## 4 Experiments and Results
### Single-Difference Residual Analysis  
To qualitatively compare the multipath characteristics of the three types of satellites, Figure 5 shows the C01/C11/C13/C29 single-difference residuals and the satellite elevation and azimuth angles of DOY 296, 302, and 303. For GEO C01 and IGSO C13 separately, the three-day single-difference residuals have high repeatability, and the elevation and the azimuth series are highly coincident. Although DOY 296 has a longer time interval than DOY 302 towards DOY 303, the single-difference residuals maintain repeatability. It can be observed from MEO C11/C29 that the single-difference residuals of two adjacent days are non-correlated, and the elevation and the azimuth angles are different. Moreover, for satellite types with large changes in IGSO and MEO elevation angles, their single-difference series are correlated with their elevation angles. For C13, as the pivot satellite at a certain time, the single-difference series changes significantly but does not affect its repeatability. Figure 4: Observation environment around the stations. We first calculate the time shift of the ORT from the broadcast ephemeris to quantitatively analyze the C01/C11/C13/C29 aligned single-difference series and the relevant physical quantities after mitigating the multipath. Moreover, we calculate the correlation coefficient between the multipath model that aligns the time shift and the target DOY single-difference series. Finally, the multipath model is used to mitigate the multipath of the target DOY. The statistical results are listed in Table 1. We observe that the correlation coefficients of GEO C01 and IGSO C13 remain stable with a value greater than 0.92, and the correlation coefficients do not decrease in the case of a long-time span. Moreover, the single-difference series corrected by the multipath model have significant improvement in RMS. The repetition time of the MEO ORT is approximately seven sidereal days. Therefore, there is almost no correlation between the C11/C29 single-difference series of two adjacent days. For DOY 296-303 and DOY 297-304, they have correlation coefficients above 0.848, which are only one day apart. However, there is a difference in correlation coefficients and corrected RMS. To analyze the multipath mitigation degree of each observed satellite single-difference series based on the ASF method, Figure 6 shows the RMS of the original single-difference series and their series with multipath mitigation for the DOY 303 observed satellite by the corresponding multipath model. Most of the observed satellites can significantly mitigate the multipath based on ASF. However, in the background, the multipath of C21 and C24 in the original series has not been effectively mitigated, which is caused by the inconsistent observation time of the corresponding multipath models of C21 and C24. Based on the ASF method, the phenomenon may affect the performance of improving baseline accuracy. Figure 5: DOY 296/302/303 single-difference residuals series of C01/C11/C13/C29 and the elevation and azimuth angles. In the process of correcting the single-difference series of each satellite based on the multipath model, we find that some satellites still have incomplete multipath correction after determining the time shift because the observation times of the two adjacent ORTs of MEO satellites appearing in the sky are not the same. The SD-MHM method can theoretically avoid the influence of this phenomenon. The SD-MHM model is established using the BDS single-difference denoising residuals from DOY 296 to 302, as shown in Figure 7a. Figure 7b shows the distribution of the single-difference residuals of each satellite dynamically calculated by DOY 303 on the sky map. Although the reconstructed single-difference residual value of the pivot satellite is distorted, the SD-MHM model and the DOY 303 single-difference residuals have a high spatial-domain correlation, which does not affect the accuracy of subsequent multipath mitigation in real-time.