# Evaluation of Ionospheric Delay Effects on Multi-GNSS Positioning Performance
## 4 Results and Discussion
### Performance of Dual-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 GR & GRAPHIC & 1.662 & 3.418 & 9.260 & 1.810 & 3.461 & 6.890 & - & - & - \\ GR & UC & 1.662 & 3.417 & 9.259 & 1.810 & 3.461 & 6.890 & - & - & - \\ GR & BIM-cons & 1.618 & 3.982 & 9.246 & 1.765 & 3.919 & 6.853 & - & - & - \\ GR & NTCM-cons & 1.662 & 3.159 & 9.268 & 1.819 & 3.172 & 6.795 & - & - & - \\ GR & GIM-cons & 1.631 & 2.876 & 9.216 & 1.821 & 3.169 & 6.779 & - & - & - \\ GE & GRAPHIC & 1.568 & 2.905 & 8.657 & 1.606 & 3.123 & 6.879 & 2.903 & 4.489 & 8.089 \\ GE & UC & 1.568 & 2.905 & 8.656 & 1.606 & 3.122 & 6.880 & 2.903 & 4.489 & 8.089 \\ GE & BIM-cons & 1.542 & 3.242 & 8.655 & 1.568 & 3.675 & 6.890 & 2.806 & 4.390 & 8.074 \\ GE & NTCM-cons & 1.585 & 3.007 & 8.634 & 1.620 & 2.899 & 6.832 & 2.864 & 4.164 & 7.837 \\ GE & GIM-cons & 1.543 & 2.480 & 8.620 & 1.618 & 2.861 & 6.819 & 2.829 & 3.235 & 7.715 \\ GCR & GRAPHIC & 1.651 & 3.385 & 9.161 & 1.711 & 3.342 & 6.775 & - & - & - \\ GCR & UC & 1.651 & 3.385 & 9.159 & 1.710 & 3.341 & 6.777 & - & - & - \\ GCR & BIM-cons & 1.550 & 3.098 & 9.013 & 1.664 & 3.840 & 6.762 & - & - & - \\ GCR & NTCM-cons & 1.591 & 2.253 & 8.932 & 1.734 & 3.145 & 6.688 & - & - & - \\ GCR & GIM-cons & 1.550 & 2.047 & 8.844 & 1.699 & 3.129 & 6.597 & - & - & - \\ GCR & GRAPHIC & 1.557 & 2.885 & 8.579 & 1.599 & 3.095 & 6.670 & - & - & - \\ GCRe & UC & 1.557 & 2.885 & 8.576 & 1.599 & 3.094 & 6.673 & - & - & - \\ GCRe & BIM-cons & 1.538 & 3.035 & 8.488 & 1.562 & 3.507 & 6.669 & - & - & - \\ GCRe & NTCM-cons & 1.578 & 2.240 & 8.408 & 1.610 & 2.802 & 6.575 & - & - & - \\ GCRe & GIM-cons & 1.541 & 1.962 & 8.316 & 1.599 & 2.753 & 6.517 & - & - & - \\ \hline \end{tabular}
\end{table} 
Table 5: _Cont._time of quad-constellation PPP in E and U components is not effectively reduced with the external ionospheric information at SEYG. The receiver DCB is estimated as an unknown parameter in the ionosphere-constrained approaches. Figure 7 shows the time series of the estimated GPS, Beidou, GLONASS and Galileo receiver DCB at SEYG. It should be noted that the b1/b3 DCB of GLONASS is not given because the GLONASS has no triple-frequency signal. The multi-GNSS MGEX DCB provided by the Chinese Academy of Sciences (CAS) (available at: [[ftp://igs.ign.fr/pub/igs/products/mgex/dcb/](ftp://igs.ign.fr/pub/igs/products/mgex/dcb/)]([ftp://igs.ign.fr/pub/igs/products/mgex/dcb/](ftp://igs.ign.fr/pub/igs/products/mgex/dcb/))) is also shown in Figure 7 for reference and comparison, together with the standard deviation (STD) and RMS of corresponding DCB (see top of each panel). It can be seen that the estimated DCB of GIM-constrained approach is much swifter than the other two schemes. Owing to growing weighting for virtual ionospheric observation in the filter process, the existing errors of the ionospheric models have little influence on the positioning accuracy after convergence and are absorbed in the estimable receiver DCB [30]. Hence, as it is shown in Figure 7, this also reflects that the GIM model has the highest accuracy in three models at SEYG. Figure 8 shows the average convergence time of b1/b2 and b1/b3 dual-frequency PPP with different schemes. Table 7 summarizes the RMS errors of dual-frequency PPP in multi-constellation combinations, the average values of all PPP tests after convergence are calculated. It can be seen that the b1/b2 based PPP performs better than the b1/b3 solutions. The performance of b1/b2 GPS/Beidou and GPS/Galileo PPP differs greatly from the b1/b3 solutions in that only GPS BLOCK-IIF can transmit signals on three frequencies. The positioning accuracy reaches approximately 0.5-2.5 cm in the horizontal and 2-5 cm in the vertical for dual-frequency PPP. Similar to single-frequency PPP, the combination of multi-GNSS speeds up the convergence process and improves the positioning accuracy.