# A Novel Method to Mitigate the Multipath Error for BDS-2 Dam Deformation Monitoring
## 3 Results
### DD Residual Analysis  
After the multipath values of the grid points are obtained, the multipath correction of any point can be interpolated. The multipath error was corrected for the observations, which were processed in real-time kinematic relative positioning mode. As shown in Table 2, the SF model has to be estimated based on the different orbital repeat times of GEO/IGSO and MEO. Since the total time of the observation is about 12 days, the SF model uses 1 day-old data for GEO/IGSO and 7 day-old data for MEO. However, MHGM can make full use of the observation data, and all the 7 day-ago data during the experiment could be used for estimating MHGMs.  
Due to using the multipath errors of different periods to correct the observations in the SF method, the corresponding observations of GEO/IGSO and MEO satellites introduce different references of the multipath errors. Thus, the DD between GEO/IGSO and MEO also introduces new error. In order to ensure and improve the modeling accuracy, only the observation data of the repeat periods are used to model in the SF method, so the multipath error of following repeat periods cannot be mitigated if the corresponding period ambiguity  
Figure 4: MHGM modeling results for DOY 53 at the C0210, C0100, C0012 and C8894 stations. The horizontal and vertical axes represent the azimuth and elevation angle, respectively. Different colors indicate different multipath error values.  
of the previous day is not effectively fixed. Moreover, the MHGM can use the data observed during different periods and multi-day historical data to improve the consistency and availability of the modeling.  
In order to assess the efficiency of the MHGM and the error caused by orbital repeat time of the SF method, the DD residuals between GEO/IGSO and MEO were analyzed separately. Therefore, there are three kinds of DD residuals according to the orbital repeat times, namely GEO/IGSO, GEO/IGSO+MEO and MEO. Since the observation conditions of the four stations are the same, the sky plots and observed BDS-2 satellites at only C0100 station given in Figure 5. Figure 6 show the DD residuals of the different strategies between different satellites for C04-C08, C09-C12 and C11-C14 at the stations C0012 and C0100 during the period of fixed ambiguity. Table 3 shows the mean RMS of three DD residuals for the three modes.  
It can be found from Figure 5 that the observation time for GEO and IGSO is relatively longer. Compared with the DD combinations of GEO/IGSO+MEO and MEO, the DD residuals of GEO/IGSO are the largest. As shown in Figure 6, the residuals of the MHGM method are the smallest. Moreover, it can be seen from Table 3 that the RMS of DD residuals with the multipath correction does not exceed 7 mm. Compared with the result without considering multipath correction, the RMS values of GEO/IGSO, GEO/IGSO+MEO and MEO for SF were improved by about 9.1%, 7.5% and 8.7%, respectively. The DD residuals of the GEO/IGSO and MEO for the MHGM method are slightly better than those of the SF method, and the improvement with respect to the SF method is 4.5% and 6.5%, respectively. Moreover, the improvement of GEO/IGSO+MEO by the MHGM can be up to 17.0%, since MHGM avoids different references of the multipath errors and solves the problem of \"zero mean\" assumption in the SF method. The performance of GEO/IGSO+MEO for MHGM method is the same as that of MEO, which is not affected by the different orbital repeat times of BDS-2 satellites, which further proves that MHGM is more effective than the SF method in some cases.  
Figure 5: _Cont._