# Initial Assessment of the LEO Based Navigation Signal Augmentation System from Luojia-1A Satellite
## 3 Ground Assessment of the Navigation Augmentation Signals  
Before satellite assembly, the navigation augmentation payload was tested on the ground to ensure its performance. Many different tests have been undertaken, while the most important is the quality of the oscillator. The short-term stability of the oscillator can be evaluated in time-domain by Allan variance/Hadamard variance [49; 50], or in the frequency domain by the phase noise [51]. The carrier phase noise is one of the most important frequency quality indicators, which directly impact the quality of the augmentation carrier phase signals. The phase noise is defined as a quality criterion for all navigation systems in their interface control documents. GPS/GLONASS requires the phase noise at f0 + 10 Hz no greater than 0.1 radians RMS [52; 53] and Galileo is no greater than 0.04 radians RMS [54]. Beidou and QZSS defined a more detailed phase noise requirement at a different frequency offset [55; 56]. The ground augmentation system Locata follows the GPS standard, but it works at 2.4 GHz [57]. The phase noise measured with the phase noise analyzer for the dual frequency band signals are presented in Figure 2. The blue lines are measured phase noise and the red lines are the smoothed phase noise. The figure indicates that the Luojia-1A satellite achieves excellent phase noise performance although it employs a miniature, low-cost OCXO. Luojia-1A satellite achieves better than \(-66\) dBc/Hz at f0 + 10 Hz and better than 88 dBc/Hz at f0 + 1 kHz, which means the short-term stability of Luojia-1A signals is comparable with the QZSS and Beidou navigation satellites. In addition to the laboratory test, the measurement precision was assessed by the field test. The payload was set up on the top of a small hill and the receiver was set up at about 2.5 km away from the transmitter. There was no tall building obstruction in the line-of-sight direction between the receiver and the transmitter, but there were a few trees and low buildings. The setup of the experiment is shown in the left panel of Figure 3. A signal attenuator is applied at the transmitter side to control the transmitting power. A chip-scale atomic clock (CSAC) is equipped at the receiver side to mitigate the receiver clock effect. The nominal one-second frequency stability of the CSAC is better than 1.5 \(\times\) 10\({}^{-10}\). Applying a high-quality oscillator at both the transmitter and receiver side is to ensure the clock frequencies are stable over the experiment period. For the ground ranging signals, the atmosphere delay is negligible, so the ranging observations can be expressed as:  
\[ \begin{split} P_{i}=\rho+c(\delta t^{5}-\delta t^{R})+\epsilon_{ pi}\\ L_{i}=\rho+c(\delta t^{5}-\delta t^{R})+\lambda_{i}N_{i}+\epsilon_{ \phi i}\end{split}  \tag{1}\]  
where \(P_{i}\) and \(L_{i}\) are the pseudorange and carrier phase measurements on the \(i\)th frequency expressed in meters. \(\rho\) is the geometrical distances. \(\delta t^{S}\) and \(\delta t^{R}\) are the satellite clock bias and the receiver clock bias, respectively. \(\lambda_{i}\) and \(N_{i}\) are the wavelength and unknown integer cycle number of carrier phase (ambiguity) on \(i\)th frequency, respectively.\(\epsilon_{Pi}\) and \(\epsilon_{\phi i}\) are the measurement noise of the pseudorange measurements and carrier phase measurements, respectively. For the static test, the geometry distance \(\rho\) does not change over time. The ambiguity can also be considered as a constant if no cycle slip occurs. The oscillators equipped in the transmitter and the receiver side are all high stable clocks, so the clock biases can be modeled as constants or slopes over the time span. In this case, the measurement noise for the ground test can be evaluated by the time differenced approach. Assuming the temporal correlation between the measurements is negligible, the measurement noise can be expressed as:  
\[