# Evaluation of Ionospheric Delay Effects on Multi-GNSS Positioning Performance
## 4 Results and Discussion
### Performance of Single-Frequency PPP
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multirow{2}{*}{**Schemes**} & \multicolumn{3}{c}{**b1**} & \multicolumn{3}{c}{**b2**} & \multicolumn{3}{c}{**b3**} \\ \cline{3-10}  & & **N** & **E** & **U** & **N** & **E** & **U** & **N** & **E** & **U** \\ \hline G & BIM & 2.084 & 1.680 & 4.092 & 2.491 & 1.806 & 5.338 & - & - & - \\ G & NTCM & 2.152 & 1.634 & 3.673 & 2.634 & 1.750 & 4.135 & - & - & - \\ G & GIM & 1.704 & 1.570 & 3.589 & 1.768 & 1.574 & 3.649 & - & - & - \\ C & BIM & 4.455 & 6.516 & 8.195 & 4.685 & 6.166 & 8.226 & 4.096 & 6.203 & 7.364 \\ C & NTCM & 4.348 & 6.112 & 7.621 & 4.683 & 5.819 & 7.423 & 4.219 & 5.810 & 7.055 \\ C & GIM & 4.052 & 6.093 & 7.717 & 4.037 & 4.801 & 7.475 & 3.681 & 5.721 & 6.990 \\ R & BIM & 2.410 & 2.168 & 5.422 & 2.607 & 2.274 & 6.382 & - & - & - \\ R & NTCM & 2.356 & 2.061 & 5.040 & 2.618 & 2.156 & 5.593 & - & - & - \\ R & GIM & 2.169 & 2.022 & 4.980 & 2.204 & 2.080 & 5.401 & - & - & - \\ E & BIM & 3.117 & 2.802 & 5.149 & 3.466 & 2.935 & 6.332 & 3.506 & 3.033 & 6.112 \\ E & NTCM & 3.190 & 2.769 & 4.754 & 3.804 & 3.026 & 5.598 & 3.767 & 3.041 & 5.443 \\ E & GIM & 2.773 & 2.704 & 4.604 & 2.936 & 2.910 & 5.166 & 3.025 & 3.011 & 2.113 \\ GC & BIM & 2.073 & 1.667 & 4.077 & 2.480 & 1.793 & 5.324 & 2.718 & 3.291 & 6.770 \\ GC & NTCM & 2.141 & 1.625 & 3.660 & 2.624 & 1.739 & 4.122 & 2.823 & 3.103 & 5.857 \\ GC & GIM & 1.690 & 1.559 & 3.578 & 1.758 & 1.562 & 3.636 & 2.136 & 2.997 & 5.413 \\ GR & BIM & 1.749 & 1.396 & 3.419 & 2.067 & 1.495 & 4.428 & - & - & - \\ GR & NTCM & 1.803 & 1.362 & 3.108 & 2.183 & 1.457 & 3.498 & - & - & - \\ GR & GIM & 1.453 & 1.312 & 3.006 & 1.507 & 1.318 & 3.092 & - & - & - \\ GE & BIM & 1.697 & 1.361 & 3.357 & 2.052 & 1.473 & 4.338 & 3.081 & 2.433 & 5.706 \\ GE & NTCM & 1.758 & 1.326 & 2.992 & 2.174 & 1.429 & 3.405 & 2.902 & 2.187 & 5.579 \\ GE & GIM & 1.368 & 1.270 & 2.912 & 1.433 & 1.277 & 2.987 & 2.129 & 1.915 & 4.781 \\ GCR & BIM & 1.748 & 1.394 & 3.414 & 2.066 & 1.493 & 4.425 & - & - & - \\ GCR & NTCM & 1.802 & 1.361 & 3.106 & 2.183 & 1.455 & 3.497 & - & - & - \\ GCR & GIM & 1.451 & 1.310 & 3.005 & 1.506 & 1.317 & 3.091 & - & - & - \\ GCRE & BIM & 1.728 & 1.376 & 3.381 & 2.062 & 1.483 & 4.429 & - & - & - \\ GCRE & NTCM & 1.786 & 1.344 & 3.061 & 2.181 & 1.445 & 3.472 & - & - & - \\ GCRE & GIM & 1.423 & 1.290 & 2.956 & 1.484 & 1.301 & 3.055 & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: RMS of single-frequency SPP with BIM, NTCM and GIM based ionospheric correction (unit: m). horizontal components of the error reach 0.3 m and keep within 0.3 m. Because the vertical positioning errors are larger than the horizontal components, the criterion is enlarged to 0.5 m in the vertical direction. The convergence time for N, E and U components are also given and marked in Figure 4. It is obvious that the GRAPHIC and UC approaches have the same convergence time for GPS-only, GLONASS-only and quad-constellation PPP. Besides, the convergence time of ionosphere-constrained PPP solutions is less than the UC solutions at MRO1 for three schemes. The convergence time of the GIM-constrained solutions is the least for its highest model accuracy. The convergence time of quad-constellation single-frequency is reduced for the improvement of spatial geometry with more GNSS satellite compared with the GPS-only solution. Figure 5 shows the average convergence time of b1, b2 and b3 single-frequency PPP with different schemes on all days over all the test stations. Table 5 summarizes the RMS errors of the single-frequency PPP in multi-constellation combinations, which is calculated from the convergence epoch to the end epoch of a day. The GLONASS-only and Beidou-only solutions clearly perform worse than other solutions, which is caused by the strong correlation between IFBs and slant ionospheric delays in GLONASS and the current distribution and orbit determination accuracy of the Beidou constellation [14].