## 4 Result and Analysis
### BDS-2 and BDS-3 Broadcast Orbit  
Since the reference point of the broadcast orbits is the antenna phase center (APC), and the reference point of the precise orbits is the center of mass (CoM), the orbit errors of precise and broadcast ephemerides can be compared directly after the PCO and PCV corrections [5]. Figure 9 illustrates the orbit errors of BDS-2 and BDS-3 broadcast orbits in radial, along-track and cross-track directions. Since the orbit accuracy of GEO satellites performs poorly, the along-orbit errors of GEO satellites are worse than 10 m in some time periods. Figure 10 shows the RMS and STD of orbit error of each satellite. Similarly, the orbit accuracy of GEO is obviously worse than that of MEO and IGSO in the along-track direction. Ignoring GEO, the orbit errors of along-track direction are roughly better than 2.8 m for MEO and IGSO. As BDS second generational satellite navigation systems, ground tracking stations used to calculate broadcast ephemeris are unevenly distributed and the orbit determination strategy is immature, which leads to lower accuracy of the BDS-2 broadcast ephemeris. It is worth noting that the accuracy and stability of BDS-3 orbit have a significant improvement over BDS-2. With the upgrade of BDS-3 satellite hardware technology, especially for inter-satellite links payload and the development of satellite orbit determination algorithm, the orbit accuracy of BDS-3 broadcast orbit has made great progress. As shown in Figures 9 and 10, the orbit errors of BDS-3 is significantly lower than that of BDS-2, and the RMS and STD of three ACs of BDS-3 satellite are better than 0.3 m and 0.2 m for radial direction, 0.5 m and 0.3 m for the along-track direction, and 0.3 m and 0.3 m for the cross-track direction, respectively.  
In order to explain the improvement of BDS-3 compared to BDS-2 more objectively and reasonably, Table 5 explains the mean RMS and STD statistical results of BDS-2 and BDS-3 orbit errors and the improvement rate of BDS-3 compared to BDS-2. The consistency of the orbit accuracy between GFZ, WHU, and SHA is relatively excellent. In radial, along-track and cross-track directions, the mean RMS and STD of all BDS-2 satellite are (1.79, 3.28, 1.39) m and (0.32, 0.99, 1.04) m for GFZ, (1.78, 3.28, 1.23) m and (0.34, 1.03, 0.98) m for WHU, (0.81, 2.56, 1.02) m and (0.37, 0.99, 0.95) m for SHA, and (1.46, 3.04, 1.21) m and (0.34, 1.00, 0.99) m for the average of three ACs, respectively. The broadcast orbit accuracy of BDS-3 is roughly improved by one order magnitude compared to BDS-2, the mean RMS and STD of all BDS-3 satellite are (0.20, 0.33, 0.29) m and (0.07, 0.25, 0.24) m for GFZ, (0.16, 0.30, 0.27) m and (0.05, 0.18, 0.21) m for WHU, (0.23, 0.35, 0.30) m and (0.09, 0.28, 0.25) m for SHA, and (0.20, 0.32, 0.28) m and (0.07, 0.23, 0.23) m for the average of three ACs, respectively. The mean RMS and STD of BDS-3 broadcast orbit errors are improved by (86.30%, 89.47%, 76.86%) and (79.41%, 77.00%, 76.78%) compared to BDS-2 in three directions, respectively.  
Figure 9: The orbit errors of BDS-2 and BDS-3 broadcast orbits relative to precise ephemerides provided by GFZ, WHU and SHA in radial, along-track and cross-track directions.