# BeiDou Augmented Navigation from Low Earth Orbit Satellites
## 4 Results and Discussion
### Pdop  
The PDOP indicates the positioning accuracy theoretically, and is related to the number of satellite tracked as well as the distribution of satellites. In general, the smaller the PDOP value is, the better accuracy for positioning is. Similar as calculation of satellite visibility, the averaged PDOP with 24 h data for the location in the center of each \(5^{\circ}\times 5^{\circ}\) grid is obtained with with 0 mask elevation and 30 s data sampling interval. Figure 4 demonstrates the global distribution of the PDOP for BeiDou-3 only and BeiDou-3 (Figure 4a) as well as LEO constellation (Figure 4b). Similar as satellite visibility, the PDOP is distributed symmetrically in Northern hemisphere and Southern hemispheres, but unevenly in the Eastern hemisphere and Western hemisphere. For BeiDou-3, the PDOP value reaches a minimum of 1.2-1.3 in the low latitudes of Asia-Pacific region, where is the great tracking ability for the three GEO and three IGSO satellites. In most areas of China, the PDOP value is about 1.5. As less satellites can be tracked, the mid-latitude regions of the north and south Americas have the largest PDOP up to 2.2. The poor positioning ability (with PDOP up to 2.2) in the north and south pole region is related to the configuration of BeiDou-3 satellites, as above mentioned, the \(55^{\circ}\) orbit inclination of MEO satellites limits the satellite visibility in these regions, resulting in larger PDOP.  
Once the LEO satellites have been used to augment the BeiDou-3, the navigation service performance in mid-latitude regions has been significantly improved. The PDOP values in the Asia-Pacific region were around 1, and low-latitude and mid-latitude show similar performance. For PDOP in the mid-latitude region of north and south Americas, it has been reduced to approximate 1.2 from abound 1.8. Thanks to the \(55^{\circ}\) orbital inclination used for LEO satellites, the PDOP has been improved to about 1.2 in the region with latitude about \(55^{\circ}\) and \(-55^{\circ}\). However, limited improvement is identified in low latitude region of north and south Americas as well as the pole regions. In statistics, as listed in Table 6, the maximum PDOP value was reduced from 2.24 to 1.93, the minimum PDOP value was decreased from 1.19 to 1.01, and the average PDOP value was reduced from 1.63 to 1.22. This again confirms that the LEO constellation can greatly improve the performance of BeiDou-3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Constellation** & **Max. PDOP** & **Min. PDOP** & **Avg. of PDOP** \\ \hline
3 GEO + 3 IGSO + 24 MEO & 2.24 & 1.19 & 1.63 \\
3 GEO + 3 IGSO + 24 MEO + 120 LEO & 1.93 & 1.01 & 1.22 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Statistical results for PDOP.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Constellation** & **Max. \# of Tracked** & **Min. \# of Tracked** & **Avg. \# of Tracked** \\  & **Satellites** & **Satellites** & **Satellites** \\ \hline
3 GEO + 3 IGSO + 24 MEO & 15.5 & 7.6 & 10.7 \\
3 GEO + 3 IGSO + 24 MEO + 120 LEO & 21.6 & 10.1 & 16.3 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Statistical results for satellite visibility.