# Precise Orbit Determination of BDS-2 and BDS-3 Using SLR
## 4 Results
### The Orbit Overlaps and Comparison with WUM Orbits  
The results of 3-, 5-, 7-, and 9-day arc solutions are presented for all nine BDS satellites from Figures 6-14 while the red, blue, magenta, and green colours in the histogram and scatter chart correspond to the results of 3-, 5-, 7-, and 9-day solutions. In each figure, the top three sub-graphs show the SLR-only orbit overlap errors between two adjacent multi-day arc solutions in the R, T, and N directions while the bottom three sub-graphs display the difference between the SLR-only orbit and microwave-based precise orbit of WUM. Meanwhile, the left four columns represent the histogram of the number of success solutions, where the vertical axis refers to the RMS for orbital difference and the horizontal axis refers to the number of success solutions that are binned into 100 pieces in accordance with the corresponding range of RMS threshold. The total number of success solutions is presented inside the sub-graphs in the first and fourth rows, while the \(D\) -value is shown inside each row. In the last column, the average RMS pattern of each success solution is depicted in the long-term time series, where the overall average RMS of success solutions by 3-, 5-, 7-, and 9-day is presented from left to right with different colours. In addition, the Sun elevation angle of \(\left|\beta\right|\) is plotted on the right side of these sub-figures. The results of SLR-only orbit determination for BDS GEO C01 is shown in Figure 6. With the increase of arc length from 3-day to 9-day, the amount of success solutions increases from 34 to 64 in the statistical results of orbit overlaps. The average RMS of 9-day solutions is 0.42, 4.96, and 2.09 m, with the \(D\) -value of 93.8%, 89.1%, and 93.8% in RTN directions respectively. However, only 22, 15, 10, and 14 groups are retained for 3-, 5-, 7-, or 9-day solutions in the comparison with WUM microwave-based orbits. The reason is that many worse solutions are treated as failure solutions, which include singular solutions and eliminated solutions, and their average RMS can be tens, or even hundreds, of metres in RTN directions. Under the premise of increasing the statistical sample, the \(D\) -value can improve by 20%-40%, from 41.2% to 87.5% in R direction from the 3-day to 9-day solutions for comparison with WUM orbit for C08, 50% to 72.5% for C10, as well as 59.3% to 85.1% for C13, as seen in Figures 7-9. The improved \(D\) -value indicates that the statistical sample becomes more and more stable and reliable with the increase in multi-day arc length. Meanwhile, the statistical results show that the C08's average RMS of 9-day solutions is 0.23, 1.65, and 1.71 m for orbit overlaps, as well as 0.29, 1.97, and 1.97 m for comparison with WUM orbits in RTN directions. Like C08, the average RMS of C13 is always steadily improved with the increase in the multi-day arcs, and it can reach 0.27, 1.07, and 1.44 m, as well as 0.30, 1.04, and 1.40 m for both comparisons in RTN directions respectively. For C10, the best average RMS of orbit overlaps is statistically solved in 3-day arcs with 0.11, 1.01, and 0.90 m in RTN directions but only with a success rate of solutions of 5.8% (as seen in Table 4). Indeed, its 9-day solutions have the most reliable average RMS of 0.34, 1.89, and 2.65 m for orbit overlaps with a success rate of 45.3%, as well as 0.43, 2.67 and 3.91 m for comparison with WUM orbit with a success rate of 46.2% respectively.