Mirmohammadian Farinaz, Asgari Jamal, Verhagen Sandra, Amiri-Simkooei Alireza
Department of Geomatics Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan, Isfahan 8174673441, Iran.
Department of Geoscience and Remote Sensing, Delft University of Technology, 2600 AA Delft, The Netherlands.
Sensors (Basel). 2022 Jul 26;22(15):5570. doi: 10.3390/s22155570.
Until now, RTK (real-time kinematic) and NRTK (Network-based RTK) have been the most popular cm-level accurate positioning approaches based on Global Navigation Satellite System (GNSS) signals in real-time. The tropospheric delay is a major source of RTK errors, especially for medium and long baselines. This source of error is difficult to quantify due to its reliance on highly variable atmospheric humidity. In this paper, we use the NRTK approach to estimate double-differenced zenith tropospheric delays alongside ambiguities and positions based on a complete set of multi-GNSS data in a sample 6-station network in Europe. The ZTD files published by IGS were used to validate the estimated ZTDs. The results confirmed a good agreement, with an average Root Mean Squares Error (RMSE) of about 12 mm. Although multiplying the unknowns makes the mathematical model less reliable in correctly fixing integer ambiguities, adding a priori interpolated ZTD as quasi-observations can improve positioning accuracy and Integer Ambiguity Resolution (IAR) performance. In this work, weighted least-squares (WLS) were performed using the interpolation of ZTD values of near reference stations of the IGS network. When using a well-known Kriging interpolation, the weights depend on the semivariogram, and a higher network density is required to obtain the correct covariance function. Hence, we used a simple interpolation strategy, which minimized the impact of altitude variability within the network. Compared to standard RTK where ZTD is assumed to be unknown, this technique improves the positioning accuracy by about 50%. It also increased the success rate for IAR by nearly 1.
到目前为止，实时动态（RTK）和网络实时动态（NRTK）一直是基于全球导航卫星系统（GNSS）信号进行实时厘米级精确定位的最流行方法。对流层延迟是RTK误差的主要来源，特别是对于中长基线而言。由于其依赖于高度可变的大气湿度，这种误差源难以量化。在本文中，我们使用NRTK方法，基于欧洲一个包含6个站点的样本网络中的完整多GNSS数据集，来估计双差天顶对流层延迟以及模糊度和位置。使用国际GNSS服务（IGS）发布的ZTD文件来验证估计的ZTD。结果证实了良好的一致性，平均均方根误差（RMSE）约为12毫米。虽然增加未知数会使数学模型在正确固定整周模糊度方面的可靠性降低，但添加先验插值的ZTD作为准观测值可以提高定位精度和整周模糊度解算（IAR）性能。在这项工作中，使用IGS网络近参考站的ZTD值插值进行加权最小二乘法（WLS）。当使用著名的克里金插值时，权重取决于半变异函数，并且需要更高的网络密度来获得正确的协方差函数。因此，我们使用了一种简单的插值策略，该策略最小化了网络内海拔变化的影响。与假设ZTD未知的标准RTK相比，该技术将定位精度提高了约50%。它还使IAR的成功率提高了近1倍。
