposed into $K$ eigen mode function components by VMD. Finally, the sample entropy is used to determine the effective modal component, which is reconstructed as an effective signal, so as to realize the effective separation of signal and noise.The GWO-VMD method is compared and analyzed with the empirical mode decomposition (EMD), wavelet denoising (WD) and IVMD methods by using the simulated signal and the measured data from 20 reference stations of the crustal movement observation network of China for experiments.
Results
The simulated signal experiments show that the three denoising evaluation indexes of root mean square error,correlation coefficient and signal-to-noise ratio of GWO-VMD denoising signal are better than EMD, WD and IVMD methods. The experiments on the measured data show that the GWO-VMD method can reduce the amplitude of noise significantly. In terms of the velocity uncertainty of the reference station, the overall GWO-VMD method reduces the velocity uncertainty better than the EMD, WD and IVMD methods.
Conclusions
The GWO-VMD method can more effectively remove the noise from GNSS coordinate time series and better preserve the original characteristics of the signal, which can provide reliable data for subsequent analysis and processing.
- GNSS coordinate time series /
- VMD /
- GWO /
- permutation entropy /
- mutual information /
- sample entropy /
- signal denoising
http://ch.whu.edu.cn/cn/article/doi/10.13203/j.whugis20220363

HTML全文

http://ch.whu.edu.cn/cn/article/doi/10.13203/j.whugis20220363

图 1 GWO-VMD降噪流程

Figure 1. Denoising Process of GWO-VMD

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图 2 仿真信号Ⅰ及其各分量波形

Figure 2. Waveforms of Simulated Signal Ⅰ and Its Components

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图 3 适应度值的收敛图

Figure 3. Convergence Diagram of Fitness Values

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图 4 仿真信号Ⅰ 4种方法的信号分解图

Figure 4. Signal Decomposition Diagrams of Four Methods for Simulated Signal Ⅰ

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图 5 仿真信号Ⅱ的波形

Figure 5. Waveform of Simulated Signal Ⅱ

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图 6 仿真信号Ⅱ 4种方法的降噪效果

Figure 6. Denoising Effect of Four Methods for Simulated Signal Ⅱ

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图 7 20个基准站的数据缺失情况

Figure 7. Missing Data from 20 Reference Stations

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图 8 20个基准站E、N、U方向的最优参数

Figure 8. Optimal Parameters of 20 Reference Stations in Directions E, N and U

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图 9 BJFS站坐标时间序列4种方法的降噪效果

Figure 9. Denoising Effect of 4 Methods for BJFS Station Coordinate Time Series

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图 10 降噪前及4种方法降噪后的基准站速度不确定度

Figure 10. Velocity Uncertainty of the Reference Station Before and After Denoising by Four Methods

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表 1 GWO-VMD分解后各IMF的样本熵

Table 1 Sample Entropy of Each IMF After GMO-VMD Decomposition

信号分量	IMF1	IMF2	IMF3	IMF4	IMF5	IMF6	IMF7	IMF8	IMF9	IMF10
样本熵	0.105 9	0.320 2	0.470 5	0.610 8	0.601 3	0.562 2	0.656 8	0.579 9	0.640 2	0.637 2

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表 2 仿真信号Ⅰ 4种方法的降噪评价指标

Table 2 Denoising Evaluation Indexes of the Four Methods for Simulated Signal Ⅰ

降噪方法	RMSE/mm	$相关系数$	SNR/dB
原始信号	1.40	0.953 3	9.87
EMD	0.91	0.979 3	13.86
WD	0.73	0.986 6	15.73
IVMD	0.48	0.994 2	19.27
GWO-VMD	0.46	0.994 8	19.74

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表 3 仿真信号Ⅱ 4种方法的降噪评价指标

Table 3 Denoising Evaluation Indexes of the Four Methods for Simulated Signal Ⅱ

降噪方法	RMSE/mm	相关系数	SNR/dB
原始信号	2.06	0.895 1	12.78
EMD	1.31	0.953 8	16.80
WD	0.48	0.993 6	25.39
IVMD	0.50	0.992 5	24.99
GWO-VMD	0.42	0.994 8	26.53

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表 4 20个基准站E、N、U分量的最优噪声模型

Table 4 The Optimal Noise Model for E, N, U Components of 20 Reference Stations

测站	最优噪声模型			测站	最优噪声模型
测站	E	N	U	测站	E	N	U
BJFS	WN+FN+RWN	WN+FN+RWN	WN+FN	SUIY	WN+FN+RWN	WN+FN+RWN	WN+FN
BJSH	WN+FN+RWN	WN+FN	WN+PL	TAIN	WN+FN	WN+FN	WN+PL
CHUN	WN+FN+RWN	WN+FN	WN+FN	URUM	WN+FN+RWN	WN+FN+RWN	WN+FN
DLHA	WN+FN+RWN	WN+FN+RWN	WN+FN	WUHN	WN+FN+RWN	WN+FN	WN+FN+RWN
GUAN	WN+FN+RWN	WN+FN	WN+FN	WUSH	WN+FN	WN+FN	WN+FN
HRBN	WN+FN+RWN	WN+FN	WN+FN	XIAG	WN+PL	WN+PL	WN+FN
JIXN	WN+FN+RWN	WN+FN+RWN	WN+FN	XIAM	WN+FN+RWN	WN+FN+RWN	WN+FN
KMIN	WN+FN+RWN	WN+FN+RWN	WN+FN	XNIN	WN+FN+RWN	WN+FN+RWN	WN+FN
LUZH	WN+FN+RWN	WN+FN	WN+FN	YANC	WN+FN	WN+FN	WN+FN
QION	WN+FN	WN+FN	WN+FN	ZHNZ	WN+FN+RWN	WN+FN	WN+FN

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表 5 E、N、U方向主要噪声模型下的噪声振幅均值

Table 5 The Mean Value of Noise Amplitude Under the Main Noise Models in E, N and U Directions

方向	噪声模型	原始数据	噪声振幅均值
方向	噪声模型	原始数据	EMD	WD	IVMD	GWO-VMD
E	WN+FN+RWN	0.76+3.46+2.72	0.00+0.00+2.78	0.00+0.00+1.78	0.00 +0.00+1.40	0.00+0.00+0.82
N	WN+FN	0.72+3.70	0.00+1.23	0.00+1.01	0.00+0.93	0.00+0.68
N	WN+FN+RWN	0.67+3.04+3.08	0.00+0.00+3.91	0.00+0.00+2.18	0.00+0.00+1.53	0.00+0.00+1.20
U	WN+FN	2.62+14.10	0.00+4.11	0.00+2.88	0.00+2.98	0.00+2.21
注：WN、FN和RWN的单位分别为 $m m$ 、 $m m / a^{0.25}$ 和 $m m / a^{0.5}$ 。

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表 6 20个基准站的速度不确定度的平均改正率/%

Table 6 Average Correction Rate of Velocity Uncertainty of 20 Reference Stations/%

方向	平均改正率
方向	EMD	WD	IVMD	GWO-VMD
E	15.6	50.3	55.8	71.4
N	29.0	58.0	66.4	72.8
U	68.4	79.2	76.8	83.3

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