# Evaluation of Ionospheric Delay Effects on Multi-GNSS Positioning Performance
## 4 Results and Discussion  
### Performance of Single-Frequency SPP  
Figure 3 depicts the positioning errors of the CUT0 station on 1 September 2018 for the north (N), east (E) and up (U) component of the b1 and b2 based nine different constellation combinations SPP. It can be seen that the SPP results with b1 and b2 code observations behave similarly. The horizonal error of single-frequency SPP with broadcast ephemeris can reach meter-level, while the vertical error is relatively larger. It is obvious that the accuracy of single-frequency SPP can be improved with multi-GNSS combination. The single-frequency SPP with GIM based ionospheric correction shows the best accuracy, especially in the U direction. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Constellation** & **Mode** & **Schemes** & **Comment** \\ \hline G, C, R, E & Single-frequency & BIM-corr; NTCM-corr; & In the BIM, different ionospheric \\ G/C & SPP: b1, b2, b3 & GIM-corr; & delay models are utilized for their \\ \hline G/R & Single-frequency & GRAPHIC; UC; BIM-cons; & corresponding systems. \\ G/E & PPP: b1, b2, b3 & NTCM-cons; GIM-cons; & Klobuchar model (G/R); \\ \hline G/C/R & Dual-frequency & IF; UC; BIM-cons; NTCM-cons; & improved Klobuchar model(C); \\ G/C/R/E & PPP: b1-b2:b1-b3 & GIM-cons; & NeQuick model(E) \\ \hline \hline \end{tabular}  
* The abbreviation G, C, R and E represent GPS, Beidou, GLONAS8 and Galileo, respectively. The abbreviation “corr” and “cons” represent “correction” and “constrained”, respectively.  
\end{table} 
Table 2: Summaries of the ionosphere processing strategy in multi-GNSS positioning. Figure 3: _Cont._  
The RMS of different single-frequency SPP solutions were calculated, and the mean values of all the tests are summarized in Table 3. As shown in Table 3, the positioning accuracy of multi-GNSS single-frequency SPP with GIM correction performs the best because the GIM is based on the interpolation of the TEC data observed on the selected day and has the highest model accuracy. The solutions from NTCM correction performed better than the BIM correction in the E and U components. Only Beidou, Galileo, GPS/Beidou, and GPS/Galileo b3 SPP solutions were tested, considering that part of the GPS satellites and GLONASS have no triple-frequency signal. For all the single-system single-frequency SPP solutions, Beidou SPP performed the worst, mainly because the satellite orbit and clock offset of the Beidou Geostationary Earth Orbit (GEO) have a relatively lower accuracy. The GPS/Beidou single-frequency SPP achieved slightly better positioning accuracy than the GPS SPP because the Beidou pseudo range observations were assigned less weight than the GPS observations. For the GPS/Galileo b3-based SPP solution, the performance was mainly influenced by the Galileo satellites because few GPS satellites have the b3 signal. For GPS/Beidou/GLONASS/Galileo b1-based SPP, the positioning accuracy was improved by 17.6%, 6.3% and 12.6%, respectively, in the N, E and U components, after the GIM ionospheric correction and compared with the BIM correction. For GPS/Beidou/GLONASS/Galileo b2-based SPP, the positioning accuracy was improved by 28.0%, 12.3% and 31.0%, respectively, in the N, E and U components. For GPS/Galileo b3-based SPP, the positioning accuracy was improved by 30.9%, 21.3% and 16.2%, respectively, in the N, E and U components. For all frequency cases, the multi-GNSS single-frequency SPP performances are improved for more satellites and constellations and the subsequently improved satellite geometry. Figure 3: Positioning error scatters of b1 or b2 SPP with different schemes in nine different constellation combinations at station CUT0 (DOY 244/2018, Kp \(\approx\) 0.92) (**a**) Horizontal error of b1 SPP (**b**) Vertical error of b1 SPP (**c**) Horizontal error of b2 SPP (**d**) Vertical error of b2 SPP. Horizontal error: the horizontal and vertical axes represent the error of the N and E component, respectively (unit: m).