# Integrated Precise Orbit Determination of Multi-Gnss and Large LEO Constellations
## 4 Result Analysis and Discussion
### Integrated POD with Full LEO Constellation  
#### 4.1.1 Integrated POD with Different Numbers of LEO  
We firstly performed the integrated POD using global network from MGEX. The ground observations from the 120-station MGEX network are processed as a reference. In order to make a fair comparison, only a 65-station network with a good global distribution from the MGEX we selected is used to perform the integrated POD (shown as red dots with a black circle edge in Figure 2). The onboard observations from 60, 66, and 96 polar-orbiting LEO satellites with altitudes of 1000 km (see Figure 1a,b,d) are processed to investigate the influence of LEO numbers on the integrated POD. Figures 3-6 present the average 3D Root Mean Square (RMS) values of orbit differences between integrated POD solution and true orbits for all satellites from GPS, GLONASS, Galileo, and BDS constellations respectively. The result shows that by using only the ground multi-GNSS observations, the majority of GNSS satellites can achieve a 3D orbit accuracy of better than 4 cm, which is comparable to the accuracy of the 24-h orbit recovered from the real ground tracking measurements. This demonstrates that the error models and simulation strategy are close to the real situation. Table 4 computes the average 3D RMS of orbit differences for four systems. The worst orbit quality can be found in BDS GEO, and the average 3D RMS values of orbit differences even exceeds 2 m. This is reasonable, because the stationary and regional coverage feature of GEO satellites lead to poor tracking geometry, greatly hampering the orbit determination for GEO satellites. Figure 3: Average 3D RMS values of GPS orbit differences for the integrated POD with different numbers of LEO satellites. P denotes the nearly-polar orbit of the LEO constellation. Figure 4: Average 3D RMS values of GLONASS orbit differences for the integrated POD with different numbers of LEO satellites. Figure 5: Average 3D RMS values of Galileo orbit differences for the integrated POD with different numbers of LEO satellites. As shown in Figures 3-6, all satellites providing global coverage can achieve a sub-centimeter level orbit with the support of LEO onboard observations, while the orbit accuracy of regional coverage satellites (BDS GEO and IGSO) is at the centimeter level. It can be seen that LEO satellites can make more contributions to GNSS orbits than the same numbers of ground stations, since they can not only provide high-quality observations, but also improve the geometry diversity. The orbit of GNSS satellites obtains a remarkable accuracy improvement after introducing the LEO observations into the POD processing. The accuracy improvement with respect to the ground-based POD result can reach over 70% for all of 60 LEO-, 66 LEO-, and 96 LEO-augmented POD schemes (as shown in Table 4). This indicates that the onboard data from the large LEO constellations can be an important supplement to the GNSS POD, even under the condition of a global network. We find that the BDS GEO satellites present the largest accuracy improvement when the integrated POD is implemented; the improvement percentage even reaches up to about 98%. This inspiring result evidences the contribution of LEO to improve the tracking geometry of GEO satellites. Furthermore, it can be seen that smaller orbit differences can be achieved when more LEO satellites are introduced into the integrated POD. The 96-LEO solution achieves a slightly better orbit accuracy than the other two LEO-augmented POD solutions. However, compared with the slight accuracy improvement of the 96-LEO solution, introducing additional 30 LEO satellites into the processing of the integrated POD leads to a huge burden on the computational efficiency because of the larger number of unknown parameters to be solved. The average computation time of integrated POD for the 96-LEO scheme is about 38 h, which is almost three times more than that of 60-LEO and 66-LEO schemes (about 13 h).