Weakening the Flicker Noise in GPS Vertical Coordinate Time Series Using Hybrid Approaches

Noises in the GPS vertical coordinate time series, mainly including the white and flicker noise, have been proven to impair the accuracy and reliability of GPS products. Various methods were adopted to weaken the white and flicker noises in the GPS time series, such as the complementary ensemble empirical mode decomposition (CEEMD), wavelet denoising (WD), and variational mode decomposition (VMD). However, a single method only works at a limited frequency band of the time series, and the corresponding denoising ability is insufficient, especially for the flicker noise. Hence, in this study, we try to build two combined methods: CEEMD & WD and VMD & WD, to weaken the flicker noise in the GPS positioning time series from the Crustal Movement Observation Network of China. First, we handled the original signal using CEEMD or VMD with the appropriate parameters. Then, the processed signal was further denoised by WD. The results show that the average flicker noise in the time series was reduced from 19.90 mm/year0.25 to 2.8 mm/year0.25. This relates to a reduction of 86% after applying the two methods to process the GPS data, which indicates our solutions outperform CEEMD by 6.84% and VMD by 16.88% in weakening the flicker noise, respectively. Those apparent decreases in the flicker noises for the two combined methods are attributed to the differences in the frequencies between the WD and the other two methods, which were verified by analyzing the power spectrum density (PSD). With the help of WD, CEEMD & WD and VMD & WD can identify more flicker noise hidden in the low-frequency signals obtained by CEEMD and VMD. Finally, we found that the two combined methods have almost identical effects on removing the flicker noise in the time series for 226 GPS stations in China, testified by the Wilcoxon rank sum test.