## 2 Improved Cycle-Slip Detection and Repair Algorithm  
In the analysis data of sixteen iGMAS stations could be obtained by the end of December 2016, among them, nine stations tracked BDS-3 signals. To understand the data quality of iGMAS, two stations (LHA1 and WHU1) were selected to conduct data quality analysis. Meanwhile, it should be noted that the corresponding MGEX stations (LHAZ and JFNG) were the same location stations and can be used for data quality comparison. In the experiments, the GPS data from day of year (DOY) 156 to 160 in 2017 were selected as examples. The observation effective rate, MP1 and MP2, and the average cycle-slip ratio (CSR) (the ratio between the number of observations and epochs with cycle slips) [29] are listed in Table 1 based on the Multi-GNSS data analysis software (MTEQC), which is developed and improved by the authors. Moreover, the effective rate and CSR of BDS-3 in iGMAS data are also listed in Table 1, while the BDS-2 of MGEX was taken as a reference to compare BeiDou data quality of both networks. In Table 1, the cut-off of elevation angle was set as 5 degrees. Analyses of observations taken at the same sites revealed that the data quality of GPS observations is considerably poorer in iGMAS than for MGEX, especially focusing on cycle slips and multipath. In addition, investigating BDS-2 and BDS-3 observations, the cycle slips are much more numerous in MGEX. However, the full exploitation of observations is necessary due to limited data availability in BDS-3 orbit determination. Thus, the high-accuracy cycle-slip detection and repair algorithm for iGMAS and MGEX is a prerequisite of the BDS-3 orbit determination. \begin{table}
\begin{tabular}{c|c c c c c c c c c} \hline \hline \multirow{2}{*}{**Stations**} & \multicolumn{3}{c}{**GPS**} & \multicolumn{3}{c}{**BDS-2**} & \multicolumn{3}{c}{**BDS-3**} \\ \cline{2-10}  & **Effective Rate** & **MPI (m)** & **MP2 (m)** & **CSR** & **Effective Rate** & **CSR** & **Effective Rate** & **CSR** \\ \hline MGEX & JFNG & 88.80\% & 0.348 & 0.424 & 681.20 & 99.66\% & 118.01 & 78.24\% & 843.11 \\ iGMAS & WHU1 & 81.60\% & 0.365 & 0.472 & 133.85 & 85.47\% & 1160.23 & 80.22\% & 942.25 \\ MGEX & LHAZ & 90.61\% & 0.418 & 0.344 & 239.40 & 95.25\% & 77.94 & 94.51\% & 334.23 \\ iGMAS & LHA1 & 99.56\% & 0.473 & 0.370 & 128.06 & 84.99\% & 4393.38 & 99.61\% & 439.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of data quality between iGMAS and MGEX stations. To optimize the observations quality in BDS-3 orbit determination, based on the traditional Turboedit algorithm [25], the following issues may occur when processing the cycle slips in iGMAS data: (1) the detection and repair of the small cycle-slips is inaccurate given the larger noise of iGMAS data (MP1 and MP2 are larger than for MGEX in Table 1); (2) the data piece with several cycle slips is eliminated directly, thereby reducing the data availability of the tracking observations; and (3) the algorithm is insensitive to some special combinations (such as the same cycle slips in each frequency), especially small cycle slips. Therefore, an improved cycle-slip detection and repair algorithm for iGMAS data is presented in the study that is based on the accurate prediction of the ionospheric delays. The corresponding algorithm is presented below. The GNSS observation equation is [30]:  
\[\left\{ \begin{array}{l}P_{i}=(\rho+c\cdot dT-c\cdot dt+d_{trop})+k_{i} \widetilde{I}+\epsilon_{i}\\ L_{i}=(\rho+c\cdot dT-c\cdot dt+d_{trop})-k_{i}\widetilde{I}+\lambda_{i}N_{i}+ \xi_{i}\end{array} \right.