# Multipath Error Fusion Modeling Methods for Multi-GNSS
## 3 Results
### Use the Observations from Multi-Day for Testing  
According to the experimental results in the previous section, MHGM and SF were comparable when using the observations from the days of the previous orbit repeat period. In this section of the experiment, we further used the observations of DOYs 215-233 in 2018 for multi-day modeling of the MHGM. Considering that Galileo had the longest orbit repeat period among the three systems involved in the solution, the duration for the multi-day modeling was set to 10 days. The start and end dates correspond to Table 5. Meanwhile, the validation data should be consistent to analyze the improvement of the MHGM modeling results by increasing the amount of data involved in the modeling. The specific test plan is listed in Table 6. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Observation Environment** & \multicolumn{3}{c}{**A (Simulated)**} & \multicolumn{3}{c}{**B (Normal)**} \\ \hline
**Processing Strategies** & **N** & **S** & **M(1)** & **N** & **S** & **M(1)** \\ \hline Positioning & N & 2.80 & 0.96 & 0.89 & 2.43 & 0.95 & 1.11 \\ accuracy & E & 4.31 & 1.84 & 1.40 & 3.33 & 1.68 & 1.92 \\ RMS (mm) & U & 9.47 & 3.10 & 1.83 & 5.84 & 2.21 & 1.54 \\
3D improvement & / & 65.3\% & 77.1\% & / & 59.0\% & 62.3\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Multi-GNSS static positioning statistics for one hour with different processing strategies. Figure 4: Distribution histogram and normal distribution curve of double-differenced residuals before and after the correction of different models. Figure 5: Double-differenced residual sequences and signal power spectrum before and after model correction. (**a**) The double differenced residual series of G19 and G22 on station B and station C and the power spectrum analysis of the residual series. (**b**) The double differenced residual series of C04 and C08 on station A and station B and the power spectrum analysis of the residual series. (**c**) The double differenced residual series of E01 and E31 on station A and station C and the power spectrum analysis of the residual series. For the verification day, the mean RMS of the double-differenced residuals in the ambiguity-fixed period after multipath error correction was compared using the observations from days of the previous orbit repeat period and the multi-day for modeling MHGMs. The results are shown in Figure 6. \begin{table}
\begin{tabular}{c c} \hline \hline
**DOYs for Modeling in 2018** & **DOY for Verification in 2018** \\ \hline
215–224 & 225 \\
216–225 & 226 \\
217–226 & 227 \\
218–227 & 228 \\
219–228 & 229 \\
220–229 & 230 \\
221–230 & 231 \\
222–231 & 232 \\
223–232 & 233 \\
224–233 & 234 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Specific test plan of multi-day modeling for MHGM. Figure 6: Mean RMSs of the double-differenced residuals in the ambiguity-fixed period after multipath error correction using the observations from the days of the previous orbit repeat period and multi-day. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**GPS** & **BDS (IGSO+GEO)** & **BDS (MEO)** & **Galileo** & **DOY for Verification in 2018** \\ \hline
224 & 224 & 218 & 215 & 225 \\
225 & 225 & 219 & 216 & 226 \\
226 & 226 & 220 & 217 & 227 \\
227 & 227 & 221 & 218 & 228 \\
228 & 228 & 222 & 219 & 229 \\
229 & 229 & 223 & 220 & 230 \\
230 & 230 & 224 & 221 & 231 \\
231 & 231 & 225 & 222 & 232 \\
232 & 232 & 226 & 223 & 233 \\
233 & 233 & 227 & 224 & 224 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experimental strategies of SF and MHGM. In Figure 6, N indicates the strategy without multipath correction, M (1) refers to the strategy of establishing MHGM for multipath error correction using the observations from days of the previous orbit repeat period, and M (10) is the strategy for establishing MHGM for multipath error correction using all ten-day observations. The left part of Figure 6 shows the change of mean RMSs of double-differenced residuals for three strategies of N, M (1), and M (10).