# Initial Assessment of the LEO Based Navigation Signal Augmentation System from Luojia-1A Satellite
## 4 In-Orbit Performance Evaluation Results
### In-Orbit Evaluation of the Orbit and Clock  
Luojia-1A satellite maintains the time and coordinate system via onboard orbit determination procedure rather than the ground test facilities. The accuracy of the time/coordinate system maintenance would affect the augmentation performance. Hence, the precision of onboard orbit and clock determination should be evaluated. The precision of the onboard orbit and clock is affected by the quality of the onboard GNSS observation quality and the algorithm implementation. In this study, the Beidou observation quality of onboard receiver is assessed and the results are presented in Figure 4.  
The left panel of Figure 4 shows the relationship between the carrier to noise ratio (C/N0) of the B1/B2 signals and the elevation angle. The data is collected with a 1 Hz sampling rate. The figure indicates that the maximum C/N0 of B1 and B2 are about 50 dB-Hz and 46 dB-Hz, respectively. The C/N0 of B2 signals is slightly lower than B1 since the antenna gain for B2 frequency is not as good as B1. The figure indicates that the C/N0 is higher for the high elevation angle case. A remarkable difference between the LEO observations and the ground observations is that LEO receivers also capable of tracking the observations with negative elevation angle. Luojia-1A is equipped with two receiving antennas facing the opposite direction, so it is capable of tracking observations up to \(-20^{\circ}\)  
Figure 3: Ground assessment of the Luojia-A ranging measurements: the test scenario (**left panel**) and measured signal samples (**right panel**). The LEOs equipped with single GNSS antennas are also capable of tracking signals up to \(-5^{\circ}\), such as the CHAMP mission [58]. The observation with negative elevation angle is received from the other side of the Earth. The signals penetrated the atmosphere of the Earth and bent by the varying atmosphere reflectivity, which can be used to retrieve the ionosphere/troposphere profile [59; 60]. The relationship between the multipath of B1 and B2 pseudorange and the elevation angle is presented in the right panel of Figure 4. The pseudorange and the carrier phase measurements from Luojia-1A satellite onboard receiver can be briefly expressed as:  
\[ \begin{split} P_{i}=\rho+\delta_{orb}+c(\delta t^{S}-\delta t^{R} )+I_{i}+\delta_{trop}+\epsilon_{Pi}\\ L_{i}=\rho+\delta_{orb}+c(\delta t^{S}-\delta t^{R})-I_{i}+\delta_ {trop}+\lambda_{i}N_{i}+\epsilon_{\phi i}\end{split}  \tag{3}\]  
where \(\delta_{orb}\) is the orbital error. \(I_{i}\) and \(\delta_{trop}\) are the ionospheric delay and tropospheric delay, respectively. The definition of the rest terms is the same as Equation (1)  
The multipath value is computed from [61]:  
\[ \begin{split} MP_{1}&=P_{1}-L_{1}+\frac{2}{\alpha- 1}(L_{2}-L_{1})\\ MP_{2}&=P_{2}-L_{2}+\frac{2\alpha}{\alpha-1}(L_{2}- L_{1})\end{split}  \tag{4}\]  
where \(MP_{1}\) and \(MP_{2}\) are the multipath statistics, \(P_{1},P_{2}\) and \(L_{1},L_{2}\) are the pseudorange and carrier phase measurements expressed in meters. \(\alpha=f_{1}^{2}/f_{2}^{2}\), where \(f_{1}\) and \(f_{2}\) are the frequency of \(L1\) and \(L2\). It is noticed that the multipath statistics includes the carrier phase bias and the pseudorange multipath. As long as the carrier phase ambiguity does not change, the standard deviation of \(MP_{1}\) and \(MP_{2}\) is the same as the pseudorange multipath. The figure indicates that the pseudorange multipath is less significant for higher elevation angle cases. Since the GNSS signals are tracked by two GNSS antennas in opposite directions, The Luojia-1A satellite is capable of tracking signals from negative elevation angle satellites. Due to the obstruction of the Earth, the satellite is not able to track observations lower than \(-20^{\circ}\). Generally, the multipath error of B1 and B2 are less than two meters. The standard deviation of B1 and B2 are 0.31 m and 0.44 m, respectively. The B2 signal is noisier due to its low C/N0.