VMD–WT-Based Method for Extracting On-the-Fly GNSS Tide Level and Its Realization

Abstract

In this paper, a method for extracting the on-the-fly (OTF) GNSS tide level was designed by combining variational modal decomposition (VMD) and a wavelet thresholding (WT) method to improve the extraction accuracy of the OTF GNSS tide level. First, the energy difference ratio method was used to determine the number of layers for the VMD. Subsequently, the VMD performed a second decomposition of the IMF1 obtained from the first VMD to achieve an efficient separation of signal and noise. The normalized cross-correlation coefficient (NCC) was applied to determine the number of layers for the WT method. Finally, experimental results showed that the VMD–WT method outperformed the other seven filtering methods in three metrics: maximum error, the root-mean-square error (RMSE), and error distribution. Therefore, the VMD–WT method was able to extract extremely accurate on-the-fly GNSS tide level and additionally obtain more accurate bathymetry data after tidal correction of the bathymetry data.