Extraction of common mode error based on SSA method and its impact analysis on GNSS vertical coordinate time series

This study, based on eight years of data from 24 Global Navigation Satellite Systems (GNSS) stations in northern Germany, introduces the singular spectrum analysis method. It proposes a common mode error identification method that considers the inter-correlation of different residual subcomponents and their contribution rates. The impact of common mode errors on GNSS coordinate time series noise and parameter estimation is explored. Compared with the principal component analysis (PCA) method, it is found that the method proposed in this paper closely aligns with the common mode errors extracted by PCA, confirming the feasibility of the new method. The GNSS common mode error sequence mainly contains white noise, flicker noise, and power-law noise with non-integer spectral indices. After removing common mode errors, the magnitude of white noise and colored noise at each station decreased by an average of 30.32% and 52.61% respectively, indicating that colored noise dominates in common mode errors. Furthermore, after correcting common mode errors, the annual and semi-annual cycle amplitudes of coordinates are reduced, and the root mean square error of parameter fitting is decreased by 16.7%. In summary, the method described in this paper is of significant practical importance in improving the quality of GNSS coordinate time series.