## 3 Results and Analysis
### GPS/BDS Single-Frequency KOD Analysis of Luojia-1A Satellite  
Orbit determination of the Luojia-1A using the C/N0-based weighting model considering the attitude impact is evaluated by adding low-elevation observations with the single-frequency KOD strategy. To validate the feasibility of the proposed weighting model, GPS/BDS observations from the Luojia-1A satellite between \(-10^{\circ}\)and \(5^{\circ}\) elevation angles are used in one scheme. For the GPS/BDS combination case, the number of satellites above the \(5^{\circ}\) and \(-10^{\circ}\) elevation mask and the position dilution of precision (PDOP) values are compared in Figure 10. It might be also interesting to investigate the contribution of the GPS and BDS combination in the single-frequency LEO KOD. To validate the speculation that combining BDS and GPS may benefit orbit determination and demonstrate the impact of the fluctuating number of visible BDS satellites, the contribution of BDS is analyzed using the observations from satellites above the \(-10^{\circ}\) elevation mask. Figure 10 shows that the number of available satellites ranges from 5 to 20 and the PDOP value ranges from 0.875 to 2.685 for the \(-10^{\circ}\) elevation mask scheme in the GPS/BDS combination, denoted by the blue line. There is an average of 10 satellites available above the \(5^{\circ}\) elevation angle and an average of 13 satellites above the \(-10^{\circ}\) elevation angle, achieving 37.5% improvement in PDOP by decreasing the elevation cutoff angle to \(-10^{\circ}\). The shadow area shows that BDS has a clear contribution to both the number of available satellites and the PDOP when the Luojia-1A satellite flies over China, since the orbit period of the Luojia-1A satellite is approximately 96 min, and Luojia-1A is designed to track the signals of the BDS regional system. During these periods, the GPS/BDS combination has on average five satellites more than the GPS-only case. The average PDOP for the cases of  
Figure 9: Number of GPS and BDS cycle slips detected by the HTD algorithm and the new algorithm considering the clock steering events. single GPS and the GPS/BDS combination are 1.526 and 1.277, respectively, which is an improvement of 16.3%. The impact of low-elevation angle measurements on orbit determination and the contribution of BDS to the KOD is shown in Figure 11, which is the cumulative distribution function of absolute orbital error in the radial, along-track, and cross-track directions, respectively. The kinematic orbital error is also evaluated in terms of root mean square (RMS) error. Table 2 shows the statistical performance of the positioning accuracy. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Scheme**} & \multicolumn{2}{c}{**Radial-Track (m)**} & \multicolumn{2}{c}{**Along-Track (m)**} & \multicolumn{2}{c}{**Cross-Track (m)**} & \multirow{2}{*}{**Epoch**} \\ \cline{2-2} \cline{5-7}  & **RMS** & **Mean** & **RMS** & **Mean** & **RMS** & **Mean** & \\ \hline GPS \(>-10^{\circ}\) & 2.302 & 1.237 & 1.965 & 0.681 & 0.993 & \(-0.680\) & 25,136 \\ GPS + BDS \(>5^{\circ}\) & 2.104 & 0.823 & 2.069 & 0.830 & 1.057 & \(-0.760\) & 23,835 \\ GPS + BDS \(>-10^{\circ}\) & 1.640 & 0.848 & 1.729 & 0.803 & 0.988 & \(-0.563\) & 27,367 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance statistics of the positioning accuracy. Figure 10: Number of available satellites and PDOP values. Figure 11 shows that the orbital error obtained from the \(-10^{\circ}\) elevation mask scheme in the GPS/BDS combination denoted with the blue line is the best in all components. The reason is that the number of available satellites increases remarkably and large residuals can be removed from the observations. Compared to the \(-10^{\circ}\) elevation mask scheme, 12.9% of epochs cannot be utilized for the \(5^{\circ}\) elevation mask scheme with the red line whose RMS values of the orbital error are 2.104, 2.069, and 1.057 m in the radial, along-track, and cross-track directions.