# Phase Imbalance Analysis of GF-3 Along-Track InSAR Data for Ocean Current Measurement
## 2 Ocean Current Measurement Method Based on GF-3 ATI Data
### Error Analysis of the Phase Imbalances between Channels
It can be seen from the geometric relationship that \(\theta\) and \(\psi\) vary with range. Therefore, \(f_{dc}\) and \(\Delta\phi\) will change approximately linearly in range caused by squint imaging and baseline error. Firstly, only considering the baseline error caused by the antenna phase center position error, that is when the squint angle is zero, the phase imbalance and the measured radial velocity error can be expressed as:  
\[\Delta\phi=\frac{2\pi}{\lambda}(\Delta z\cos\theta-\Delta x\sin\theta), \tag{19}\]  
\[\Delta V_{r}=\frac{V_{s}}{d}(\Delta z\cos\theta-\Delta x\sin\theta)=\frac{V_{ s}}{d}B_{\parallel}, \tag{20}\]  
Performing the Taylor expansion of Equation (20) and ignoring higher order terms,  
Figure 2:0  
where \(B_{\parallel}\) and \(B_{\perp}\) represent the baseline component parallel to the slant direction and the baseline component perpendicular to the slant direction caused by the antenna phase center position error, respectively. Define \(\Delta\theta=\theta_{far}-\theta_{near}\), where \(\theta_{far}\) and \(\theta_{near}\) represent the look angle of the image far range and near range, respectively. Obviously, the error increases with the increase of \(B_{\perp}\). On the one hand, \(B_{\parallel}\) must reach an accuracy of 0.1 mm to make the constant term of velocity error less than 0.1 m/s. On the other hand, four sets of look angle parameters of GF-3 FSI imaging mode, which are shown in Table 1, are selected to calculate the maximum allowable \(B_{\perp}\), ensuring that the calculated radial velocity along the range is less than 0.1 m/s in GF-3 ATI mode. For example, when GF-3 imaging is at the antenna beam of 162, the antenna baseline error component \(B_{\parallel}\) caused by antenna phase center position error must be less than 0.1 mm, and component \(B_{\perp}\) must be less than 1.58 mm, where the look angle under the center is 18.22\({}^{\circ}\), \(\Delta\theta=3.63^{\circ}\). Moreover, \(\Delta x\) and \(\Delta z\)must be in the quadrilateral surrounded by the four constraint curves shown in Figure 3a, so that the radial velocity measurement error caused by antenna phase center position error can be ignored for current measurements. Secondly, considering the baseline error caused by the attitude error and ignoring the squint angle caused by it, the position error of the antenna phase center introduced by the attitude error can be expressed as:  
Figure 2:1  
where \(\Delta\theta_{pitch}\) is the pitch error and \(\Delta\theta_{yaw}\) is the yaw error. Similarly, \(\Delta\theta_{pitch}\) and \(\Delta\theta_{yaw}\) must be within a quadrilateral surrounded by four constraint curves, which is shown in Figure 3b. Therefore, attitude control and antenna phase center position must be sufficiently accurate in ocean surface radial velocity measurement. Moreover, it can be found that the accuracy requirement of \(\Delta z\) is higher than that of \(\Delta x\), and the accuracy requirement of the pitch angle is higher than that of the yaw angle. Generally speaking, when \(B_{\perp}\) and \(B_{\parallel}\) is out of range, the phase imbalance of the antenna in the ocean scene needs to be eliminated by using the phase imbalance of the land scene. Thirdly, the phase imbalance caused by the baseline error will be affected by the target elevation from Equation (17). For the spaceborne ATI-SAR system, \(\Delta z\) is generally in the order of mm and \(R_{0}\) in the order of several hundred kilometers, so the space-varying of phase imbalance caused by target elevation is too small to be ignored. Therefore, the target elevation factor is not the main cause of phase imbalance in range for the spaceborne ATI-SAR system.