# Multipath Error Fusion Modeling Methods for Multi-GNSS
## 3 Results
### Use the Observations from Days of the Previous Orbit Repeat Period for Testing  
According to the introduction in previous section, when using the observations of the previous orbit repeat period for SF, it is necessary to set their respective repeat periods for different constellation types of different GNSSs. At the same time, the same data are used for multipath error modeling and verification in order to compare the effectiveness of SF and MHGM. Table 3 shows the double-differenced residuals of each GNSS with ambiguity-fixed solutions for the verification days, before and after multipath error correction. In Table 3, N represents the processing strategy without model correction, S refers to the processing strategy of correcting multipath error with the SF method, and M(1) refers to the strategy of correcting the multipath error by MHGM. The average RMSs of the double-differenced residuals were distinguished by GPS, BDS, and Galileo. The test results of the tenth-day show that the double-differenced residual after multipath error correction was significantly reduced compared with the uncorrected one. The average improvement rates of SF and MHGM were 49.6% and 53.7%, respectively. We also gathered the statistics on the average values of each double-differenced residuals in the ambiguity-fixed period for the ten-day verification data and fit a normal distribution of these residuals, so as to further reflect the change of carrier phase residuals before and after the multipath error correction. The results are shown in Figure 4.  
It can be seen from Figure 4 that the distributions of the double-differenced residuals in N of each system are more scattered without multipath error correction and the data distribution of S and M are more centralized. Taking GPS as an example, only 37.5% of the uncorrected double-differenced residuals were distributed between \(\pm\)2.5 mm. The percentage of data in the range of \(\pm\)2.5 mm increased to 46.7% after the SF model correction, and 50.7% of the double-differenced residuals were concentrated in the range of \(\pm\)2.5 mm after MHGM correction. The statistical results of BDS and Galileo were similar to these of GPS. Multipath errors caused by different reflectors have different forms in the frequency domain. We also analyzed the changes of three groups of double-differenced residual sequences and signal power spectrum before and after multipath error correction under different systems. As shown in Figure 5, the results of the power spectrum analysis prove that the two studied methods can effectively mitigate the low frequency multipath signal in the sequence. For a noise signal greater than 0.1 Hz, the correction of SF and MHGM was relatively consistent. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & \multicolumn{6}{c}{**Mean Value of RMS of Double-Differenced Residuals/mm**} \\ \cline{2-10}
**DOY in 2018** & \multicolumn{2}{c}{**GPS**} & \multicolumn{3}{c}{**BDS**} & \multicolumn{3}{c}{**Galileo**} \\
**N** & **S** & **M(1)** & **N** & **S** & **M(1)** & **N** & **S** & **M(1)** \\ \hline
225 & 8.54 & 3.48 & 3.47 & 5.99 & 2.66 & 2.57 & 8.67 & 3.74 & 3.01 \\
226 & 8.38 & 5.29 & 5  
Compared with the observation residuals, the improvement of the multipath error correction on the positioning results may be more intuitive in practical application. Therefore, we also collected statistics on the positioning results for the verification days before and after correction with SF and MHGM methods. Station C was fixed and the coordinates of Stations A and B were solved according to the static relative positioning mode during the experiment. The observation time involved in the data processing was set to one hour and the positioning results for a total of 240 tests in 10 days were counted. It can be seen from Table 4 that the positioning accuracy after model correction was better than that without model correction. For Station A with baffle to simulate a strong multipath, the improvement of the positioning accuracy was more obvious.