# Navigation in GEO, HEO, and Lunar Trajectory Using Multi-GNSS Sidelobe Signals
## 3 Results
### Signal Visibility and GDOP
Mean visible satellites of BDS-3, GPS, Galileo and GLONASS over 24 h were 22.9/19.8/17.0/15.9, respectively. From Figure 12a,b, we can see that three GEO satellites of BDS-3 were about 94.0% time visible during the whole simulation period. This is why the visible satellites of BDS-3 were more than that of GPS. Considering that there were 24 satellites of Galileo and GLONASS, less visible satellites from the two systems are reasonable. Since the Galileo altitude was slightly higher than GLONASS, more signals of Galileo from the other side of the Earth could be received. GDOP of the HEO spacecraft is shown in Figure 13, it rose and fell. We obtained the best satellite geometry near perigee, and the worst satellite geometry near apogee. GDOP of BDS-3 ranged from 0.96-6.64. With GPS included, GDOP decreased to 0.71-5.30. GDOP of GREC combination varied from 0.52-4.42. Mean GDOP of BDS-3, BDS-3/GPS and GREC combination was 3.57, 2.88 and 2.3, respectively. This good satellite geometry also resulted from the large number of visible satellites. For the HEO spacecraft, radi- and zenith-pointing antennas were mounted; therefore, good satellite visibility could be realized. Figure 11: Visible satellites. Figure 10: GDOP of GEO spacecraft. Visible satellites and GDOP of lunar probe with thresholds of 20 and 15 dB-Hz are shown in Figures 14 and 15, respectively. Figure 12: Satellite visibility of HEO. (**a**) Satellite visibility of BDS-3. (**b**) Satellite visibility of GPS. (**c**) Satellite visibility of Galileo. (**d**) Satellite visibility of GLONAS. Figure 13: GDOP of HEO spacecraft. The lunar probe experienced larger signal attenuation than the GEO and HEO spacecraft. It received most signals near departing epochs, then the visible satellites decreased as the lunar probe was flying near the moon. We saw that, for the threshold of 20 dB-Hz, with only BDS-3 satellites involved, satellite geometry was rather poor, and the lunar probe could only track about 2 visible satellites as it was moving towards the moon. When more systems were included, the situation of sparse signal was still not improved. Mean visible satellites of BDS-3, GPS, Galileo, and GLONASS over the simulation period, i.e., 76.2 h were 7.7/ 4.9/ 3.5/ 3.1, respectively. As the receiver threshold increased to 15 dB-Hz, we could see that there was a significant increase in visible satellites. However, the satellite geometry was still poor for BDS-3 only. It improved as GPS was combined with BDS-3. When four systems were included, the GDOP decreased further and reached a maximum of 3392. Mean visible satellites of BDS-3, GPS, Galileo and GLONASS were 13.0/ 8.6/ 6.3/ 5.8, respectively. GEO and IGSO satellites of BDS-3 were 47.4% visible during the whole simulation time, which was almost twice compared with the MEO satellites from BDS-3, GPS, Galileo and GLONASS. Unlike the GEO and HEO spacecraft, signal reception interruption was likely to happen for the lunar probe. As shown in Table 8, with a receiver threshold of 20 dB-Hz, the lunar probe could not track 1 or 4 satellites continuously for all the combinations. When mainlobe and sidelobe signals were both considered, the availability of at least 1 BDS-3 satellite was almost the same as the B2 signal in Table 8 of ref [30], in which real BDS 3D antenna patterns were used. The availability of at least 4 BDS-3 satellites was slightly higher than the results of all the signals in Table 8 of ref [30]. When the receiver threshold improved to 15 dB-Hz, the lunar probe was able to receive at least 1 satellite continuously for all the combinations. Meanwhile, BDS-3/GPS and GREC combinations were able to offer four visible satellites continuously. Due to the large GDOP of these conditions, it  
Figure 8.0 Visible satellites and GDOP of lunar probe with 20 dB-Hz threshold. Figure 8.1 Visible satellites and GDOP of lunar probe with 15 dB-Hz threshold. made no sense to discuss position, velocity, and time navigation performances, even if there were at least four visible satellites.