# A Novel Method to Mitigate the Multipath Error for BDS-2 Dam Deformation Monitoring
###### Abstract  
The multipath effect on carrier-phase observations is related to the observational environment of the station, and cannot be eliminated or attenuated by the differential method. In the actual dam environment of deformation monitoring, multipath is very complicated. It is the main error source of BDS-2 for high precision data processing. In this paper, a new method called the multi-point hemispherical grid model (MHGM) is studied and evaluated. This method uses the hemispheric grid model to attenuate the influence of multipath errors. The effectiveness and improvement of the new method with respect to the popular sidereal filter (SF) method were assessed and verified by the actual dam monitoring data with only the BDS-2. The MHGM and SF approach calculates the multipath corrections from multi-days historical data, and then corrects the multipath error from the observations on the day of interest. Compared with the SF method, the MHGM can also effectively provide a graphical display of multipath error interference around the stations, which matches the surrounding observation environment. The results show that the double-differenced (DD) residuals of the MHGM for GEO/IGSO and MEO satellites are slightly better than those of SF, but the RMS of MHGM for GEO/IGSO+MEO DD residuals is improved by about 17.0%. The performance of the MHGM method for different satellite constellations is consistent and not affected by the different orbital repeat times, which could solve the \"zero mean\" assumption problem of the SF method. Meanwhile, the RMS of static with a 2 h interval and kinematic positioning errors of the MHGM method in the horizontal and vertical direction can be up to 1.7, 3.6 and 2.4, 8.1 mm, respectively. The MHGM model could avoid the multipath reference problem caused by different orbital repetition periods, making it more suitable for the combined multipath modeling of BDS-2 and BDS-3. deformation monitoring; BDS-2; multipath error; multi-point hemispherical grid model; sidereal filter 19 March 2021 27 April 2021 4 May 20 out over a limited period of data, and probably induce spurious deformation signals as well as bias the displacement estimations. In addition to improving the observation environment and reducing reflection, multipath error could be also mitigated and reduced using hardware and software methods. Hardware methods mainly use the suppression board to attenuate the multipath, which is widely used but has high cost [4]. Software strategies are often used in high precision applications, such as weighting GNSS observation based on signal-to-ratio or satellite elevation angle [5; 6], employing filter methods to extract and mitigate multipath error. Filter methods have included finite impulse response (FIR) filter [7], wavelet analysis [8; 9], Vondrak Filter with cross validation [10], adaptive filtering [11; 12], and rotating antennas [13]. These methods can reduce the influence of multipath to a certain extent, but the interference of other random noise limits their effectiveness. Currently, sidereal filtering (SF) is a widely used method to mitigate multipath error [14; 15]. Based on the assumption that when the spatial relationship between the antenna and the observation environment remains unchanged, the SF method assumes that the multipath error of the station should mainly depend on the change of the signal propagation direction. Therefore, through the spatial relationship between the satellites and the station, the multipath error could be determined by the repetition of each sidereal day, then the observation of the following days can be corrected to reduce its impact [16; 17; 18]. The multipath error for the SF method is extracted from the coordinate sequence for correction of positioning results on subsequent sidereal days as well as observation domain. [PERSON] et al. (2000) proposed a method to isolate the multipath effect by transforming double-differenced residuals to improve precipitable water vapor (PWV) [19]. [PERSON] et al.