# Integrity Monitoring of PPP-RTK Positioning: Part II: LEO Augmentation
## 2 Measurement Geometry under LEO Augmentation
### Satellite Numbers  
With more constellations contributing to the positioning service of the same user, the measurement geometry and the positioning precision can with no doubt be improved. Figure 3 are colormaps of the mean visible GNSS + LEO satellite numbers, transmitting signals on L1 and L5 frequencies, in \(5^{\circ}\times 5^{\circ}\) grids on a daily basis, calculated with a sampling interval of 10 min. The international GNSS service (IGS) [30] multi-GNSS experiment (MGEX) [31] orbits from the center for orbit determination in Europe (CODE) [32] on 26 June 2021, were used for the plots, which did not include the BDS GEO satellites. The elevation mask is set to 5 degrees. The LEO satellite configuration introduced in Section 2.1 is used for generation of the plots. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Layer** & \(\mathbf{H}\) [km] & \(\mathbf{N}\) & \(\mathbf{P}\) & \(\mathbf{F}\) & \(\mathbf{I}\) [\({}^{\circ}\)] \\ \hline A & 975 & 120 & 12 & 0 & 55 \\ \hline B & 1100 & 30 & 3 & 0 & 87.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Details of the tested LEO satellite constellation. \(H\) is the orbital height. \(N\) and \(P\) denotes the number of satellites and orbital planes in the corresponding layer, respectively. \(F\) describes the phase shift between adjacent planes, and \(I\) denotes the inclination. Figure 2: The tested LEO constellation (see Table 1) around the Earth. The red and yellow lines represent layers A and B, respectively. From Figure 3, it can be observed that adding the proposed LEO constellation (right-bottom subplot) has increased the visible satellite numbers to around or more than 30 in most places in the world. The distribution of the satellite numbers is generally latitude-dependent. Figure 4 illustrates in a colormap the number of simultaneously visible LEO satellites on a daily average basis with an elevation mask of 5 degrees. The latitude-related colors show that the proposed LEO constellation is especially beneficial to the mid-latitude areas. Several large cities are marked in the figure as examples. It can be observed that Moscow, Beijing, New York, Los Angeles and Berlin are all within the red areas, i.e., having more than nine satellites simultaneously visible on average. The LEO satellites under the given configuration, however, are mostly visible at low elevation angles. Taking Beijing as an example, as shown in Figure 5, a much more rapid  
Figure 4: Daily averaged number of the simultaneously visible satellites of the tested LEO constellation. Figure 3: Colormaps of the daily mean numbers of satellites transmitting signals on L1 and L5. decrease can be observed in the LEO satellite numbers compared to other constellations when increasing the elevation mask. For an elevation cut-off angle of 10 degrees, the visible LEO satellite number is decreased to about 7. Still, it can be observed that for elevation masks smaller than 20 degrees, the number of visible LEO satellites is higher than that of the current L1/L5 GPS satellites. The different nature of the LEO and GNSS signals do show advantages for LEO-augmented positioning in complicated measurement environments such as urban canyons. In such environments, GNSS signals under low elevation angles are partially blocked by high infrastructures around the receiver, leading to a limited visible area only for satellites of high elevation angles. The other tracked signals from low elevation angles are often disturbed by high multipath effects, which bias the results and are often screened out or strongly down-weighted in the positioning. All these are more or less equivalent to manually setting a high elevation mask in the processing. Benefiting from the much lower orbital altitude, the LEO signals occupy a much stronger signal strength than the GNSS signals, which helps the LEO signals penetrate obstacles and possibly enable even indoor positioning [7]. In addition, the fast speed of LEO satellites whitens the multipath effects around the user [6].