# Navigation in GEO, HEO, and Lunar Trajectory Using Multi-GNSS Sidelobe Signals
## 5 Conclusions  
To explore the navigation performance of BDS-3 and the contribution of multi-GNSS, pseudorange observations were simulated for three classical types of orbits, including GEO, HEO and lunar trajectory. Based on available GNSS transmitter antenna pattern and two receivers in nadir and zenith direction, C/N0 were calculated in order to determine the visible satellites. Number of observations show that 92.4%, 86.5% and 86.8% of the received signals are sidelobe signals for GEO, HEO and lunar trajectory, respectively (The GEO and HEO spacecraft were evaluated with a threshold of 20 dB-Hz and lunar probe with 15 dB-Hz). Even BDS-3 only can ensure a continuous navigation solution for GEO and HEO. On the other hand, to ensure a continuous navigation solution for a lunar probe, it was necessary to combine BDS-3 with GPS or other GNSS systems, with a receiver threshold of 15 dB-Hz. All three space vehicles received more BDS-3 signals, owing to the GEO and IGSO satellites. Meanwhile, Galileo provided more visible satellites than GLONASS due to the smaller Earth block angle. With only BDS-3 signals considered, mean visible satellites were 25.4 and 22.9 for the GEO and HEO spacecraft, respectively, yielding mean GDOP  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Position (km)** & **BDS-3** & **BDS-3/GPS** & **GREC** \\ \hline X & 2.419 & 2.053 & 1.779 \\ Y & 3.540 & 2.016 & 1.914 \\ Z & 0.471 & 0.291 & 0.276 \\
3D & 4.313 & 2.892 & 2.628 \\ \hline \hline \end{tabular}
\end{table}
Table 11: RMS of Position with different system combinations.  
Figure 18: Differences between GREC SPP and the nominal lunar trajectory.  
of 3.4 and 3.6. Combining GPS with BDS-3, the positioning accuracy increased by 18.6% and 6.1%. For the lunar probe, signal geometry was less optimistic. All the combinations cannot provide a continuous navigation solution with a receiver threshold of 20 dB-Hz. The best signal geometry was provided by the GREC combination, which produced a max GDOP of 3392 when receiver sensitivity was 15 dB-Hz.  
Our investigation indicates that BDS-3 is capable of providing good navigation performance for the GEO and HEO spacecraft. For lunar missions, the SPP accuracy delivered by GREC combination was rather poor, even with 15 dB-Hz receiver thresholds. Significant improvements on SPP accuracy are hard to realize due to the high GDOP; therefore, a software receiver with an orbital filter or GNSS/INS/Star tracker integration may be necessary for lunar missions. Last but not least, the lunar mission discussed in this paper only covered the trajectory that moved from the Earth to the Moon. The realistic lunar mission included lunar orbits, final descent, and landing phase, which may require other navigation sensors or lunar navigation infrastructure; it is an interesting topic to investigate in the future.  
Conceptualization, M.G. and T.X.; methodology, M.G.; formal analysis, M.G., M.L., F.G. and D.M.; writing--original draft preparation, M.G.; writing--review and editing, T.X., M.L., F.G. and D.M.; funding acquisition, T.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Key Research and Development Program of China (2020 YFB0505800 and 2020 YFB0505804), National Natural Science Foundation of China (41874032 and 41704018).  
Not applicable.  
The authors would like to thank the Lockheed Martin Space Systems Company for publishing the GPS antenna patterns.  
The authors declare no conflict of interest.