# LEO Constellation-Augmented Multi-GNSS for 3D Water Vapor Tomography
## 3 Experiments and Results
### Tomographic Observation Distribution
Figure 13 shows the number of empty and two-station voxels for different constellations, such as G, L60, and L288, with sampling rates of 1, 5, 10, 15, 30, 60, 120, and 300 s, respectively, within 30 min. The number of empty voxels for the three satellite systems with different sampling rates is plotted in Figure 13a. L60 had the largest number of empty voxels, followed by G and L288. The sampling rate had little effect on the number of empty voxels for the G scheme because the G scheme had a small trajectory across the sky in a short period of time, and the ray movement was limited in a short period of time, which made it difficult to enter other new voxels. Compared to the G scheme, the variation in empty L60 and L288 voxels with the sampling rate was larger, because LEO satellites can traverse longer sky tracks in a short period of time, and some valid LEO observations are not effectively captured after increasing the length of the sampling interval. Figure 13b shows the two-station voxels for three systems with different sampling intervals. The value of L288 was the largest, followed by those of G and L60. Similarly, the value of G was nearly the same with different sampling rates. The two-station voxels of the L60 and L288 also varied more with the sampling rate than the G scheme. The two-station voxels of L288 were twice as large as those of G. The above indicators show that L60 ray distribution was the weakest when viewed from a single system. The L288 scheme could increase the observed ray distribution and decrease the number of empty voxels. More importantly, the L288 scheme could greatly increase the number of nonparallel observed rays. Therefore, the sampling rates of GNSS and LEO, for all the following experiments, were set to be 300 and 15 s, respectively. Moreover, the distribution of the five schemes' rays, namely, G, GREC, GRECL60, GRECL288, and L288, at different times within 1 day, is shown in Figure 14; the observation time was 30 min. Figure 14a shows that, for the empty-voxel indicator, G had the largest value and varied the most throughout the day. The variation was smoother for the other combined systems. The value of GRECL288 was the smallest at any time of the day. The performance of L288 was very promising, and although the number of visible satellites was about the same as that for G, the number of empty voxels was smaller than that of the \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **GREC (10 min)** & **GREC (30 min)** & **GRECL288** & **GRECL288** \\  & & **(10 min)** & **(30 min)** \\ \hline
**Effective Rays** & 1192 & 2539 & 2840 & 7181 \\
**Voxel Passed** & 1038 & 3548 & 3834 & 9821 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistics of the effective observation ray and the number of times that the top voxels were passed by the effective observation ray. integrated model of GREC. This suggests that, with enough LEO satellites, LEO satellites can obtain the same ray distribution as that of the GNSS constellation. Figure 14b shows the two-station voxels of the five schemes at different times. GRECL288 was the largest at any time, followed by L288, and the smallest was still G. The two-station voxels of L288 were, on average, 37.8 more than those of GREC, indicating that L288 was better than GREC in terms of distribution. Compared with GREC and G, the average empty voxels of GRECL288 were improved by 2.12% and 10.68%, respectively; the average two-stations voxels of GRECL288 were improved by 7.67% and 33.29%, respectively. This suggests that LEO could generate more useful redundant observations than GRECE and G, even in relatively small discrete regions. The increase in two-station voxels was greater than that in empty voxels, indicating that LEO brought more useful cross-rays with the same station distribution.