# 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
Comparing the Beidou observations collected by Fengyun-3C [62], the Luojia-1A GNSS observations have lower pseudorange noise level. Figure 4: C/N0 (**Left**) and multipath (**Right**) of Luojia-1A onboard Beidou B1/B2 observation. Luojia-1A equipped two receiving antennas for GNSS signals retrieving since the solar panel of the satellite faces toward the sun in standby mode. The number of tracked GPS/Bedou is presented in Figure 5. The figure shows there is a significant period on the tracked satellite number and two antennas work in turn. The onboard receiver is capable of retrieving 12 GPS satellite and 12 Beidou satellites simultaneously. The maximum visible satellite number for \(-\)z antenna reaches 18, while \(+\)z tracked 15 satellites at maximum. The \(-\)z antenna tracked more visible satellites than the \(+\)z antenna since the Beidou satellites are not evenly deployed. The figure also indicates that there is some loss of lock events that happened on both the \(+\)z antenna and \(-\)z antenna, which still need to be investigated. Considering the latency of onboard data processing, the real-time orbit is extrapolated for a short period and encoded into the broadcast ephemeris. The receivers decode the broadcast ephemeris and extrapolating the orbit to the time of concern. Due to the short visible window, the broadcast ephemeris design has different requirements as current GNSS satellites. There are a few studies discussing how to reasonably select the broadcast parameters to represent the centimeter-level LEO orbit [28; 29; 30]. However, all these methods are curve fitting based on precise orbit determination results. They are not suitable for onboard autonomous ephemeris generation. Instead of long-term fitting algorithms, Luojia-1A employs a rapid updating rate algorithm for the broadcast ephemeris. The orbit elements in the broadcast ephemeris are updated every 30 s, and the clock information is updated every 6 s. The clock information is updated more frequently to mitigate its extrapolation error. Considering the complexity of the ground observing condition, broadcast ephemeris redundancy scheme and parity scheme is adopted to facilitate the error correction during the ephemeris decoding procedure. Currently, Luojia-1A only broadcasts the navigation augmentation signal over China, so only a short-arc orbit is accessible from the broadcast ephemeris. The Luojia-1A satellite is not equipped with laser retroreflector arrays. Therefore, the external validation with the laser ranging technique is not feasible. Furthermore, the absolute orbit precision assessment is not feasible for the Luojia-1A satellite. In this study, the orbit calculated from the broadcast ephemeris is compared with the dynamic smoothed orbit. The dynamic smoothed orbit is a fusion solution of GNSS observations and satellite dynamic information with a Kalman smoothing algorithm in post-processing mode. Since only a part of the orbit is visible, the dynamic smoothed orbit subject to systematic bias with respect to its true position. As this bias can be assimilated into the clock term, the bias has limited adverse impact on positioning. The satellite orbit is extrapolated to 1 Hz with the user algorithm of the Luojia-1A broadcast ephemeris and compared with the dynamically-smoothed orbit. The comparison results are presented in Figure 6. The figure indicates that the internal precision of the Luojia-1A broadcast ephemeris is 0.09 m, 0.08 m and 0.11 m for the X, Y, and Z direction in the Earth center Earth-fixed (ECEF) frame. The maximum discrepancy between the broadcast ephemeris and the dynamic smoothed orbit is about 0.3 m for 30 s extrapolation. The discontinuity of the orbit error is caused by the ephemeris update. The figure indicates that the user algorithm introduces decimeter level orbit error after 30 s  
Figure 5: Visible satellite number of different \(+\)Z and \(-\)Z GNSS antennas. extrapolation, which is considered acceptable. On the other hand, it also shows that 30 s updating interval is proper for the current user algorithm.