# A Novel Method to Mitigate the Multipath Error for BDS-2 Dam Deformation Monitoring
###### Abstract
(2007) found that the SF method based on the coordinate domain was more computationally efficient, but the observation domain was more accurate [20]. Based on a short baseline of SF correction observation, [PERSON] et al. (2010) obtained better positioning results than those with corrections in the coordinate domain [21]. The SF method can correct multipath to a certain extent. However, when the interval between the first day and subsequent days increases, the degree of repeatability will decrease. When the degree is reduced to a low value, the SF method is not able to effectively attenuate the multipath error. Therefore, as with modeling multipath in coordinate domain or observation domain, modeling multipath in space domain (sky grid of orbit trace) can effectively mitigate its impact based on the repeatability of the satellite orbit period. Based on the assumption of \"zero mean\", [PERSON] et al. (2014) proposed an empirical site model (ESM) to mitigate the unmodelled site-specific errors [22]. A site-specific correction map is obtained with zero-differenced (ZD) carrier phase residuals in this method. However, when more precise double-differenced (DD) residuals are used, this method may be not suitable to transform DD residuals into ZD residuals due to the assumption [23]. Therefore, [PERSON] et al. (2016) proposed a lookup table method for multipath reduction based on a multipath hemispherical map (MHM) and compared the technique with SF/advanced SF (ASF) [24]. In this method, the observation residual of the fixed single-difference (SD) ambiguity between the two antennas is averaged. The low frequency multipath effect is retained and can be modeled while the noise effect is weakened. Moreover, [PERSON] et al. (2019a) proposed a modified multipath hemispherical map model (M-MHM), which constructs grids from raw carrier-phase residuals [25]. The M-MHM exhibits the most improvement compared with the SF method and original MHM, but the model residuals using the PPP technique may include orbital, clock and atmosphere errors [26]. Most of the above studies are for GPS, for which the orbital repetition period is about one sidereal day. However, BDS-2 has three constellation satellites with different orbital repetition periods. [PERSON] et al. (2015) analyzed the repeat period of different BDS-2 satellites and used sidereal filtering to mitigate BDS-2 carrier phase multipath errors [27]. The improvement of the positioning results is obvious. It is well known that the SF using single difference can mitigate GPS multipath effectively, [PERSON] et al. (2015) recovered the SD residuals from DD residuals based on the assumption that the sum of observed SDresiduals is zero [27]. However, the application of the simple \"zero mean\" assumption will introduce new errors to BDS-2 positioning. Therefore, the MHM proposed by [PERSON] et al. (2016) solves the problem of \"zero mean\" assumption, but its effective distance is limited by the common receiving clock of two antennas [28]. In addition, most of the research was conducted through artificial simulation of multipath environment for model verification, which is different from the actual application environment, such as for dam deformation monitoring. The observation environment of dam deformation monitoring is relatively complex, with multipath interference of water surface and slope. Most of these studies have confirmed that the positioning accuracy and application of BDS-2 DD are comparable to that of GPS. However, there is little research on the multipath correction methods of BDS in the actual and complex environment. For the complex actual environment and the multi-constellation characteristics of BDS-2, based on the multipath hemispherical map, we studied and assessed the multi-point hemispherical grid model (MHGM) and SF methods with actual BDS-2 dam monitoring data. Firstly, the new errors introduced by the simple \"zero mean\" assumption existing in the SF method do not need to be considered with this technique.