Tropospheric tomography is one of the most important techniques to reconstruct three-dimensional (3D) images of the tropospheric water vapor fields using a local GNSS network. In the conventional tropospheric tomography method, called voxel-based tropospheric tomography, the 3D space is divided into many voxels and the amount of water vapor is estimated for each voxel. This method suffers from three disadvantages. First, it needs empirical constraints in order to fix the rank deficiency of the coefficient matrix. Second, the amount of water vapor is assumed to be constant in the 3D space of a voxel despite the large spatial variations of this parameter. Third, the number of unknown parameters is high compared to the number of observations. Therefore, an approach based on mathematical functions, called function-based tropospheric tomography, is presented to overcome these problems. The tropospheric tomography using the voxel-based and function-based approaches is performed using 17 GPS stations. Radiosonde observations and precise point positioning results are used to validate the obtained results. A comparison of the results with the radiosonde data indicates that using the function-based method reduces the mean RMSE by about 0.3 gr/m³. Validation using positioning under different wet conditions shows that in wet weather conditions the difference between the RMSE of the two tropospheric tomography approaches is significant. All the validations show the ability and applicability of the function-based tropospheric tomography approach.

中文翻译：

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基于B样条函数的GPS对流层层析成像方法

对流层层析成像技术是使用本地GNSS网络重建对流层水蒸气场的三维（3D）图像的最重要技术之一。在传统的对流层层析成像方法（称为基于体素的对流层层析成像方法）中，将3D空间划分为许多体素，并为每个体素估算水蒸气的量。该方法具有三个缺点。首先，它需要经验约束才能解决系数矩阵的秩不足。其次，尽管该参数的空间变化很大，但假设水蒸气的量在体素的3D空间中是恒定的。第三，与观察值相比，未知参数的数量很多。因此，一种基于数学函数的方法称为基于函数的对流层层析成像，提出克服这些问题。使用17个GPS站执行使用基于体素和基于函数的方法的对流层层析成像。探空仪的观测结果和精确的点定位结果可用来验证所获得的结果。结果与无线电探空仪数据的比较表明，使用基于函数的方法可使平均RMSE降低约0.3 gr / m³。在不同的潮湿条件下使用定位进行的验证表明，在潮湿的天气条件下，两种对流层层析成像方法的RMSE之间的差异非常明显。所有的验证都表明了基于功能的对流层层析成像方法的能力和适用性。