## 4 Result of the Experiment and Discussion
### Signal Error Estimation Simulation  
The distributed SAR system simulated in this section has four uniformly and co-linearly arranged channels with mixed baselines between channels, and the system parameters are shown in Table 1 for a typical hypersonic platform.  
Figure 6: Equivalent trajectory offset after signal error compensation.  
In this section, the estimation result curves of the TDCM and OSM in the presence of motion errors are obtained by simulation, as shown in Figure 7. The SNR of the simulation scene is 30 dB, containing 41 range samples and 512 azimuth samples. Channel 1 is the reference channel, Channel 2 has a phase error of 90\({}^{\circ}\), and Channels 3 and 4 have no phase error. To illustrate the effect of motion error, the radial velocity of the platform is set at 2 m/s and the acceleration at 5 m/s\({}^{2}\). The azimuth axis of the OSM represents the azimuth Doppler frequency; the azimuth axis of the TDCM represents the slow time. When there is no motion error, the two methods should be estimated as straight lines. However, due to the existence of motion errors, the OSM estimation fails. The TDCM estimation results have a certain slope and deviate from the true value. From Equation (15), the slope is caused by the \(4\pi d_{m}a_{c}\eta/(\lambda v_{a})\) term; the shift of the mean value is caused by both velocity and acceleration.  
By averaging the sampling points without estimating the motion error and with deviations from the true channel error, the OSM and the traditional TDCM obtained channel error estimates of 42.6\({}^{\circ}\) and 50.7\({}^{\circ}\), respectively. The radial acceleration of the platform is not estimated by the TDCM or OSM. There are still large residual signal errors that remain after only compensating for the channel error estimated by the TDCM or OSM. Comparing the TDCM to the OSM, radial acceleration can be obtained by fitting the result of the TDCM but not the OSM. Therefore, the proposed method is based on the TDCM.  
The proposed method obtains a constant term phase error of 50.7\({}^{\circ}\) and a radial acceleration estimate of 5.1 m/s\({}^{2}\) by linearly fitting the TDCM estimation results. The proposed method has the same bias related to the channel phase error as the traditional TDCM. However, from the analysis in Section 3.2, after compensating for the phase error obtained  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Platform velocity & 1700 m/s \\ Wavelength & 0.03 m \\ Channel spacing (\(x\), \(y\), \(z\)) & (10 m, 4.8 m, 4 m) \\ Antenna azimuthal size & 1.5 m \\ Transmit signal bandwidth & 200 MHz \\ Pulse repetition frequency & 900 Hz \\ Platform height & 20 km \\ Radial velocity & 2 m/s \\ Radial acceleration & 5 m/s\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Distributed SAR simulation system parameters.  
Figure 7: Phase error estimation results using the OSM and TDCM.  
from the fit by considering the radial acceleration, the remaining phase error is equivalent to making the sampling point arrangement offset from the ideal trajectory, which does not affect the subsequent imaging. In contrast, the traditional TDCM does not estimate the motion error, and the phase error caused by the residual acceleration will affect the imaging quality. The effect on the imaging results is shown in the scene simulation in Section 4.2 and the processing of the real data in Section 4.3.