The tropospheric delay is one of many error sources that affect the Global Navigation Satellite System (GNSS) positioning solutions. The widely used troposphere models assume a homogeneous atmosphere so that only the zenith delay needs to be determined and is mapped through an elevation-dependent mapping function. This procedure is to reduce the computational burden and keep the positioning model full-rank. However, this assumption fails for a realistic description of the troposphere, which is always asymmetrical at a certain elevation angle, especially during a weather event when the weather conditions are very complex. These imperfectly modelled tropospheric delays may influence the positioning accuracy and integer ambiguity resolution performance. In this case, this contribution aims to investigate the effects of the model errors due to the asymmetrical troposphere on GNSS estimations. The Numerical Weather Prediction (NWP) model is applied to generate the actual ray-tracing tropospheric delay in Western Europe, and the tropospheric model errors are calculated in a normal weather condition and a weather event condition by comparing the slant delay calculated from the NWP model and the mapping function. Case studies on the same GNSS station are conducted in two weather conditions: a normal troposphere condition and a weather event with heavy rainfall. The results based on the case studies show that the troposphere in the normal weather condition is nearly homogeneous that the azimuthal-dependent discrepancies of the tropospheric delay are less than $1\mathrm{c}\mathrm{m}$ at a very low elevation angle; meanwhile, the discrepancies between different azimuthal angles can reach to more than $25\mathrm{c}\mathrm{m}$ in the weather event. A single-frequency Single Point Positioning (SPP) model and a Precise Point Positioning (PPP) model that preserves the integer property of ambiguity are chosen for studying the estimation biases caused by the troposphere model errors. It turns out that almost all horizontal positioning biases of SPP and PPP are less than $1\mathrm{c}\mathrm{m}$ in the normal weather condition; however, the scales of the horizontal and $3\mathrm{D}$ biases are concentrated in $1$ to $10\mathrm{c}\mathrm{m}$ in the weather event for these two models. This contribution also contains the study of the actual integer ambiguity resolution success rate in the presence of the tropospheric model errors by applying the Monte Carlo simulation, and the success rates of PPP in the normal weather condition are consistent with the theoretical values calculated with the ideal troposphere which is totally symmetrical. However, the actual success rates in the weather event are extremely low at some epochs due to the tropospheric model errors, which means that wrong fixing may occur since the theoretical values cannot take into account these model errors. Note that the horizontal tropospheric gradients are not involved in the processing, which means that an optimistic performance might be expected if the gradients are considered.

对流层延迟是影响全球导航卫星系统（GNSS）定位解决方案的众多误差源之一。广泛使用的对流层模型假定大气是均匀的，因此仅需要确定天顶延迟，并通过与仰角有关的映射函数进行映射。此过程是为了减轻计算负担并保持定位模型的排名。但是，这种假设无法对现实的对流层进行描述，对流层在某个仰角始终不对称，特别是在天气条件非常复杂的天气事件期间。这些不完全建模的对流层延迟可能会影响定位精度和整数歧义分辨率性能。在这种情况下，该贡献旨在研究由于对流层不对称而引起的模型误差对GNSS估计的影响。应用数值天气预报（NWP）模型来生成西欧的实际射线追踪对流层延迟，并通过比较从NWP模型计算出的倾斜延迟来计算正常天气条件和天气事件条件下的对流层模型误差和映射功能。在相同的GNSS站上进行的案例研究是在两种天气情况下进行的：对流层正常情况和强降雨天气事件。基于案例研究的结果表明，正常天气条件下的对流层几乎均匀，对流层延迟的方位角相关差异小于 应用数值天气预报（NWP）模型来生成西欧的实际射线追踪对流层延迟，并通过比较从NWP模型计算出的倾斜延迟来计算正常天气条件和天气事件条件下的对流层模型误差和映射功能。在相同的GNSS站上进行的案例研究是在两种天气情况下进行的：对流层正常情况和强降雨天气事件。根据案例研究的结果表明，正常天气条件下的对流层几乎均匀，对流层延迟的方位角相关差异小于 应用数值天气预报（NWP）模型来生成西欧的实际射线追踪对流层延迟，并通过比较从NWP模型计算出的倾斜延迟来计算正常天气条件和天气事件条件下的对流层模型误差和映射功能。在相同的GNSS站上进行的案例研究是在两种天气情况下进行的：对流层正常情况和强降雨天气事件。根据案例研究的结果表明，正常天气条件下的对流层几乎均匀，对流层延迟的方位角相关差异小于 通过比较从NWP模型和映射函数计算得到的倾斜延迟，可以计算出正常天气条件和天气事件条件下的对流层模型误差。在相同的GNSS站上进行的案例研究是在两种天气情况下进行的：对流层正常情况和强降雨天气事件。根据案例研究的结果表明，正常天气条件下的对流层几乎均匀，对流层延迟的方位角相关差异小于 通过比较从NWP模型和映射函数计算得到的倾斜延迟，可以计算出正常天气条件和天气事件条件下的对流层模型误差。在相同的GNSS站上进行的案例研究是在两种天气情况下进行的：对流层正常情况和强降雨天气事件。根据案例研究的结果表明，正常天气条件下的对流层几乎均匀，对流层延迟的方位角相关差异小于$\mathrm{1个}\mathrm{C}\mathrm{米}$以非常低的仰角；同时，不同方位角之间的差异可以达到$25\mathrm{C}\mathrm{米}$在天气事件中。选择单频单点定位（SPP）模型和保留模糊度整数属性的精确点定位（PPP）模型来研究由对流层模型误差引起的估计偏差。事实证明，SPP和PPP的几乎所有水平定位偏差都小于$\mathrm{1个}\mathrm{C}\mathrm{米}$在正常天气情况下；但是，水平和$3\mathrm{d}$ 偏见集中在 $\mathrm{1个}$ 到 $10\mathrm{C}\mathrm{米}$这两个模型的天气事件。该贡献还包括通过应用蒙特卡洛模拟研究在对流层模型误差存在下实际整数模糊度解决方案的成功率，并且在正常天气条件下PPP的成功率与理想值下的理论值相符。对流层是完全对称的。但是，由于对流层模型误差，在某些时期，天气事件的实际成功率极低，这意味着可能会发生固定错误，因为理论值无法考虑这些模型误差。请注意，处理过程中不涉及水平对流层梯度，这意味着如果考虑这些梯度，则可以期望获得乐观的性能。