In computerized ionospheric tomography (CIT) with ground-based GNSS, the voxels without satellite-receiver ray traversing cannot be reconstructed directly. We present a CIT algorithm based on virtual reference stations (VRSs), called VRS–CIT, to decrease the number of unilluminated voxels and improve the precision of the estimated ionospheric electron density (IED). The VRSs are set at the nodes of grids with a 0.5° × 0.5° resolution in longitude and latitude. We generate the virtual observations with the observations from nearby six or three stations selected according to azimuths and distances. The generation utilizes multi-quadric surface fitting with six stations and triangular linear interpolation with three stations. With the virtual observations added, the IED distribution is reconstructed by the multiplicative algebraic reconstruction technique with the initial values obtained from IRI-2016. The performance of VRS–CIT is examined by using the data from 127 GNSS stations located in 24–46° N and 122–146° E to derive the IED every 30 min. The study focuses on April 29, 2014, with the adaptability of VRS–CIT analyzed by 12 days, evenly distributed around equinoxes and solstices of 2014. The accuracy of the virtual observation is about 1 TECU. Comparing to that derived from CIT with only real observations, the unsolvability of VRS–CIT declined by 4–12% for the whole region, and for the main area, the improvement can be up to 70%. Taking two IED profiles from radio occultation as reference measurements, the mean absolute error (MAE) of IED by VRS–CIT decreases by 6.88% and 8.43%, respectively. Comparing with slant total electron content (STEC) extracted from five additional GNSS stations, the MAE and the root mean square error of the estimated STEC can be reduced up to 17.24% and 33.81%, respectively.

在具有地面GNSS的计算机电离层层析成像（CIT）中，无法直接重建没有卫星接收器射线遍历的体素。我们提出了一种基于虚拟参考站（VRS）的CIT算法，称为VRS–CIT，以减少未照明体素的数量并提高估算的电离层电子密度（IED）的精度。VRS设置在经度和纬度分辨率为0.5°×0.5°的网格节点处。我们使用根据方位角和距离选择的来自附近六个或三个站点的观测值生成虚拟观测值。该代利用具有六个测站的多二次曲面拟合和具有三个测站的三角形线性插值。添加虚拟观察后，IED分布通过乘法代数重建技术从IRI-2016获得初始值。通过使用位于北纬24–46°和东经122–146°的127个GNSS站的数据，每30分钟导出IED来检查VRS–CIT的性能。该研究集中在2014年4月29日，对VRS-CIT的适应性进行了为期12天的分析，均匀分布在2014年的春分和溶胶点之间。虚拟观测的准确性约为1 TECU。与仅基于实际观察的CIT得出的结果相比，VRS–CIT的不可解决性在整个区域内下降了4–12％，对于主要区域，可提高到70％。以无线电掩星的两个IED剖面作为参考测量，VRS–CIT的IED的平均绝对误差（MAE）分别降低了6.88％和8.43％。