## 3 Results
### Satellite Signature Effect of BDS
Figure 5 shows the variation in the SLR residuals with regard to the nadir angle observed by Shanghai. The slope with regard to the nadir angle was \(-1.73\), \(-0.95\), \(-0.99\), \(-0.76\), \(-80\), and \(-0.68\) mm/deg for COMPASS-I3, COMPASS-I5, COMPASS-I6B, COMPASS-M3, Beidou3-M2, and Beidou3-M9. We found that the slopes of Yarragadee with regard to the nadir angle were larger than those of Shanghai. This suggests that the signature effect exists in the SLR residuals observed by multi-photon stations. In low-energy mode, single-photon stations are not subject to the issues of varying nadir angles since the probability of photon reflection is equal for every corner cube. However, it can be seen that the SLR residuals are also dependent on the nadir angle, which may be attributed to the requirement for post-processing rejection of high-rate data and changes in the optical path of the laser pulse as it passes through the troposphere during observations at different elevation angles [17]. To further investigate the signature effect in SLR observations, we analyzed the residuals as a function of the nadir angle for four types of satellites (BDS-2 IGSO, BDS-2 MEO, BDS-3 CAST, and BDS-3 SECM) and divided them into three station groups (CSPAD, MCP, and PMT), as shown in Figure 6. For MCP and CSPAD stations, the slope with regard to the nadir angle was around \(-2.5\) to \(-2.0\), \(-0.4\) to \(-0.3\), and \(-1.2\) to \(-0.6\) mm/deg for BDS-2 IGSO, BDS-2 MEO, and BDS-3 SECM satellites, respectively. The results indicate that IGSO satellites exhibit a larger slope than MEO satellites. Moreover, it can be seen that MCP stations have a stronger correlation between the nadir angle and SLR residuals than CSPAD stations, and the difference in slope has a maximum of about \(0.6\) mm/deg for BDS SECM satellites. For BDS-3 CAST satellites, a slope with a positive value also existed in GFZ and ESA. Among eight long-term tracked satellites, the two CAST satellites were manufactured by NCRIEO, while the other six satellites were made by SHAO (see Table 1). According to the published information [30; 31; 32], the prism cubes on those three types of LRA are made of quartz. Additionally, all the surfaces of the corner cubes on the two types  
Figure 4: The variation in SLR residuals for six satellites with regard to the nadir angle observed by Yarragadee. of LRAs made by SHAO are uncoated, while for the LRAs manufactured by NCRIEO, it is still unknown whether some surfaces of the prism cubes are coated or not, which may have an impact on the SLR residuals. For PMT stations, the slope with regard to the nadir angle was approximately \(-0.1\), \(-0.4\), \(-0.8\), and \(-1.1\) mm/deg for the four types of satellites, respectively. However, the reader should also note that the slope of the PMT stations may not be reliable, considering that the PMT stations only had a few BDS observations (about 2% and 4% of those by made CSPAD and MCP stations, respectively). After analyzing the SLR residuals of different constellations, we selected several stations with a significant number of observations to evaluate their performance in tracking BDS. Matera is another MCP station as well as Yarragadee, and can provide a large number of observations. The RMS of SLR residuals and the slope with regard to the nadir angle observed by Matera was approximately 45 mm and \(-2.21\) mm/deg, respectively, which shows a good performance among multi-photon stations. Herstmoneux is equipped with an uncompensated SPAD and its SLR residuals had a positive slope. This phenomenon was also observed in Grasse, where a SPAD detector is installed. Changchun had an RMS of 59 mm and a large positive slope. The positive slope anomaly may indicate the presence of amplified noises at Changchun [33]. Shanghai had a slope of \(-0.40\) mm/deg and a mean offset of 8 mm, which represents most high-performance CSPAD stations including Mt Stromlo, Beijing, and Wettzell.