# Improved PPP Ambiguity Resolution with the Assistance of Multiple LEO Constellations and Signals
## 3 Results
### PPP AR with the Augmentation of Multi-Frequency LEO Observation
#### 3.2.1 PPP AR with the Different LEO Constellation  
Figure 6 shows the positioning errors of GPS, BDS, and GREC PPP fixed solutions at station ASCG on 1 January 2017. The blue, green, and red lines refer to the results of GPS, BDS, and GREC, respectively. For single-system PPP ambiguity resolution, it takes about 30 min to achieve an accuracy of millimeter-level in all three components. Compared to the single-system PPP AR, the GREC PPP AR presents obviously faster convergence. It requires approximately 8 min to achieve the first fix. The inclusion of LEO constellation can shorten the convergence of the PPP float solutions, which has been proved in previous studies [14; 15]. It is anticipated that the PPP ambiguity resolution can also be improved with the augmentation of LEO satellites. The static GREC PPP fixed solutions with the inclusion of 0, 60, 192, and 288 LEO satellites at stations ASCG, CEBR, and YEL2 are shown in Figure 7. It can be obviously found that the inclusion of LEO satellites can significantly shorten the initialization time of multi-GNSS PPP AR. Furthermore, a shorter initialization time can be achieved with more visible LEO satellites. With observations of the 288-LEO constellation, the GREC fixed solutions can converge to 5 cm in all three directions within 1 minute for all three stations. The corresponding total  
Figure 5: Residual distribution of narrow-lane UPDs for GPS, GLONASS, Galileo, BDS, and LEO. numbers of visible satellites (NSAT) and the position dilution of precision (PDOP) values are also shown in Figure 7, respectively. Taking the YEL2 station as an example, the average NSAT and PDOP are 35.6 and 0.8 for the GREC solution. With the augmentation of 60-, 196-, and 288-LEO constellations, the corresponding NSAIDs increase by 4.6, 13.3, and 19.9, respectively, while the averaged PDOP values decrease to 0.78, 0.70, and 0.66, respectively. In addition, the NSAT and PDOP values change quickly with the inclusion of LEO satellites. The results demonstrated that the inclusion of LEO constellation can increase visible satellites and optimize the spatial geometry, which is beneficial for the rapid ambiguity resolution of PPP. The averaged TTFF of LEO-augmented PPP fixed solutions of all user stations was calculated and the corresponding results are shown in Table 1. We can see that the inclusion of LEO satellites can significantly shorten the TTFF for single- and multi-GNSS PPP ambiguity resolution and more LEO satellites will contribute to shorter TTFF. The TTFF of GPS-only and BDS-only PPP ambiguity resolution is 17 and 15.9 min, respectively, which can be improved to 0.94 and 0.99 min with the augmentation of 288-LEO constellation, with the improvement of 94.4% and 93.7%, respectively. As for the GREC fixed solutions, the TTFF can be shortened from 7.1 to 4.8, 1.1, and 0.7 min by introducing observations of 60-, 192-, and 288-LEO constellations. With the augmentation of the 288-LEO constellation, the TTFF values of GPS, BDS, and GREC PPP AR are all less than 1 min. Moreover, for GREC PPP AR, with the 288 LEO satellites, it only takes about 40s to achieve the first ambiguity resolution. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**LEO**} & \multicolumn{2}{c}{**GPS**} & \multicolumn{2}{c}{**BDS**} & \multicolumn{2}{c}{**GREC**} \\ \cline{2-7}  & **TTFF** & **Reduction** & **TTFF** & **Reduction** & **TTFF** & **Reduction** \\ \hline
0 & 17 & 0\% & 15.9 & 0\% & 7.1 & 0\% \\
60 & 7.4 & 56.4\% & 6.4 & 59.7\% & 4.8 & 32.3\% \\
192 & 1.4 & 91.7\% & 1.3 & 91.6\% & 1.09 & 84.6\% \\
288 & 0.94 & 94.4\% & 0.99 & 93.7\% & 0.70 & 90.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: TTFF of GPS, BDS, and GREC PPP AR without or with the augmentation of 60, 192, and 288 LEO satellites (unit: min). Figure 6: Static PPP AR solutions of GPS, BDS, and multi-GNSS (GREC) at station ASCG from 19:00 to 20:00 on 1 January 2017.