# GNSS Real-Time Precise Point Positioning in Arctic Northeast Passage
## 3 Results
### RT-PPP Performance in NEP
#### 3.2.2 Performance of SF RT-PPP in the NEP  
Although multi-GNSS data can be collected by low-cost receivers, some of them can only obtain the single-frequency data of a certain system. Therefore, we took an SF RT-PPP model into account to evaluate performance in the Arctic regions. Table 5 summarizes the multi-GNSS SF RT-PPP data processing strategies.  
We used the data collected by the M/V TIANHUI from 10:00 to 22:00 on 12 September 2019 to evaluate the positioning performance of SF RT-PPP in the NEP. We analyzed single-GPS and multi-GNSS combinations of SF RT-PPP performance in this section. Due to the lack of reference base stations in polar regions, we obtained the reference solutions by post-processing PPP based on GBM products. Figure 9a,b show the position errors in the east, north, and up components, as well as the NSAT and PDOP values of GPS and multi-GNSS. In the east direction, both the GPS and multi-GNSS of the SF RT-PPP can achieve meter-level positioning accuracy, and the combined precision is slightly higher than that of GPS. However, we observed large fluctuations for GPS in the north and up directions, and the errors are even greater than 10 m in the north. Moreover, multi-GNSS is more stable and meter-level accuracy can be realized in each direction because the number of combined GNSSs are twice that of GPS, and they also have a better satellite space structure. Although GPS always has six or more satellites, the PDOP values are occasionally larger and show more variations than the multi-GNSS.  
Figure 10 illustrates the 11-day RMS values of SF RT-PPP positioning results in the east, north, horizontal, up, and 3D components. The GPS SF RT-PPP solution is shown in blue while the combined solution is in red. The positioning accuracy of the north component is lower than that of the east. In addition, the accuracy in the north is roughly equivalent to that in the vertical direction, resulting in a lower horizontal precision. This phenomenon is due to the poor north-south structure of the GNSS satellites in the NEP.  
Table 6 shows the mean RMS values in each direction of SF RT-PPP in the NEP. In general, the accuracy of SF RT-PPP is significantly improved by using multi-GNSS--an increase of approximately 29.3% in 3D, from 7.268 m to 5.138 m. In the east and north coordinates, 20.6% and 27.0% improvements are achieved, revealing an improvement of approximately 26.0% in the horizontal component after the combination. Moreover, the vertical direction shows an improvement of approximately 32.5%.  
\begin{table}
\begin{tabular}{l l l} \hline \hline  & **STD (ns)** & **RMS (ns)** \\ \hline GPS & 0.130 & 0.332 \\ GLONASS & 0.623 & 3.622 \\ Galileo & 0.084 & 0.254 \\ BDS & 0.346 & 0.802 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Eleven–day mean STD and RMS values of CLK93 products’ clocks.  
Figure 8: STD and RMS values of CLK93 products’ clocks with reference to the GFZ’s final products.  
Figure 10: RMS values of SF RT–PPP in east, north, horizontal (2D), up, and 3D directions for GPS and multi–GNSS from 10 to 20 September 2019.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Items** & **Models/Strategies** \\ \hline Satellites & GPS/GPS+Galileo+BDS \\ Observations & Uncombined code and carrier–phase measurements \\ Sampling rate & 1 s \\ Elevation cutoff & 10\({}^{\circ}\) \\ Observation weight & Elevation–dependent weight; GPS:Galileo:BDS = 1:1:2 \\ Precise products & CLK93 real–time stream from CNES \\ Satellite antenna phase center & igs14.atx \\ Phase–windup effect & Corrected [24] \\ Ionospheric delay & Klobuchar model \\ Tropospheric delay & GPT2 + GMF \\ Tide effects & Solid Earth + pole + ocean tide \\ Phase ambiguities & Real value \\ \hline \hline \end{tabular}
\end{table}
Table 5: SF RT–PPP data processing strategy.  
Figure 9: (**a**) SF RT–PPP position errors in the east, north, and up directions for the GPS and multi–GNSS; and (**b**) NSAT and PDOP values for GPS and multi–GNSS from 10:00 to 22:00 on 12 September 2019.