Article Details

Abstract

To address the issue that random noise components in GNSS vertical time series are complex and tend to mask low-frequency deformation signals, this study proposes an adaptive two-stage denoising method based on SVMD-FE-SGGT. This method first employs Successive Variational Mode Decomposition (SVMD) to decompose the noisy sequence into several Intrinsic Mode Functions (IMFs). Subsequently, the Fuzzy Entropy (FE) of each IMF is calculated, and the IMFs are classified into three categories. For the noise-containing components, an improved wavelet threshold function is applied for secondary denoising to reduce the constant bias inherent in traditional soft thresholding and enhance detail fidelity. Finally, the denoised noise-containing components are reconstructed with the signal-dominant IMFs to obtain a cleaned sequence, with the noise-dominant components removed. The denoising performance of several methods is analyzed using both simulated and measured data. On the measured data, the proposed method achieves a signal-to-noise ratio of 85.52 dB, a Root Mean Square Error of 0.79, and a correlation coefficient of 0.963. Compared to the WST method, the SNR and correlation coefficient are improved by 10.2% and 6.3%, respectively, and the RMSE is reduced by 21%. Experimental results demonstrate that the proposed method can effectively suppress noise while preserving the GNSS vertical deformation trend with acceptable computational cost. This method provides a reliable technical solution for the preprocessing of mining area subsidence monitoring data.

Keywords

signal denoising; SVMD; improved wavelet soft threshold; GNSS sequence denoising

References

1. [1] Lu Tieding, Tao Rui, Cheng Yuanming, etc Optimization of Adaptive GNSS Elevation Time Series Denoising Method for EWT-NLM [J]. Geodesy and Geodynamics, 2022, 42 (5): 451-456
2. [2] Huan Yueyang, Chang Guobin, Feng Yong Selection of GNSS coordinate time series noise model considering suboptimal noise model [J]. Chinese Journal of Geophysics, 2023, 66 (10): 4045-4056
3. [3] Wei Jialin, Yin Min, Wang Shitai, etc GNSS time series denoising method combining Hilbert transform and VMD [J]. Journal of Navigation and Positioning, 2025, 13 (5): 155-164
4. [4] Zhou Jinqun, Hu Zhonghua, Sun Xiaojie Research on Improving Wavelet Threshold Algorithm in Signal Processing [J]. Intelligent Computers and Applications, 2025, 15 (2): 91-95
5. [5] Wang Chunhua, Wang Fangchao SAR image wavelet denoising method based on improved threshold function [J]. Microelectronics and Computer, 2022, 39 (5): 39-44
6. [6] Gu Xuan, Zhang Wei Optimization of VMD and improvement of wavelet threshold for ECG electromyographic interference denoising algorithm [J]. Computer Applications and Software, 2025, 42 (11): 277-284
7. [7] Torres M E，Colominas M A，Schlotthauer G，et al. A complete ensemble empirical mode decomposition with adaptive noise [C]//IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)，2011：4144-4147.
8. [8] Yang Bing, Yang Zhiqiang, Tian Zhen, etc GNSS coordinate time series denoising analysis using joint EMD-HD and wavelet decomposition [J]. Journal of Surveying and Mapping, 2022, 51 (9): 1881-1889
9. [9] Liang Pei, Yang Zhiqiang, Yang Bing, etc CEEMD denoising method considering seasonal signals in GNSS coordinate time series [J]. Geodesy and Geodynamics, 2022, 42 (10): 1010-1014
10. [10] Yu Hongxu, Wen Hanjiang, Liu Huanling, etc GNSS elevation time series denoising method based on CEEMDAN and wavelet packet multi threshold [J]. Geodesy and Geodynamics, 2022, 42 (10): 1005-1009
11. [11] Zheng Canguang, Zheng Hui, Xie Shicheng, etc GNSS vertical time series denoising method for mining subsidence monitoring [J]. Global Positioning System, 2024, 49 (3): 28-37
12. [12] Luo Yiyong, Huang Cheng, Zhang Jingying A denoising method for deformation monitoring data based on variational mode decomposition [J]. Journal of Wuhan University (Information Science Edition), 2020, 45 (5): 784-790
13. [13] Nazari M，Sakhaei S M. Successive variational mode decomposition [J/OL].Signal Processing， 2020，174，107610（2020-05-17）.https://doi.org/10.1016/j.sigpro.2020.107610.
14. [14] Gao S Z，Li T C，Zhang Y M，et al. Fault diagnosis method of rolling bearings based on adaptive modified CEEMD and 1DCNN model [J].ISA transactions，2023，140：309-330.
15. [15] Zhou Botao, Peng Hao, Lu Hailin, etc Application of CEEMDAN Improved Wavelet Threshold Joint Denoising Algorithm in Surface Settlement Prediction [J]. Journal of Wuhan University of Engineering, 2025, 47 (4): 455-460

About the authors

Wang Renyi (1997-), male, Han ethnicity, from Hefei, Anhui Province, teacher, master's student, research direction: 3S technology.