## 2 Quality Assessment of COSMIC-2 GPS Observations
### Ionospheric Delay Rate  
The change rate of ionospheric delay refers to the change of ionospheric delay in unit time [34]. Influenced by the ions in the ionosphere, the propagation speed and propagation path of the signals emitted by GPS satellites change as they pass through the ionosphere, which has an effect on the time of signal propagation, thus changing the geometric distance  
Figure 5: Multipath errors of each COSMIC-2 satellite during DOY 138–142, 2021.  
Figure 6: Mean multipath errors of six COSMIC-2 satellites during DOY 138–142, 2021.  
between the source and the receiver [30]. The ionospheric delays on the L1 and L2 carriers are obtained by making a difference between the dual-frequency carrier-phase observations, assuming that the carrier waves of both frequencies have the same propagation path in the atmosphere [26]:  
\[I_{1}=\frac{1}{\alpha-1}(\lambda_{1}\varphi_{1}-\lambda_{2}\varphi_{2}-n_{1} \lambda_{1}+n_{2}\lambda_{2}) \tag{4}\]  
\[I_{2}=\frac{\alpha}{\alpha-1}(\lambda_{1}\varphi_{1}-\lambda_{2}\varphi_{2}-n_{ 1}\lambda_{1}+n_{2}\lambda_{2}) \tag{5}\]  
where, \(\varphi_{1}\), \(\varphi_{2}\) are the phase observations. \(IOD\) is computed in TEQC as follows [30]:  
\[IOD=\frac{\alpha}{\alpha-1}[(L_{1}-L_{2})_{i}-(L_{1}-L_{2})_{j-1}]/(t_{j}-t_{j- 1}) \tag{6}\]  
when \(IOD\geq 400\) cm/min, it is considered that the ionosphere jumps [25; 35; 36]. If the data of a whole day is selected, the 24-h window will make the image too dense to clearly display the changes. Therefore, the time period of 21:00:00-21:59:59 of Sat-2 is selected to analyze the ionospheric delay change rate, as shown in Figure 7.  
It can be seen from Figure 7, where when no cycle slips are present, the \(IOD\) is quite smaller than 400 cm/min [36], that since at the 500 km\(\sim\)525 km (height of the COSMIC-2), the observed ionosphere effect is only a small fraction of the total effect. It is also apparent from Figure 7, the \(IOD\) increases significantly at the end of the data acquisition cycle. And  
Figure 7: Ionospheric delay rate of Sat-2 ((**a**–**e**) are DOY 138–142 respectively).  
that the main reason for this phenomenon is the discontinuity of carrier phase data and the emergence of abnormal values [37].  
From the above GPS data quality analysis, it can be seen that the number of the visible GPS satellites of six COSMIC-2 satellites in the five days is mostly 7-10, and there are few epochs with the number of the tacked GPS satellite below 3; The low utilization of observations indicates that the quality of the surrounding observation environment is not high; The average cycle slip ratios of five days is relatively low, which indicates that the frequency of cycle slip of COSMIC-2 is high and the number of cycle slips is large during the observation period; In terms of SNR, the average value of six COSMIC-2 satellites is more than 300, and SNR1 and SNR2 are far greater than the threshold. In terms of multipath error, the RMS of \(MP1\) and \(MP2\) of COSMIC-2 are within the index value range, indicating that the satellite signal is less subject to multipath interference. In terms of \(IOD\), it is obviously found that the \(IOD\) changes greatly at the end of the data acquisition cycle, mainly due to the discontinuity of carrier-phase data and the emergence of outliers. Generally speaking, the GPS observation data quality of DOY 138-142, for five days, is general, the data loss is serious, and the cycle slip occurs frequently, but its signal-noise ratio is high, and the error caused by the multipath effect is small.