Discontinuity problem in nominal precision of velocity estimation for GNSS coordinate series

Accurate construction of noise models is essential for obtaining reliable velocity fields and their associated nominal precision in the analysis of global navigation satellite system (GNSS) coordinate time series. We analyze coordinate series from 46 representative International GNSS Service stations spanning the past 30 years, supplemented by simulated series. Our investigation focuses on the influence of two key factors: (1) series with different durations (4–28 years) and (2) series of equal length but with varying initial epochs. We examine their impact on the optimal selection of noise models and velocity precision assessment. The results reveal a phase transition phenomenon in the nominal precision of velocity estimation, characterized by shifts in the optimal noise model as the series length increases, leading to abrupt changes in velocity precision. Moreover, this phase transition exhibits significant directional differences. In contrast, the initial epoch has minimal impact on noise model selection and the calculation of nominal velocity precision. Through simulation studies, we examine the variation of the calculated nominal velocity precision relative to its ‘true value’ or reference value. By setting the background noise to WN + PL + RWN (white noise + power-law noise + random walk noise), we obtain conclusions consistent with the measured data. Notably, only when the series length exceeds 24 years does the proportion of cases where the true value model is selected exceed 50%. The phase transition phenomenon in the nominal velocity precision is attributed to the discreteness of the candidate models in the model selection process.