## 3 Results
### BDS-3 Joint POD Results Based on Ground-Monitoring Stations and LEO Satellites  
To analyze the effect of different numbers of LEO satellites on BDS-3's space signal [44] enhancement, we simulated three types of LEO satellite constellations, namely LEO12, LEO30, and LEO60. The orbital altitude of all LEO satellites is 975 KM, and they are equally distributed in six orbital planes namely Walker 12/6/1, Walker 30/6/1, and Walker 60/6/1, with an orbital inclination of 55\({}^{\circ}\).  
Both analog ground stations and LEO satellite-monitoring stations can receive navigation signals from the BDS-3 satellites navigation constellation to obtain carrier and pseudorange observation of all visible satellites in the epoch. We added 1.000 m of random noise and 0.030 m of pseudorange systematic error [29; 39], as well as 0.002 m of random noise and 0.030 m of carrier system error, to the simulated observations data, and the orbital arc is 3 days. As shown in Figure 8, the average 3D accuracies of all LEO satellite orbits in 3D are 1.7 cm, 1.6 cm, and 0.6 cm, respectively.  
We used four different schemes, of 7 sta, 7 sta and 12 LEO, 7 sta and 30 LEO, and 7 sta and 60 LEO, for the distribution of the number of LEO satellites for the POD, and counted the average 3D accuracies. The average 3D accuracies of the four schemes were 95.1 cm, 3.1 cm, 2.4 cm, and 2.0 cm, respectively, as shown in Figures 9 and 10.  
As shown in Figure 9, in the seven sta scheme, the orbit accuracy of the BDS-3 satellites is in the decimeter or meter range. In the seven sta + LEO12 scheme, the orbit error of the BDS-3 satellites has been increased from decimeters to centimeters. This shows that the LEO satellite can indeed improve the orbit accuracy of BDS-3. The centimeter accuracy can be achieved using only seven ground monitoring stations and the LEO12 constellation. The experiments show that the LEO satellite, as a highly dynamic mobile station, participates in the orbit of BDS-3, which causes rapid changes in the tracking geometry between satellites and increases the amount of observation data. However, it is worth noting that, as the number of LEO constellation satellites increases, the orbit accuracy gradually improves, but the accuracy improvement becomes smaller and smaller. This is related to the LEO force model and the accuracy limit of orbit determination.  
Figure 8: 3D accuracy of the LEO POD using ground stations combined with different LEO constellations.  
Four different LEO satellite distribution schemes of 7 sta, 7 sta and 12 LEO, 7 sta and 30 LEO, and 7 sta and 60 LEO were used to carry out time synchronization experiments, and as shown in Figure 11, resulting in the average values of RMS1 statistical accuracy of clock offset being 0.72 ns, 0.37 ns, 0.25 ns, and 0.10 ns, respectively. As shown in Figure 12 the average values of RMS2 statistical accuracy of clock offset are 0.68 ns, 0.33 ns, 0.21 ns, and 0.07 ns, respectively. The results show that LEO satellites can improve the accuracy of the BDS-3 satellite's clock offset solution. Compared to the results of clock offset using only ground stations, the addition of 12 LEO satellites resulted in an improvement of 49% for RMS1 and 52% for RMS2, the addition of 30 LEO satellites resulted in an improvement of 66% for RMS1 and 70% for RMS2, and the addition of 60 LEO satellites resulted in an improvement of 87% for RMS1 and 90% for RMS2.  
Figure 10: The 3D accuracy of the BDS-3 POD using ground stations combined with different LEO constellations (Upper limit 20 cm).  
Figure 9: The 3D accuracy of the BDS-3 POD using ground stations combined with different LEO constellations.