## 3 Effect of Fixed-Altitude Heterogeneous LEO Constellations on CIT
### Results of Geometric Distribution of Rays  
The spatial distributions of GNSS observations and GNSS + 192 LEO satellites observation rays at 300 km altitude at 00:00:00 UT on 19 March 2024 is given in Figure 2. When only GNSS observations are used for the discretized grid delineation, the GNSS rays show an approximately vertical (i.e., limited variation in elevation angle) form globally and the rays are more sparsely distributed. When 192 LEO satellites at an altitude of 300 km are added, the area below 300 km is significantly increased with different elevation angle observation rays from ground-based GNSS stations to LEO satellites, i.e., the red rays in Figure 2. At the same time, the observation rays from LEO satellites to GNSS satellites are also increased in the region above 300 km, which is equivalent to adding 192 virtual reference stations at 300 km; this significantly increases the denseness of the ray distribution in the region above 300 km. \begin{table}
\begin{tabular}{c c} \hline \hline
**Items** & **Design Parameters** \\ \hline Top ionosphere & NeQuick \\ F2 layer model & URSI foF2 \\ D layer model & D-reg-IRI-1990 \\ hmF2 model & Shubin-COSMIC \\ Ion model & RBV10 + TBT15 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: IRI2020 model parameters. The number of ray-crossing voxels for GNSS and GNSS + 300 km altitude LEO satellites at 00:00:00-00:00:10 UT on 19 March 2024 is given in Figure 3. It can be determined that the number of ray-crossing voxels at each altitude is the least when only GNSS rays are used, the total number of voxels containing observational rays is 70,939, and while the total number of voxels containing observational rays increases by 8448 when 15 LEO satellites are added; this is 468, 2793, 3602, and 1585, respectively, at different altitude intervals (100-300 km, 300-500 km, 500-800 km, and 800-1000 km). When the number of LEO satellites added reaches 96, the number of ray-crossing voxels in the altitude intervals above 300 km (300-500 km, 500-800 km, and 800-1000 km) are 20,363, 30,620, and 20,253, respectively, but after the number of LEO satellites is increased to 192, the number of ray-crossing voxels in this altitude interval does not increase. On the contrary, the number of radially covered voxels decreased by 112, 72, and 34, respectively, and the number of radially covered voxels increased by 506, but only in the altitude interval from 100 km to 300 km. This may be due to the overlap between the LEO and GNSS rays, which together cross the same voxel. Since LEO satellites are positioned at an altitude of 300 km while GNSS satellites orbit at approximately 20,200 km, the ray paths form an inverted conical shape. As a result, rays are denser near the LEO satellite orbit, while they become more dispersed at higher altitudes, leading to slightly reduced ray overlap. This explains the progressively smaller difference in the number of ray-crossing voxels between 96 and 192 LEO satellites across the altitude intervals of 300-500 km, 500-800 km, and 800-1000 km. Alternatively, it could be due to the different constellation structure of the 96 LEO satellites compared with the 192 LEO satellites, which could also lead to differences in the number of ray-crossing voxels. Figure 3 shows only the number of ray-crossing voxels from LEO satellites increasing at an altitude of 300 km, and we count in Figure 4 the percentage gain of increasing the number of ray-crossing voxels from LEO satellites for different numbers of LEO satellites at altitudes of 300 km, 500 km, 800 km, and 1000 km, respectively, compared to the observations using only GNSS. First, according to the overall percentage gain, it can be seen that the number of ray-crossing voxels increases after adding LEO satellites at different altitudes, and the plan of adding LEO satellites at an altitude of 300 km has the largest gain, at close to 20% when 60 LEO satellites are added.