# A Novel Method to Mitigate the Multipath Error for BDS-2 Dam Deformation Monitoring
## 3 Results
### Positioning Performance of SF and MHGM Methods  
In order to assess the performance of multipath error correction using the SF and MHGM methods in the positioning domain, relative positioning was carried out. Station C0012 was set as the base station and fixed in the data processing, and the position of static stations C0100, C0210 and C8894 were estimated according to Tables 1 and 2 in real-time static and kinematic relative positioning mode. In the static mode, the data were processed with a 2 h interval. Taking the DOY 51 test as an example, the positioning errors of static and kinematic relative positioning for station C0100, C0210 and C8894 are displayed in Figure 7. Moreover, the mean RMS of position errors for DOY from 51 to 55 is presented in Table 4 among all the three stations solutions.  
Figure 5: Sky plots (**a**) and observed BDS-2 satellites (**b**) at C0100 station (It should be noted that C13 and C16 belong to ICSO during the observation period in this study).  
Figure 6: _Cont._Figure 6: DD residuals of C04-C08 (DD between GEO and ISGO), C09-C12 (DD between ISGO and MEO) and C11-C14 (DD between MEO and MEO) between the stations 0012 and 0100, NO indicates that no multipath error correction has been made, SF represents the sidereal filtering model and MHGM represents the multi-point hemispherical grid model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Satellites for DD** & \multicolumn{3}{c}{**DD Residuals (mm)**} \\ \cline{2-4}
**Combinations** & **GEO/IGSO** & **GEO/IGSO+ MEO** & **MEO** \\ \hline NO & 6.6 & 5.3 & 4.6 \\ SF & 6.0 & 4.9 & 4.2 \\ MHGM & 5.7 & 4.0 & 3.9 \\ \hline \hline \end{tabular}
\end{table}
Table 3: DD residuals of three different models, GEO/IGSO represents the DD between GEO and ISGO satellites, GEO/IGSO+MEO represents the DD between GEO/IGSO and MEO satellites and MEO represents the DD between MEO and MEO satellites.  
Figure 7: Static with a 2 h interval (**a**) and kinematic positioning error sequence (**b**) of station 0210 (static with a 2 h interval result is from DOY 51 to 55, kinematic result is form DOY 51).  
It can be seen from Figure 7 that the error in the north direction is periodic in kinematic mode, which may be caused by the influence of reservoir flow. This phenomenon and the specific reasons need further study. When the multipath error is uncorrected, the horizontal and vertical positioning errors of stations in static with a 2 h interval and kinematic mode are 2.3, 4.3 and 3.7, 9.4 mm, respectively. After using SF method to mitigate multipath error, the static and kinematic positioning errors of stations were improved, reaching 1.8, 3.8 and 2.6, 8.6 mm in the horizontal and vertical direction, respectively, and the improvement was as high as 21.7%, 12.1% and 29.7%, 9.0%. Moreover, the MHGM improved by 5.4%, 5.3% in the vertical direction compared with the SF method, and the improvement rate in static with a 2 h interval and kinematic mode was 4.3%, 4.6% in the horizontal direction, respectively. Moreover, for static with a 2 h interval and kinematic mode, the MHGM method improved about 26.1%, 16.3% and 35.1%, 13.8% with respect to the without multipath correction in the horizontal and vertical direction. It can therefore be found that the SF method is not as effective as the MHGM method in the presence of accurate BDS deformation monitoring environment.