# Adaptive 3D Imaging for Moving Targets Based on a SIMO InISAR Imaging System in 0.2 THz Band
## 3 Adaptive Tracking of the Moving Targets Using Multiple Beams
### Target Locating with Phase Difference of Multiple Beams  
Taking the advantage of multiple receiving channels of the system, the angular information of the targets can be acquired using the response difference in different channels according to the monopulse technique [31], making it possible to track the moving targets. Since the phase centers of the receiving antennas are located in the same plane along baselines lying in the azimuth and elevation directions, they constitute a typical antenna structure for phase-comparison monopulse technique, which accomplishes angle measurement by analyzing the phase response difference in different channels. Figure 4 gives an illustration of the angular measurement using the phase difference of two receiving channels. The red dot denoted with \"Tx0\" indicates the transmitting antenna, while the green dots denoted with \"Rx1\" and \"Rx2\" stand for the two receiving antennas. Under the plane-wave assumption, the wave paths in the two channels are different due to the displacement of their antennas, which will cause phase difference in the received echoes. The phase difference \(\Delta\phi\) is mainly determined by the baseline length \(L\) and target deviation angle \(\Delta\phi\), whose relationship obeys the formula:  
\[\Delta\phi=\frac{2\pi L\sin\Delta\phi}{\lambda} \tag{13}\]  
In practice, the value of \(\Delta\phi\) is usually obtained from the HRRPs of the receiving channels. The angular information can be immediately obtained with the following equation:  
\[\Delta\varphi=\text{asin}\frac{\lambda\Delta\phi}{2\pi L} \tag{14}\]  
Generally, the angle measurement requires two receiving antennas which can form a baseline in a certain direction. A possible combination may be that Rx1 & Rx2 are used for azimuth angle measuring, and Rx1 & Rx4 are used for elevation angle measuring. Otherwise, the angle measurement in the azimuth direction can be accomplished using Rx3 & Rx4 couples, while the Rx3 & Rx2 couples can be used in elevation direction, with the same manner as shown in the above. In this paper, in order to track the moving targets with high accuracy, a geometric center based tracking method is adopted. Since the large bandwidth of the FMCW signal enables a finer range resolution, scatterers from different parts of the targets can be resolved in the HRRP and the targets can be precisely located with the position information of multiple scatterers. Without losing generality, three receiving channels Rx1, Rx2, and Rx4 were selected to illustrate the moving targets tracking processing with the SIMO system in this paper, and the whole flowchart is shown in Figure 5. Practically, the target tracking process includes the following steps. Firstly, the target detection is performed based on the HRRP of the virtual sum signal to detect the scatterers. Then, the angle measurement is performed to get the angular positions of each scatterer. Next, the geometric center of the target is synthesized using the range and angle information of the detected scatterers. After that, the measured results are input to a tracking filter to get a smooth and stable tracking trajectory. Finally, the antenna pointing direction is adaptively updated according to the output of tracking filter, ensuring a continuous beaming of the targets. Generally, the Kalman filter is preferred considering its robustness in most tracking scenarios [32]. If the targets undergo complex maneuvering movement, more comprehensive tracking algorithm like interactive multiple model (IMM) [33] can be selected. In this paper, since the targets mainly undergo translational movement, the Kalman filter is applied. In addition, to ensure a high tracking stability, the radar works in the step-tracking mode, which measures the target's location using a consecutive number of echoes; more practical processing is explained in detail in [34].