# Adaptive 3D Imaging for Moving Targets Based on a SIMO InISAR Imaging System in 0.2 THz Band
## 4 Three-dimensional Imaging of Moving Targets with InISAR Technology  
### ISAR Imaging with Combined Motion Compensation  
The adaptive tracking enables the continuous observation of the moving targets, which then provides a foundation for acquiring the high-resolution images using the ISAR imaging technique. Furthermore, the multiple receiving channels of the system make it possible to achieve the 3D imaging utilizing the interferometric technique. In this study, a combined motion compensation method was developed to fit in the special SIMO system \begin{table}
\begin{tabular}{l} \hline \hline Input: Received raw echoes from Rx1–Rx4 in real-time. \\ \hline Step 1: Synthesize the virtual sum signal by accumulating the echoes from the four receiving channels, and extract the echoes from Rx1, Rx2, and Rx4. \\ Step 2: Perform range compression to produce the HRRPs for the virtual sum channel, receiving channel Rx1, Rx2, and Rx4. \\ Step 3: Conduct target detection based on the virtual sum HRRP to find the range cells in which scatterers locate. The range information of each detected scatterer can be obtained at the same time. \\ Step 4: Extract the complex responses of each scatterer in the HRRPs of Rx1, Rx2, and Rx4 according to their range cell numbers. Then extract the phase response differences in the two receiver couples Rx1 \& Rx2 and Rx1 \& Rx4, respectively. \\ Step 5: For each scatterer, following equation (14), calculate its azimuth deviation angle with the phase response difference of Rx1 \& Rx2, and calculate its elevation deviation angle with the phase response difference of Rx1 \& Rx4. \\ Step 6: Determine the \((x,y,z)\) coordinates of each scatterer using corresponding range and angle information obtained in Step 3 and Step 5. Then synthesize the target geometric center to realize target locating. \\ Step 7: Perform Kalman filtering to get the tracking result, based on which the relative deviation of target from the antenna axis can be determined. \\ Step 8: Adjust the antenna pointing direction according to the relative deviation. \\ \hline \hline Output: Real-time tracking of the moving target. \\ \hline \end{tabular}
\end{table} 
Table 1: Detailed procedures of the target locating and tracking. Figure 5: Flowchart of target locating and tracking with multiple beams. configuration, with which the well-focused and coherent ISAR images are obtained for each channel. Motion compensation is a critical procedure in ISAR imaging, which includes envelope alignment and phase correction [35]. The target range may vary during imaging interval and migration through range cell (MTRC) may occur, hence envelope alignment is necessary to remove the MTRC. After that, a phase correction is performed to eliminate the phase error caused by the noise or induced in range alignment operation. In (7) and (8) it can be seen that the main part of the range term from the target to the receiving antenna is approximately equal to that to the transmitting antenna, so it's practical to estimate the target movement component based on the virtual sum signal, whose phase history is dependent on the range from the target to the transmitting antenna. After the range alignment for the virtual sum channel is finished, time-varying phase errors may still exist along the slow-time, hence the phase correction is required to compensate this phase error, for the purpose of achieving focused ISAR images. In this paper, the phase gradient autofocus (PGA) algorithm [36] is applied to estimate the phase errors. The estimated range migration and phase error based on the virtual sum signal are utilized to perform motion compensation on the four receiving channels, which is called combined motion compensation. This operation not only guarantees the coherence of the signals in different channels, but also improves the quality of compensation, considering the high SNR of the virtual sum signal.