Abstract It is well known that GNSS permanent station coordinate time series exhibit time-correlated noise. Spatial correlations between coordinate time series of nearby stations are also long-established and generally handled by means of spatial filtering techniques. Accounting for both the temporal and spatial correlations of the noise via a spatiotemporal covariance model is however not yet a common practice. We demonstrate in this paper the interest of using such a spatiotemporal covariance model of the stochastic variations in GNSS time series in order to estimate long-term station coordinates and especially velocities. We provide a methodology to rigorously assess the covariances between horizontal coordinate variations and use it to derive a simple exponential spatiotemporal covariance model for the stochastic variations in the IGS repro2 station coordinate time series. We then use this model to estimate station velocities for two selected datasets of 10 time series in Europe and 11 time series in the USA. We show that coordinate prediction as well as velocity determination from short time series are improved when using this spatiotemporal model, as compared with the case where spatiotemporal correlations are ignored.

中文翻译：

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考虑 GNSS 坐标时间序列的时空相关性以估计台站速度

摘要 众所周知，GNSS 永久台站坐标时间序列存在时间相关噪声。邻近台站坐标时间序列之间的空间相关性也由来已久，通常通过空间滤波技术处理。然而，通过时空协方差模型考虑噪声的时间和空间相关性还不是一种普遍的做法。我们在本文中展示了使用这种 GNSS 时间序列随机变化的时空协方差模型来估计长期站坐标，尤其是速度的兴趣。我们提供了一种方法来严格评估水平坐标变化之间的协方差，并使用它来推导出一个简单的指数时空协方差模型，用于 IGS repro2 站坐标时间序列中的随机变化。然后，我们使用该模型来估计欧洲 10 个时间序列和美国 11 个时间序列的两个选定数据集的站点速度。我们表明，与忽略时空相关性的情况相比，当使用这种时空模型时，坐标预测以及短时间序列的速度确定得到了改进。