We perform a statistical sensitivity analysis on a parametric fit to vertical daily displacement time series of 244 European Permanent GNSS stations, with a focus on linear vertical land motion (VLM), i.e., station velocity. We compare two independent corrections to the raw (uncorrected) observed displacements. The first correction is physical and accounts for non-tidal atmospheric, non-tidal oceanic and hydrological loading displacements, while the second approach is an empirical correction for the common-mode errors. For the uncorrected case, we show that combining power-law and white noise stochastic models with autoregressive models yields adequate noise approximations. With this as a realistic baseline, we report improvement rates of about 14% to 24% in station velocity sensitivity, after corrections are applied. We analyze the choice of the stochastic models in detail and outline potential discrepancies between the GNSS-observed displacements and those predicted by the loading models. Furthermore, we apply restricted maximum likelihood estimation (RMLE), to remove low-frequency noise biases, which yields more reliable velocity uncertainty estimates. RMLE reveals that for a number of stations noise is best modeled by a combination of random walk, flicker noise, and white noise. The sensitivity analysis yields minimum detectable VLM parameters (linear velocities, seasonal periodic motions, and offsets), which are of interest for geophysical applications of GNSS, such as tectonic or hydrological studies.

我们对 244 个欧洲永久 GNSS 站的垂直每日位移时间序列的参数拟合进行了统计敏感性分析，重点是线性垂直陆地运动 (VLM)，即站速度。我们将两个独立校正与原始（未校正）观测到的位移进行比较。第一种修正是物理修正，考虑了非潮汐大气、非潮汐海洋和水文载荷位移，而第二种方法是对共模误差的经验修正。对于未经校正的情况，我们表明将幂律和白噪声随机模型与自回归模型相结合可以产生足够的噪声近似值。以此作为现实的基线，我们报告在应用校正后，测站速度灵敏度的改善率约为 14% 至 24%。我们详细分析了随机模型的选择，并概述了 GNSS 观测到的位移与加载模型预测的位移之间的潜在差异。此外，我们应用限制最大似然估计（RMLE）来消除低频噪声偏差，从而产生更可靠的速度不确定性估计。 RMLE 表明，对于许多站点来说，噪声最好通过随机游走、闪烁噪声和白噪声的组合来建模。灵敏度分析产生最小可检测 VLM 参数（线速度、季节性周期性运动和偏移），这些参数对于 GNSS 的地球物理应用（例如构造或水文研究）很重要。