Application of combination of denoising methods and Complementary Ensemble Empirical Mode Decomposition in GNSS time series analysis

The article proposes to combine a methods based on wavelet denoising (WDN) and Shannon entropy (DSE) for GNSS station position time series denoising and Complementary Ensemble Empirical Mode Decomposition (CEEMD) for the decomposition of the time series into frequency components, namely intrinsic mode functions (IMFs). First, we used WDN as well as DSE to denoise the GNSS time series. They were then decomposed with CEEMD, which is dedicated to analysing non-stationary time series. The proposed WDN + CEEMD and DSE + CEEMD methods were then employed to analyse several GNSS station position time series in Poland. We used daily time series of position residues for 15 GNSS stations of the EUREF Permanent Network (EPN) classified as the Polish national control network. The station time series were decomposed into IMF frequency components, of which IMF5 and IMF6 represented semi-annual and annual signals. We noted an annual oscillation for all the reference stations in the horizontal and vertical components. A semi-annual oscillation was found for all the stations only in the vertical component. The study confirms that the WDN + CEEMD as well as DSE + CEEMD method is capable of limiting the absorption of some noise by seasonal signals. The values of the spectral indices of the station position time series after subtracting the seasonal signals modelled by the WDN + CEEMD or DSE + CEEMD methods assumed values from the range of the power law noise model. GNSS station position time series analysis with WDN + CEEMD and DSE + CEEMD yielded satisfactory results and can be a good alternative for modelling time-dependent seasonal signals in GNSS time series, particularly the annual and semi-annual signals.