Velocity Estimation of GNSS Coordinate Time Series Accounting for Stochastic Seasonality Revisited

Summary We revisit the challenge of estimating velocities from global navigation satellite system (GNSS) coordinate time series by incorporating stochastic processes to address the quasi-periodic oscillations (QPOs) in weighted least-squares estimation. We examine two advanced stochastic seasonal models (i.e., Fractional Sinusoidal Waveform (FSW) and Varying Periodic Band-Pass (VPBP)) and evaluate their efficacy on mitigating velocity biases by using both synthetic data and 14 Antarctic GNSS stations. The result shows that pure FSW cannot fully capture the spectral shape of the QPOs since the FSW's spectral shape is controlled by the fractional parameter d, which is unfortunately dependent on the global spectra slope of the GNSS data. In contrast, VPBP can fit the QPOs more freely by using the parameter phi. Nevertheless, both FSW and VPBP models, when used without augmentation, tend to underestimate velocity uncertainties due to spectral flattening at low frequencies. This poses a risk for applications requiring high-confidence geodetic velocity estimates. To solve this issue, adopting a hybrid noise model that is compensated with an additional appropriate noise background (e.g., power law) is recommended. This knowledge can guide future research on secular velocity estimation of GNSS stations.