It is well known that unmodeled offsets in Global Navigation Satellite System (GNSS) position time series can introduce biases into the station velocities. Although large offsets are usually reported or can be visually detected, automated offset detection algorithms require further investigation. This problem is still challenging as (small) geophysical offsets are usually covered by coloured noise and remain undetected. An offset detection algorithm has recently been proposed, which can detect and estimate offsets in both univariate and multivariate analyses. Although efficient in truly detecting offsets, this method still suffers from a high rate of detected fake offsets. To improve the offset detection performance, we attempt to stabilize the offset power spectrum to reduce the number of false detections. The spline function theory is adopted in the smoothness process of the power spectrum. The algorithm modified using the spline functions, referred to as As-mode, is compared with its original counterpart, called A-mode. The GNSS position time series consisting of a linear trend, seasonal signals, offsets, and white plus coloured noise are simulated for the numerical comparison. The overall performance of the algorithm is significantly improved using the As-mode algorithm. The multivariate analysis shows that the truly detected offsets' percentage (true positive) increases from 52.9 per cent for A-mode to 61.1 per cent for As-mode. Further, the falsely detected offsets' percentage (false positive) is reduced from 40.6 per cent to 29.8 per cent. The algorithm was also tested on the DOGEx dataset. The results indicate that the proposed method outperforms the existing solutions, with TP, FP, and FN being 33.3 per cent, 32.3 per cent, and 34.4 per cent, respectively. Also, in 90 per cent of the station, velocities are estimated at a 0.8 mm/year distance from the simulated values.

中文翻译：

---

基于样条函数理论的GNSS位置时间序列偏移检测算法的改进

众所周知，全球导航卫星系统（GNSS）位置时间序列中未建模的偏移量可能将偏差引入站速。尽管通常会报告或可以通过视觉方式检测到较大的偏移量，但自动偏移量检测算法仍需要进一步研究。由于（小的）地球物理偏移通常被有色噪声覆盖并且仍然未被检测到，因此该问题仍然具有挑战性。最近提出了一种偏移检测算法，该算法可以在单变量和多变量分析中检测和估计偏移。尽管在真正地检测偏移量方面是有效的，但是该方法仍然遭受高的伪造偏移量检测率的困扰。为了提高偏移检测性能，我们尝试稳定偏移功率谱以减少错误检测的次数。功率谱的平滑过程采用样条函数理论。将使用样条函数修改的算法（称为As-mode）与原始算法（称为A-mode）进行比较。GNSS位置时间序列由线性趋势，季节性信号，偏移量以及白色和彩色噪声组成，用于数值比较。使用As-mode算法可显着提高算法的整体性能。多元分析显示，真正检测到的偏移量百分比（真实正值）从A模式的52.9％增加到As模式的61.1％。此外，错误检测的抵消的百分比（误报）从40.6％降低到29.8％。该算法也在DOGEx数据集上进行了测试。结果表明，所提出的方法优于现有解决方案，TP，FP和FN分别为33.3％，32.3％和34.4％。同样，在90％的测站中，速度与模拟值之间的距离估计为0.8毫米/年。