Presence and detection methods of pseudo-periods in GNSS coordinate time series

Periodic detection of Global Navigation Satellite System (GNSS) coordinate time series is crucial for establishing nonlinear motion models of reference stations. However, uncleaned outliers, offset, and the limited precision of periodic detection methods may introduce pseudo-periodic signals. To address this, we employed the Modified Least Squares Harmonics Estimation (MLSHE) method, Complementary Ensemble Empirical Mode Decomposition (CEEMD), Monte Carlo Singular Spectrum Analysis (MCSSA), and the Lomb-Scargle method to validate the existence of abnormal pseudo-periods and biased pseudo-periods through synthetic time series. Our results indicate that the MCSSA method exhibits the most severe pseudo-periods, with a semiannual signal amplitude deviation of 2.2 mm, which is 37 times larger than that of the MLSHE method. When modeling pseudo-periods, the Akaike Information Criterion (AIC) value increases significantly, whereas decreases for real periodic signals. Based on this observation, we proposed the AIC_diff (Akaike Information Criterion Difference) pseudo-period detection method with the threshold as −5, indicating that the signal is more likely to be a pseudo-period, if the AIC_diff exceeds −5. To evaluate the effectiveness of this approach, we conducted experiments on multi-period synthetic time series containing various types of noise. The results demonstrate that the AIC_diff method improves the period detection accuracy of MLSHE, Lomb-Scargle, CEEMD, and MCSSA by 3.3, 3.7, 8.3, and 9.1 times, respectively, under the kappa = 0.5 noise model, which is most representative of GNSS data. Further analysis of 52 detrended GNSS observed coordinate time series spanning 13 years, provided by JPL, reveals that the AIC_diff pseudo-period detection method effectively explains most previously unaccounted-for periodic signals. By combining the AIC_diff method with MLSHE or Lomb-Scargle, pseudo-periods resulting from the relatively poor robustness and accuracy of period detection methods can be mitigated. This integration has the potential to establish a more accurate coordinate reference frame and provide more reliable data for geophysical signal analysis.