GNSS Velocity Estimation Using Adaptive Monte Carlo SSA

Accurate estimation of GNSS station velocities requires careful consideration of the stochastic properties of their position time series, which are commonly affected by white and flicker noise. In this study, we propose a non-parametric approach combining Singular Spectrum Analysis (SSA) with an adaptive Monte Carlo SSA (MC-SSA) to estimate station velocities and their uncertainties, explicitly accounting for the noise spectrum. Using SSA, the trend and seasonal components are removed from the analyzed GNSS time series, after which the residual noise is analyzed using Welch’s spectral method to identify its noise type. Monte Carlo simulations are then employed to generate synthetic realizations of white and/or flicker noise according to the detected type, and the trend is reconstructed with SSA for each realization.

The proposed methodology is applied to daily position time series from 28 International GNSS Service (IGS) stations located on the African plate. The data are expressed in the local topocentric reference frame (North, East, Up), referenced to ITRF2020, and cover the period from 1999 to 2026. The results show that the average velocities of the analyzed stations are about 17.625, 19.446, and -0.749 mm/yr in the North, East and Up components, respectively. For stations whose position time series are dominated by white noise, the uncertainties associated with the estimated horizontal and vertical velocities range from 0.001 to 0.027 mm/yr and from 0.010 to 0.086 mm/yr, respectively. In contrast, the velocities affected by flicker noise exhibit a significantly larger uncertainty, varying from 0.045 to 0.260 mm/yr for the horizontal components and from 0.148 to 0.628 mm/yr for the vertical component. The proposed MC-SSA approach was validated using synthetic GNSS position time series generated with prescribed velocities and well-defined noise characteristics, spanning the same time intervals as the used data. The results demonstrate that MC-SSA yields velocity estimates that are very close to the simulated values and provides more realistic uncertainty estimates than ordinary least squares solutions. Moreover, this study provides a consistency assessment of velocities from regional GNSS stations on the African plate through comparison with nearby IGS stations in the ITRF2020 reference frame.