## 3 Experiment and Results
### Evaluation Results of SBAS Orbit and Clock Corrections  
As the references, the IGS final orbit and clock products during the entire evaluation period are downloaded and the orbits are interpolated to the time epochs of IGS clock products with the interval of 30 seconds. The Lagrange interpolation with the polynomial degree of 8 is adopted. The accuracy of IGS precise orbits after interpolation is at cm level, which is accurate enough for reference [42]. On the other hand, the SBAS-derived orbits and clocks are also calculated at the same time epochs by using SBAS messages and GPS broadcast navigation data. The orbit differences, caused by the situation that SBAS-derived orbits are originally referred to APC and IGS precise orbits are referred to the satellite COM, are corrected according to Equation (6). Similarly, the clock differences due to the inconsistency between C1 signal and P1/P2 ionosphere-free combination adopted by SBAS clock corrections and IGS final clock products respectively, as well as the different underlying realization of the SBAS and IGS precise clock time scales, are also removed by using the method mentioned in Section 2.1.2. Afterward, the orbit and clock errors are calculated by SBAS-derived orbits/clocks minus IGS precise orbits/clocks, the orbit errors are then represented in satellite along-track, cross-track and radial frame based on Equation (9). In addition, the orbit and clock errors of GPS broadcast navigation data have also been calculated at the same time epochs during the evaluation period according to the calculation procedure described in [30]. Figures 2-11 show the probability distributions of satellite orbit errors in the directions of along-track, cross-track, radial and clock errors for SBAS-derived orbits and clocks, which are obtained with orbit and clock corrections from different SBAS satellites. These errors are calculated over the entire evaluation period. Three statistics, including bias, standard deviation (STD) and RMS, are counted and presented in each figure. It should be noted that these three statistics are calculated for each SBAS satellite by using 181-day along-track/cross-track/radial/clock error time series of all available GPS satellites with SBAS corrections. The accuracy of orbit and clock corrections from the same SBAS system only show slight differences, which indicates the consistency of correction messages among SBAS satellites in the same system. When comparing the accuracies of orbit and clock corrections from different SBAS systems, it is found that the SDCM has the best accuracy in terms of along-track, cross-track, radial and clock errors, followed by WAAS and EGNOS, whereas the \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**System** & **WAAS** & **EGNOS** & **MSAS** & **GAGAN** & **SDCM** \\ \hline PRN & 135 & 138 & 120 & 123 & 129 & 137 & 127 & 128 & 125 & 140 \\ \hline Number of missing epochs & 3 & 0 & 187 & 171 & 11,284 & 1361 & 9853 & 626,877 & 2,212,623 & 880,653 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The number of missing epochs for each satellite-based augmentation system (SBAS) satellite. MSAS and GAGAN have worse accuracy. The average RMS of orbit and clock corrections for the two SDCM satellites are 0.871, 0.539, 0.624 and 0.689 m in the along-track direction, cross-track direction, radial direction, and clock error, respectively. Accordingly, the corresponding average RMS values in three orbit directions and clock for WAAS and EGNOS are 1.783, 1.531, 1.341, 1.054 and 2.145, 1.150, 0.774, 0.817 m, respectively, whereas the values for MSAS and GAGAN are 4.027, 4.643, 2.894, 2.251 and 2.999, 3.215, 2.438, 2.155 m. Figure 12 shows the probability distributions of orbit errors in the directions of along-track, cross-track, radial as well as clock errors for the GPS broadcast navigation data. The RMS values are 0.942, 0.543, 0.637 and 0.702 m in the along-track, cross-track, radial and clock error respectively.