An Improved Adaptive IVMD-WPT-Based Noise Reduction Algorithm on GPS Height Time Series

Huaqing Xu; Tieding Lu; Jean-Philippe Montillet; Xiaoxing He

doi:10.3390/s21248295

An Improved Adaptive IVMD-WPT-Based Noise Reduction Algorithm on GPS Height Time Series

Sensors (Basel). 2021 Dec 11;21(24):8295. doi: 10.3390/s21248295.

Authors

Huaqing Xu^{1

2}, Tieding Lu¹, Jean-Philippe Montillet^{3

4}, Xiaoxing He⁵

Affiliations

¹ School of Surveying and Mapping Engineering, East China University of Technology, 418 Guanglan Road, Nanchang 330013, China.
² Key Laboratory for Digital Land and Resources of Jiangxi Province, East China University of Technology, Nanchang 330013, China.
³ Physikalisch-Meteorologisches Observatorium Davos/World Radiation Center (PMOD/WRC), Dorfstrasse 33, CH-7260 Davos, Switzerland.
⁴ Space and Earth Geodetic Analysis Laboratory (SEGAL), University of Beira Interior, 6201-001 Covilhã, Portugal.
⁵ School of Civil and Surveying & Mapping Engineering, Jiangxi University of Science and Technology, No. 86 Hongqi Ave., Ganzhou 341000, China.

Abstract

To improve the reliability of Global Positioning System (GPS) signal extraction, the traditional variational mode decomposition (VMD) method cannot determine the number of intrinsic modal functions or the value of the penalty factor in the process of noise reduction, which leads to inadequate or over-decomposition in time series analysis and will cause problems. Therefore, in this paper, a new approach using improved variational mode decomposition and wavelet packet transform (IVMD-WPT) was proposed, which takes the energy entropy mutual information as the objective function and uses the grasshopper optimisation algorithm to optimise the objective function to adaptively determine the number of modal decompositions and the value of the penalty factor to verify the validity of the IVMD-WPT algorithm. We performed a test experiment with two groups of simulation time series and three indicators: root mean square error (RMSE), correlation coefficient (CC) and signal-to-noise ratio (SNR). These indicators were used to evaluate the noise reduction effect. The simulation results showed that IVMD-WPT was better than the traditional empirical mode decomposition and improved variational mode decomposition (IVMD) methods and that the RMSE decreased by 0.084 and 0.0715 mm; CC and SNR increased by 0.0005 and 0.0004 dB, and 862.28 and 6.17 dB, respectively. The simulation experiments verify the effectiveness of the proposed algorithm. Finally, we performed an analysis with 100 real GPS height time series from the Crustal Movement Observation Network of China (CMONOC). The results showed that the RMSE decreased by 11.4648 and 6.7322 mm, and CC and SNR increased by 0.1458 and 0.0588 dB, and 32.6773 and 26.3918 dB, respectively. In summary, the IVMD-WPT algorithm can adaptively determine the number of decomposition modal functions of VMD and the optimal combination of penalty factors; it helps to further extract effective information for noise and can perfectly retain useful information in the original time series.

Keywords: grasshopper optimisation algorithm; improved variational mode decomposition; variational mode decomposition; wavelet packet transform.

Abstract

Grants and funding