# LEO Constellation-Augmented Multi-GNSS for 3D Water Vapor Tomography
## 3 Experiments and Results
### Tomographic Observation Distribution  
The observations that are collected by a single navigation system are distributed unevenly, and vary with time [42]. Figure 9 shows the distribution of observations received by ground-based GNSS stations, within one epoch. The center point in Figure 9 denotes the zenith direction of the station; 0\(-\)360\({}^{\circ}\) clockwise represents the azimuth angle of the satellites, and the length of the arrow represents the cosine of the elevation angle. In total, 47 satellites were observed for the station, including 8 GPS satellites, 6 GLONASS satellites, 7 Galileo satellites, 18 BDS satellites, 7 LEO constellations with 288 satellites, and 1 LEO constellation with 60 satellites. The BeiDou navigation system has more visible satellites in the Asia-Pacific region. The LEO constellation, with 60 satellites only, has one visible satellite, which is related to the purpose for which the constellation was designed. Sixty satellites were primarily designed from a communications perspective, ensuring that they can be seen from anywhere in the world. L288 is comparable to GPS in terms of the number of visible satellites on the same station, although it has a greater total number of satellites. The multisystem combination is richer in the number of observations and more uniform in its distribution. Therefore, the LEO constellation can enrich the data sources for tomography. In traditional tomography, in order to obtain reliable results and solve the ill-posed problem of the tomography equation, it is necessary to assume that the spatial distribution of water vapor does not change within a certain period (usually 30 min). Thus, enough observations can be obtained by extending the observation time. Figure 10 shows the distribution of GPS and L288 visible satellites during the 30-min observation period at  
Figure 8: Relationship between water vapor density and altitude calculated from radiosonde data from 2016 to 2017. Figure 9: An epoch observation ray distribution received by a GNSS station. HKSC station. From Figure 10a, it is shown that at HKSC station and at 12 o'clock UTC time, six GPS satellites can be seen during the entire 30-min observation period. Figure 10b is the visible satellite distribution of L288. In the L288, 17 LEO satellites can be successively observed during the entire observation period. It can also be seen, from the figure, that some LEO satellites only take about 7 min from entering to leaving the tomographic area. This shows that LEO satellites have the characteristics of rapid geometric movement. Then, GPS satellites have high orbits, slow angular velocity, and slow geometric changes. Even if the observation time is 30 min, the observation rays of the six satellites are still within the tomographic range. This situation will cause GPS satellite rays to always pass through the same voxel repeatedly, and cause many identical equations in the tomographic design equation. This not only increases the ill-posedness of the inversion of the tomographic design equation, but also increases the time to build the tomographic model, and even increases the computational load. This shows that simply increasing the observation time, although increasing the number of collected observation rays, will also bring many invalid repeated observations. The distribution of all the observed GPS rays at a station is shown in Figure 11a. The position of the rays varied with the motion of the satellite, within 30 min. The length of the trajectory of a GPS satellite across the sky within 30 min was finite, leading to the rays only being within a finite number of voxels. In addition, the distribution of the L288 rays is given in Figure 11b. The distribution of these rays was more extensive than that of the GPS, reaching the edge of the voxel due to the rapid motion of the LEO satellites. Furthermore, 30 min was a sufficient amount of time for the LEO satellites to enter and leave the study area.