# Initial Assessment of the LEO Based Navigation Signal Augmentation System from Luojia-1A Satellite
## 4 In-Orbit Performance Evaluation Results
### Navigation Augmentation Signal Noise Evaluation  
The first navigation augmentation experiment of Luojia-1A is carried out on 9 June 2018 and the navigation augmentation signals from Luojia-1A were successfully tracked. The ground receiver of the Luojia-1A satellite is installed in Wuhan. The Luojia-1A receiver is capable of tracking GPS/Beidou dual-frequency observations and the Luojia-1A ranging signals. The Luojia-1A satellite ground track is presented in the left panel of Figure 8. Luojia-1A transmits ranging signals only in China to avoid potential signal inference to these international satellite operators. During the experiment period, the satellite moves toward the south direction. Although the GNSS antenna has been installed on the roof of the building, it is still obstructed by a roof ridge on the south direction. One satellite pass lasts about 10 min and the sky plot during the experiment is presented in Figure 9. The figure indicates that the elevation angle of the slow-moving GPS and Beidou ascends or descends 9.24\({}^{\circ}\) at most, while the elevation angle of the Luojia-1A varies more than 107\({}^{\circ}\) over the 10 min. For this particular satellite pass, the maximum elevation angle for the Luojia-1A satellite reaches 70\({}^{\circ}\). One of the most significant benefits of LEO navigation satellite is its fast-changing geometry, which helps to reduce the convergence time of PPP and long baseline RTK. For the Wuhan station, the Luojia-1A satellite has 4-5 visible passes per day and the total visible time is 30-40 min. Figure 8: Luojia-1A satellite footprint (**left panel**) and the setup of the ground receivers on a rooftop structure (**right panel**). Figure 7: Hardamard variance of the satellite clock (**left panel**) and the frequency drift of the satellite clock (**right panel**). The tracked navigation augmentation signals from Luojia-1A satellite is used for the pseudorange noise analysis. Since there is only one LEO satellite in orbit, it is impossible to evaluate the receiver noise with the popular double differenced method. Therefore, the pseudorange noise is evaluated with the single receiver approach. The test statistics are constructed with:  
\[ \begin{array}{rl}\hat{\varepsilon}_{p,i}&=(P_{i,t}-P_{i,t-1})-(L_{i,t}-L_{i,t- 1})\\ &\qquad\approx 4\Delta I_{i}+2(1-\rho)\varepsilon_{P}\end{array}  \tag{6}\]  
where \(\hat{\varepsilon}_{p,i}\) is the test statistics for the pseudorange noise on \(i\)th frequency. \(P_{i}\), \(L_{i}\) are the pseudorange, carrier phase measurement on \(i\)th frequency expressed in meters. The subscript \(t,t-1\) refers the current epoch and previous epoch.\(\Delta I_{i}\) refers to the time-differenced ionosphere delay. \(\rho\) refers to the autocorrelation between the pseudorange measurement. \(\varepsilon_{P}\) refers to the pseudorange noise. In the equation, the carrier phase noise is ignored and no cycle slip is assumed. The ionosphere variation rate is normally less than 1 cm/s, so it can be neglected [63]. The pseudorange measurement is not filtered, hence the autocorrelation also can be neglected, and then the observed test statistics approximated equals to twice pseudorange noise. The observed pseudorange noise for the frequency H1 is presented in Figure 10. The figure shows that the tracked satellite path length is about 7 min. The signals are locked when the satellite elevation is at 25\({}^{\circ}\) and lost lock at eight degrees. The elevation angle of acquisition and loss-of-lock is not the same since the acquisition sensitivity and the tracking sensitivity of the receiver are not the same. In addition, the signal tracking is a time-consuming procedure especially for these LEOs with large Doppler frequency shift. The figure shows that the signal is stably locked and no loss of lock occurs during the satellite pass.