## 4 Experimental Results
### Reference Channel Processing Results  
The reference channel data were processed using the proposed method in Section 3.2. Taking the first set of experimental data (7:59 on 17 April 2023) as an example, Figure 13 shows the results of GPS satellite acquisition and tracking. More than four GPS satellites were successfully captured. In order to make the transmitter and receiver located on the same side of the imaging observation scene, forming a typical bistatic configuration, the GPS satellite PRN4 was selected as the transmitter. Figure 14 shows the precise carrier frequency obtained by continuous tracking for 300 s for this satellite. After partial amplification, it can be clearly seen that the measured carrier frequency (Doppler) had been experiencing severe jitter. The tracked carrier frequency could be used to calculate the Doppler phase, which still contained intermediate frequency information of the receiver.  
According to Equations (12) and (13), the measured value and theoretical value of the Doppler phase of the reference channel could be calculated, and the results are shown  
\begin{table}
\begin{tabular}{c c c c} \hline
**Quantity** & **Value** & **Quantity** & **Value** \\ \hline Satellite signal source & GPS L5 PRN 4 & Pulse width & 1 ms \\ Signal bandwidth & 20.46 MHz & Equivalent PRF & 1000 Hz \\ Receiver IF & 139.95 MHz & Reflect antenna gain & 12 diBi \\ Sampling Rate & 62 MHz & Integration time & 300 s \\ \hline \end{tabular}
\end{table}
Table 1: The parameters used in the experiment.  
Figure 14: The reference channel carrier frequency tracking results.  
Figure 13: GPS satellite acquisition results and sky map. (**a**) Sky map at the test time; (**b**) acquisition results at the test time.  
in Figure 15. There was a clear difference in Doppler center frequency. Moreover, since the measured Doppler phase was obtained by the tracked carrier frequency (as shown in Figure 14), it was not as smooth as the theoretical Doppler phase and has fluctuations. Due to the long synthetic aperture time, if the theoretical phase curve is directly used to achieve phase compensate for the echo, the energy of the target between different pulses will be directed at different phase angles, or even cancel each other, making effective energy integration impossible.  
Furthermore, using the proposed error extraction method in Section 3.2, the ionospheric scintillation error could be extracted from the measured Doppler phase. Figure 16 shows the total Doppler phase error and the fitted ionospheric scintillation error extracted from the three sets of data in the morning, midday, and evening. The three experiments used GPS satellite PRN 4, 30, and 18 as transmitters, respectively. The sky map at that moment of the experiment can be found on the public website, which is consistent with the results obtained by acquisition and tracking. The trends of the total Doppler phase errors obtained from the three experiments were generally consistent. This was because the azimuth angles and trajectories of the three satellites were relatively close at that time of observation. Polynomial fitting was performed on the total phase error, and the residual value after fitting mainly reflected the influence of the ionospheric scintillation error. Regarding these three data sets, the ionospheric scintillation phase during the morning and noon remained within two radians, while it increased at night, reaching up to five radians. It can be preliminarily verified that there were changes in ionospheric scintillation at different times of the day. In addition, the specific curve that can reflect the diurnal variation of ionospheric scintillation requires more experimental data for statistical analysis to be obtained.  
Figure 16: Reference channel Doppler phase errors extraction results from three sets of experimental results. (**a**) In the morning; (**b**) at midday; (**c**) in the evening.  
Figure 15: Comparison of the theoretical value and the measured value of the reference phase.