A new adaptive WVS based denoising method on GNSS vertical time series

Improper selection of modal decomposition numbers and penalty factors in Variational Modal Decomposition (VMD) can result in over-decomposition and under-decomposition issues, impacting the analysis of high-precision Global Navigation Satellite System (GNSS) time series for geodynamics and geophysics research purposes. This work shows a new WOA-VMD-SSA (WVS) denoising method combining Whale Optimization Algorithm (WOA) and the VMD together with the Singular Spectrum Analysis (SSA) method. Simulated data comprising a combination of Flicker noise plus White noise (FN+WN) and General Gauss-Markov plus White noise (GGM+WN) were utilized in our experiments. That the simulation results show that WVS root mean square error (RMSE) decreased by 0.88 to 0.91mm compared to Empirical Mode Decomposition (EMD), Ensemble Empirical Mode Decomposition (EEMD) and Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN). The signal-to- noise ratio (SNR) and correlation coefficient (CC) increased by 1.08 to 1.12 dB and 0.17 to 0.18, respectively. And the WVS method has the smallest difference from the true value. Finally, experimental analysis was conducted by using the vertical component of the GNSS time series from 100 GNSS sites located in the west coast of the USA. The real data results show that compared with EMD, EEMD and CEEMDAN methods, WVS can effectively reduce the uncertainty of station velocity and obtain more accurate velocity values, which is consistent with the conclusions of our simulations. Besides, the WVS algorithm can adaptively determine the optimal parameters for VMD decomposition, and it is also more efficient in time series noise removal.