## 4 Assessment and Analysis of LeGNSS Precise Positioning
### Assessment and Analysis of LeGNSS PPP Performance  
In order to fully demonstrate the contribution of the LeGNSS system to PPP solutions, four stations located at P1 (80\({}^{\circ}\)S, 30\({}^{\circ}\)W), P2 (0\({}^{\circ}\)S, 30\({}^{\circ}\)W), P3 (30\({}^{\circ}\)N, 120\({}^{\circ}\)E), and P4 (75\({}^{\circ}\)N, 120\({}^{\circ}\)E) are adopted for the kinematic mode of PPP tests with GPS-only, GPS/BDS (G/C), GPS/LEO (G/L), and GPS/BDS/LEO (G/C/L) (i.e., the LeGNSS system). The locations of the stations are shown in Figure 3. In this study, the convergence time of the positioning solution is defined as the time when the positioning errors for each component reaches \(\pm\)10 cm and stays within that value. As clearly shown in Figure 4, the time span of each GPS satellite differs from locations. For higher latitude location, e.g., P1, the GPS time span of every pass is shorter than that at lower latitude location, such as P2 where the time span is almost 8-10 h. The visibility is very different for the various orbital types, especially for the regional satellite system. At station P2, some BDS MEO satellites are tracked while most of the BDS satellites are tracked at stations P3 and P4 because they are located within the current BDS service region. For P1, BDS GEO cannot be observed, while all the IGSO and MEO can be tracked. The time span is also different depending on the orbital types. The BDS GEO satellites have the longest tracking periods. The BDS IGSO satellites are tracked relatively shorter than those of GEO satellites with data gaps of about 5 h at low latitude for one day. The tracking periods of BDS MEO satellites are the shortest compared to GEO and IGSO satellites. Figure 3: The location of four stations. The tracking period of LEO satellites is shown in Figure 5. We can easily see the very short time span of LEO satellites with respect to the ground station. It is only about 5-10 min and much shorter than that of GNSS satellites. This is mainly because of the low Earth orbit of LEO satellites, causing the fast motion with respect to the ground stations. Such fast motion gives an opportunity to shorten the convergence time. On the other hand, since the LEO satellites are usually polar satellites with the orbital period of about 1.5 h, every LEO satellite in one orbit plane would be tracked by polar stations for every 1.5 h, e.g., P1 and P4. Thus, stations at high latitude can track one specific LEO satellite by more than ten times a day, e.g., P1 and P4, while only four to five times for stations in low and medium latitude, e.g., P2 and P3 because of the polar orbit and small footprint of LEO satellites, which were already mentioned in the section of satellite visibility and availability. To clearly show the convergence process for different situations, one hour of data of these four stations is calculated as an example. Figure 6 shows the sky plots (azimuth (0-360\({}^{\circ}\)) vs. elevation (0-90\({}^{\circ}\))) of GPS, BDS, and LEO, respectively. The elevation variations of GNSS satellites are generally from 0\({}^{\circ}\) to 30\({}^{\circ}\) over one hour, while those of LEO satellites are quite large and from 1 to 90\({}^{\circ}\). In particular, the sampling interval between adjacent dots are 30 s. As we can see, the elevation change of a LEO satellite can reach up to 5\({}^{\circ}\), or even 20\({}^{\circ}\) over 30 s.  
This fast motion can also be observed from the quick variation of GDOP values. Figure 7 shows the number of satellites and their corresponding GDOP values for different combinations of four stations. These four stations can generally observe seven to ten GPS satellites and the GDOP of GPS-only is generally from 2 to 4. The number of tracked BDS satellites mainly depend on the location of stations since BDS provides service only in Asia-Pacific areas currently. The GDOP values of G/C are much smaller than those of GPS-only, except for stations P1 and P2.