# Integrated Precise Orbit Determination of Multi-Gnss and Large LEO Constellations
## 4 Result Analysis and Discussion
### Integrated POD with Partial LEO Constellation  
The previous results demonstrate the strong enhancement of the entire LEO constellation to the GNSS orbit estimation. However, it can be seen that the integrated POD suffers from a long computation time when a large number of LEO satellites are introduced. The computation time of the 60-LEO scheme is about 13 h, while for 96-LEO scheme, it reaches about 38 h. Only moderate accuracy differences are obtained for the 60-, 66- and 96-LEO constellations. In order to balance the conflict between orbit accuracy and computational efficiency, it is worthwhile to investigate the integrated POD with a partial LEO constellation, and to explore how many LEO satellites can be used as an auxiliary to improve the orbit accuracy of GNSS satellites. In this section, we process the observation from 65 MGEX stations and a partial LEO constellation. The 60 polar-orbiting LEO constellation and 60 sun-synchronous-orbiting LEO constellation at an altitude of 1000 km are chosen.  
Figure 12 shows the average 3D RMS of GNSS orbit differences for the integrated POD as a function of the number of LEOs. We find that with only adding 10 LEO satellites, BDS GEO satellite orbits can already achieve an accuracy of better than 10 cm, while the orbit differences of other satellites are below 2 cm. The corresponding computation time is less than 2 h (shown in Figure 13). This result indicates that the introduction of a small number of LEO satellites can not only obtain a relatively high accuracy GNSS orbit, but that it also limits the computation time, which is very beneficial to the GNSS application with high timeliness requirements. For both, the orbit differences of GNSS satellites decrease monotonically as the number of introduced LEO satellites increases. However, with more LEO satellites included, the improvement of orbit accuracy gradually becomes smaller. A reduction of about 0.5-4 cm can be observed in the orbit differences when the LEO increases from 10 to 20, whereas the additional 10 LEO satellites can only contribute to an accuracy improvement of less than 0.2 cm as the LEO increases from 40 to 50. On the other hand, the increase of LEO satellites introduces a large number of parameters to be estimated, resulting in a steep rise in computational time (shown in Figure 13). For example, the computation time of the integrated POD greatly rise from 9.46 h to 13.42 h when the LEO number increases from 50 to 60. But the addition of 10 LEO satellites only yields an orbit accuracy improvement of about 1 mm for the majority of GNSS satellites.  
Figure 12: Average 3D RMS of GNSS orbit differences for the integrated POD with different numbers of LEO satellites.  
In addition, it can be seen that the sun-synchronous LEO satellites exhibit a stronger enhancement to the GNSS orbits than those in nearly-polar orbit, no matter how many LEO satellites are introduced. The accuracy differences between the sun-synchronous LEO scheme and nearly-polar LEO scheme is very small for the GPS, GLONASS, Galileo, BDS IGSO, and MEO satellites. This is because the relative motion between these satellites and ground stations already yields good geometric diversity, so that the small contribution differences in tracking geometry between sun-synchronous LEO and nearly-polar LEO satellites have little impact on the orbit determination of these satellites. However, differences of more than 1 cm are visible in the BDS GEO orbits between the two solutions. Evidently, the combination of global stations and sun-synchronous LEO satellites result in better quality GEO orbits. This is because LEO satellites in sun-synchronous orbit can give rise to faster variations of observation geometry for BDS GEO satellites (see Figure 8).