Troposphere’s asymmetry can introduce errors ranging from centimeters to decimeters at low elevation angles, which cannot be ignored in high-precision positioning technology and meteorological research. The traditional two-axis gradient model, which strongly relies on an open-sky environment of the receiver, exhibits misfits at low elevation angles due to their simplistic nature. In response, we propose a directional mapping function based on cyclic B-splines named B-spline mapping function (BMF). This model replaces the conventional approach, which is based on estimating Zenith Wet Delay and gradient parameters, by estimating only four parameters which enable a continuous characterization of the troposphere delay across any directions. A simulation test, based on a numerical weather model, was conducted to validate the superiority of cyclic B-spline functions in representing tropospheric asymmetry. Based on an extensive analysis, the performance of BMF was assessed within precise point positioning using data from 45 International GNSS Service stations across Europe and Africa. It is revealed that BMF improves the coordinate repeatability by approximately \(10\%\) horizontally and about \(5\%\) vertically. Such improvements are particularly pronounced under heavy rainfall conditions, where the improvement of 3-dimensional root mean square error reaches up to \(13\%\).

对流层的不对称性会在低仰角时引入厘米至分米级的误差，这在高精度定位技术和气象研究中是不可忽视的。传统的两轴梯度模型强烈依赖于接收器的开放天空环境，由于其简单化的性质，在低仰角下表现出不适合。为此，我们提出了一种基于循环 B 样条的方向映射函数，称为 B 样条映射函数（BMF）。该模型通过仅估计四个参数来取代基于估计天顶湿延迟和梯度参数的传统方法，这四个参数能够连续表征任何方向上的对流层延迟。基于数值天气模型的模拟试验验证了循环B样条函数在表示对流层不对称性方面的优越性。基于广泛的分析，使用来自欧洲和非洲 45 个国际 GNSS 服务站的数据在精确单点定位中评估了 BMF 的性能。结果表明，BMF 在水平方向上将坐标重复性提高了大约 \(10\%\)，在垂直方向上提高了大约 \(5\%\)。这种改进在强降雨条件下尤其明显，3维均方根误差的改进高达\(13\%\)。