The length of the convergence time in Precise Point Positioning (PPP) is a result of unmodeled errors. The tropospheric delay error is considered a major error source that affects the PPP solution accuracy and convergence time, especially in the height coordinates. Recent research showed that Numerical Weather Models (NWM)-based tropospheric correction models are superior to traditional empirical tropospheric models. We investigate the tropospheric delay difference between the ray-traced NWM and the final troposphere estimates from the International GNSS Service (IGS). Long time series of about 5 years of tropospheric delay are obtained from the European Centre for Medium-Range Weather Forecast and compared with the final IGS tropospheric delay time series for 30 globally distributed IGS stations. It is shown that the ray-traced tropospheric delay differences depend on time and experience seasonal variations with a non-zero mean. The mean is found to be 0.47 cm and the standard deviation is 1.40 cm. To model such differences, the least-squares spectral analysis approach is used to estimate the deterministic part of the tropospheric residuals (linear trend and periodic signals). The remaining tropospheric differences are estimated as a random walk process with 5 mm/√h random noise. To study the effect of the developed model on both station position and tropospheric delay estimate, we implement our model in GPS processing software, and the data from 15 IGS stations are processed. These stations are divided into two groups. The first group consists of nine IGS stations from the same network used to estimate the model, and their corresponding model values are extrapolated to the test epochs in 2018. However, the second group consists of six IGS stations, and their corresponding values are interpolated from the nearby stations. It is shown that the root means square error (RMSE) of station position in both groups can be improved by 5.68%, 0.76%, and 11.88% in Easting, Northing, and Up directions, respectively. In addition to the improvement in the RMSE of station positions, an improvement of 7.91% is obtained for total tropospheric delay estimates.

中文翻译：

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IGS最终和射线追踪的对流层延迟之间的特征差异及其对精确点定位和对流层延迟估计的影响

精确点定位（PPP）中收敛时间的长度是未建模误差的结果。对流层延迟误差被认为是影响PPP解精度和收敛时间的主要误差源，尤其是在高度坐标中。最近的研究表明，基于数值天气模型（NWM）的对流层校正模型优于传统的经验对流层模型。我们调查了射线追踪的NWM与来自国际GNSS服务（IGS）的最终对流层估计之间的对流层延迟差。从欧洲中距离天气预报中心获得了大约5年对流层延迟的长时间序列，并将其与30个全球分布的IGS台站的最终IGS对流层延迟时间序列进行了比较。结果表明，射线追踪的对流层延迟差异取决于时间，并且经历季节性变化，且均值非零。发现平均值为0.47cm，标准偏差为1.40cm。为了对这种差异进行建模，最小二乘频谱分析方法用于估计对流层残差的确定部分（线性趋势和周期信号）。剩余的对流层差异估计为随机游走过程，随机噪声为5 mm /√h。为了研究开发的模型对台站位置和对流层延迟估计的影响，我们在GPS处理软件中实现了该模型，并对15个IGS台站的数据进行了处理。这些站分为两组。第一组由来自用于估计模型的同一网络的9个IGS站组成，并将其对应的模型值外推到2018年的测试纪元。然而，第二组包括六个IGS站点，并且它们的对应值是从附近的站点进行内插的。结果表明，两组的站位均方根误差（RMSE）在东，北和上方向上分别可提高5.68％，0.76％和11.88％。除了改善站位的均方根误差外，对流层总延迟估算也获得了7.91％的改善。东，北和上方向分别占88％。除了改善站位的均方根误差外，对流层总延迟估算也获得了7.91％的改善。东，北和上方向分别占88％。除了改善站位的均方根误差外，对流层总延迟估算也获得了7.91％的改善。