Archives
 
Year 2026
 
Vol 67, Issue 3, [06 - 2026]

Application of Wavelet Filtering for continuous GNSS signals and comparison with Kalman Filtering

DOI:10.46326/JMES.2026.67(3).09

  • Affiliations:

    Hanoi University of Mining and Geology, Hanoi, Vietnam

  • *Corresponding:
    This email address is being protected from spambots. You need JavaScript enabled to view it.
  • Received: 17th-Dec-2025
  • Revised: 1st-Apr-2026
  • Accepted: 21st-Apr-2026
  • Online: 1st-June-2026
Pages: 107 - 115
Views: 32
View onlineView online
Downloads: 1
Downdload PDF
★★★★★Rating: , Total rating: 0
  • ★
  • ★
  • ★
  • ★
  • ★
Yours rating

Abstract:

Wavelet filtering is now effectively applied in many fields such as denoising audio signals, medical signals, GNSS; filtering and analyzing biological signals… thanks to its ability to separate noise, preserve signal characteristics, and handle both time and frequency domains well. In this study, we investigate Wavelet filtering for continuous GNSS data (ENH coordinate series) collected in Vietnam, with the aim of reducing GNSS signal noise to improve the accuracy of continuous GNSS measurements for monitoring structural displacement. The filtering results using Daubechies-4 Wavelet (db4) show that this method can be fully utilized for GNSS data filtering. Accuracy indicators such as standard deviation, root mean square error, and mean absolute error decreased by a maximum of 12.58% and a minimum of 1.07%. Compared to Kalman filtering in terms of noise reduction and stability of the filtered data series, Wavelet-db4 is more effective in smoothing signals after filtering but less effective than Kalman filtering in prediction capability. Specifically, the standard deviation of Wavelet-db4 is 9.9% lower, and the root mean square error is 9.5% lower than Kalman filtering; mean absolute error is similar, while data dispersion after filtering is 3.4% lower with Kalman. Therefore, to achieve better results when filtering continuous GNSS data, the two filtering methods can be combined.

How to Cite
Pham, K.Quoc 2026. Application of Wavelet Filtering for continuous GNSS signals and comparison with Kalman Filtering (in Vietnamese). Journal of Mining and Earth Sciences. 67, 3 (Jun, 2026), 107-115. DOI:https://doi.org/10.46326/JMES.2026.67(3).09.
References

Barthelmes, F., Ballani, L., Klees, R. (1994). On the application of wavelets in geodesy. IAG Symposia, 114, 394–403.

Davide A. Cucci Lionel Voirol Gael Kermarrec Jean-Philippe Montillet Stephane Guerrie  (2023). GMWMX for GNSS time series. Journal of Geodesy, 97(14). (Article 14)

Dương, N. H., Nguyễn, M. T., Nguyễn, T. L., Nguyễn, T. H., and Nguyễn, T. D. (2024). Ứng dụng kết hợp lọc Wavelet tiền xử lý dữ liệu cho mạng GCN LSTM. TNU Journal of Science and Technology – Đại học Thái Nguyên, 229(6). Truy cập từ http://jst.tnu.edu.vn.

Dương, Q. C. T., Nguyễn, H. H., Trương, Đ. A. K., and Hứa, G. K. (2024). Nghiên cứu áp dụng Continuous Wavelet Transform kết hợp thuật toán Marquardt. Tạp chí Khoa học Đại học Cần Thơ, 60(2), 65–74. https://doi.org/10.22144/ctujos.2024.266.

Ghaderpour, E., Ince, E.S.,  Pagiatakis, S.D., (2018). Least-squares wavelet analysis and its applications in geodesy and geophysics. Journal of Geodesy, 92, 1223–1236. https://doi.org/10.1007/s00190-018-1156-9.

Keller, W. (2004). Wavelets in geodesy and geodynamics. De Gruyter.

Kumar, P., and Foufoula-Georgiou, E. (1997). Wavelet analysis for geophysical applications. Reviews of Geophysics, 35(4),

385–412. https://doi.org/10.1029/97RG00427.

Li, D., Zhang, P., Zhao, J., Cheng, J., and Zhao, H. (2019). MP mitigation in GNSS positioning by GRU NNs and adaptive wavelet filtering. IET Communications, 13(17), 2756–2766. https://doi.org/10.1049/iet-com.2018.5792.

Nguyễn, V. K., Huỳnh, T. H., and Nguyễn, H. D. (2019). Lọc thích nghi tín hiệu điện não dựa trên Wavelet. Tạp chí Khoa học Trường Đại học Cần Thơ, 55(4), 21–30. https://doi.org/10.22144/ctu.jvn.2019.092.

Tao, Y., Liu, C., Liu, C., Zhao, X., Wu, H.(2021). Empirical wavelet transform method for GNSS coordinate series denoising. Journal of Geovisualization and Spatial Analysis, 5(1), Article 7. https://doi.org/10.1007/s41651-021-00078-7.

Trần, T. H. (2017). Ứng dụng wavelet để chiết xuất điểm đặc trưng phục vụ đồng đăng ký ảnh SAR. Tạp chí Khoa học Đo đạc và Bản đồ, (33), 30–34. https://doi.org/10.54491/jgac.2017.33.227.

Wang, W., Guo, M., and Chen, J. B. (2014). A new narrowband interference mitigation algorithm based on adaptive wavelet packet decomposition. In Proceedings of the 2014 International Conference on Mechatronics and Control (IMCCC) (pp. 6–11). https://doi.org/10.1109/IMCCC.2014.10.

Wapenaar, K., Ghose, R., Toxopeus, G. and Fokkema, J. (2005). Wavelet transform as a tool for geophysical data integration. Integrated Computer Aided Engineering, 12(1), 1–15. https://doi.org/10.3233/ICA-2005-12102.

David A. Yuen, Alain P. Vincent, Motoyuki Kido, Luděk Vecsey (2002). Geophysical applications of multidimensional filtering with wavelets. Pure and Applied Geophysics, 159, 2309–2385.

Yusri, M. S. (2021). Characterization of DWT as denoising method for φ-OTDR signal. International Journal of Nanoelectronics and Materials, 14(Special Issue), 333–340.

Zhong，P., Ding，X.L., Zheng，D.W., Chen，W.,Huang, D.F. (2008). Adaptive wavelet transform based on cross-validation method and its application to GPS multipath mitigation. GPS Solutions, 12(2), 109–117.

Zulfiqar, A., and Farooq, S. Z. (2023). Multipath mitigation for single frequency stand-alone receivers using wavelet denoising. In 2023 International Conference on Advances in Computing, Communication and Applied Sciences (ICACS) (pp. 6–11). IEEE. https://doi.org/10.1109/ICACS55311.2023.10089676.

Other articles