# An Approach to Speed up Single-Frequency PPP Convergence with Quad-Constellation GNSS and GIM
## 4 Single-Frequency PPP Processing Results and Analysis
### Convergence Performance Assessment  
In order to assess the convergence time of our proposed single-frequency PPP approach, the convergence time of GPS-only PPP, GPS/GLONASS PPP, and GPS/GLONASS/BDS/Galileo PPP are compared with the quad-constellation GNSS plus GIM PPP using datasets collected at twelve MGEX stations over seven consecutive days during 4-10 September 2016. In this study, the position filter is considered to have converged when the absolute values of the positioning errors in the horizontal directions reach 0.3 m and keep within 0.3 m. Given that the PPP errors in the height component are relatively larger than its horizontal components, the convergence criterion in the vertical directions is enlarged to 0.5 m. The convergence time is the period from the first epoch to the converged epoch. For each day, datasets are divided into five-hour sessions to ensure convergence of position solutions so each day includes four complete sessions. Datasets in each session are processed independently. As the DYNG dataset on 5 September 2016 is missed, a total of 332 sets of results are obtained to derive a statistical estimate on the convergence time as well as the positioning accuracy. The distribution of the 332 sets of convergence time in the east, north and up components is plotted in unit of minutes in Figure 6. It is visible that the GPS/GLONASS combination distinctly reduces the convergence time over the GPS-only PPP. This convergence time is further reduced in the quad-constellation PPP, but to a slight degree. In conjunction with the GIM data, the convergence time is significantly decreased especially in the horizontal directions. Using our proposed single-frequency PPP approach, the horizontal position solutions accounting for over 25% can converge within 5 min. The reason why the convergence performance can be improved after the GIM data is introduced is because the correlations among parameters of the IHD, receiver clock offset and ambiguities are decreased. The vertical direction is more sensitive to the ionospheric errors. As a result, the improvement in the vertical direction is less significant than the horizontal directions due to the limited accuracy of the GIM data. Table 2 lists the convergence time of single-frequency PPP for different processing scenarios. The percentages in the brackets refer to the improvement over the GPS-only case. The average convergence time for the GPS-only case is 68 min, 43 min, and 93 min in the east, north, and up directions. With the integration of GPS and GLONASS, the convergence time is reduced by 38%, 42%, and 34% in the three directions, respectively. Using our proposed single-frequency PPP approach, the convergence time is further improved down to 30 min, 23 min, and 55 min in the east, north, and up directions. Compared to the GPS-only case, the improvement rate reaches 56%, 47%, and 41% in the three directions, respectively. It is noted that the east coordinate component needs longer convergence time than the north coordinate component for the reason of the satellite constellation configuration [17]. As a result, the improvement of the convergence time in the east direction is more significant after adding GIM data. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & **GPS** & **GPS/GLO** & **GPS/GLO/BDS** & **GPS/GLO/BDS/GAL** & **GPS/GLO/BDS/GAL+GIM** \\ \hline FTNA & East & 0.053 & 0.001 & 0.001 & 0.002 & 0.009 \\  & North & 0.005 & 0.006 & 0.006 & 0.008 & 0.010 \\  & Up & 0.008 & 0.027 & 0.028 & 0.025 & 0.016 \\  & 3-D & 0.054 & 0.027 & 0.029 & 0.026 & 0.020 \\ \hline SEGY & East & 0.065 & 0.059 & 0.062 & 0.058 & 0.067 \\  & North & 0.030 & 0.017 & 0.017 & 0.017 & 0.014 \\  & Up & 0.037 & 0.060 & 0.060 & 0.051 & 0.036 \\  & 3-D & 0.081 & 0.086 & 0.087 & 0.079 & 0.078 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: RMS statistics of single-frequency PPP coordinate deviations for five different processing scenarios (m).