## 3 Results and Analysis
### Validation of the C/N0 Based Weighting Model  
Luojia-1A is a nanosatellite that employs the sun-pointing attitude mode differently from that of GPS satellites. In Luojia-1A, the negative Z-axis is fixed toward the sun to obtain enough energy in standby mode, so the boresight direction of the GNSS antenna does not always point toward the zenith direction. Consequently, the C/N0 of the GNSS signals collected from the onboard receivers is significantly different from that of the ground receiver. The elevation dependence on the C/N0 of GPS/BDS measurements collected from the Luojia-1A satellite is presented in Figure 7.  
Figure 7 indicates that the satellite is capable of tracking observations of low-elevation angles, even negative angles, and the low-elevation measurements (<20\({}^{\circ}\)) contribute to about 50% of total measurements. The LEO onboard receiver still tracks the signals with a sufficient amount of C/N0 strength, which shows a parabolic relationship with the elevation angle caused by the satellite attitude mode. The C/N0 in Figure 7 denotes the \begin{table}
\begin{tabular}{c c} \hline \hline
**Items** & **Models** \\ \hline Observations & Ionospheric-free L1 GRAPHIC combination and pseudorange observations \\ Observation weight & Proposed method \\ Estimator & Extended Kalman filter \\ Phase-windup effect & Corrected [46] \\ Satellite antenna phase center and variation & GPS, BDS: IGS14 \\ Receiver antenna phase center and variation & Not corrected \\ Tide displacement & Not corrected \\ DCBs & GPS P1C1/P1P2 product from CODE \\ Relativistic effects & Corrected (International Earth rotation and reference systems, IERS 2003) \\ Satellite orbit and clock of GPS/BDS & German research center for geosciences (GFZ) precise products \\ Tropospheric delay & Not considered \\ Receiver clock & Estimated as white noise for GPS and BDS, respectively \\ Carrier Phase ambiguities & Constants for each continuous tracking arc \\ LEO satellite position & Estimated as white noise \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Processing configuration of the Luojia-1A kinematic orbit determination method with single-frequency data. Figure 7: Percentage and signal strength of observations. The histogram is the percentage of observations and the blue line denotes the signal strength. average value in the range of ten degrees. The average C/N0 is calculated every ten degrees as the elevation angle increases. It can be seen from Figure 7 that the signal strength of observations from the LEO onboard receiver in the range of \(-10^{\circ}\) to \(10^{\circ}\) elevation is close to that of the \(10^{\circ}\) to \(20^{\circ}\) elevation angle and is on average 1.8 dB-Hz lower than that above the \(20^{\circ}\) elevation angle. It shows that the signal strength of the \(-10^{\circ}\) to \(10^{\circ}\) elevation angle observations has about the same data quality as that of the observations in the range of \(10^{\circ}\) to \(20^{\circ}\) elevation. Therefore, the low-elevation observations can be used if a suitable weighting model is built for the LEO KOD. The elevation-dependent weighting model cannot describe the data quality of low-elevation observations correctly for the sun-pointing attitude mode. To build and validate the C/N0-based weighting model, the multipath and observation noise of the pseudorange is first calculated and is both geometry-free and ionosphere-free. The ambiguity biases are assumed to be constant unless there is a slip in the tracking of phases. The effect of the phase multipath is much smaller in magnitude than the pseudorange multipath, and thus can be neglectable. To cope with the satellite attitude impact, the weighting model is established in advance based on the variation of the multipath and observation noise with the C/N0 for the onboard Luojia-1A GNSS receiver, which is presented in Figure 8.  
Figure 8 indicates that the multipath and observation noise is strongly correlated to the C/N0, and thus the weighting model is reasonable, especially during the attitude maneuver.