# 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  
### Model of GF-3 ATI Ocean Current Measurement  
The GF-3 ATI-SAR system applies two antennas arranged along the track direction to acquire the echo reflected by the same observation area. The interferometric phase of the echo signals acquired by two channels is proportional to the target's speed in the LOS of the SAR. The geometric model in the azimuth-slant range plane of the GF-3 ATI system is shown in Figure 1, which has two along-track receiving apertures. The satellite platform's velocity is \(V_{s}\), and the closest slant range from the satellite platform to the center of the observation scene is \(R_{0}\). The phase center of the entire antenna, \(T_{x}\), transmits pulses, while the dual-channel antenna phase centers, \(R_{x1}\) and \(R_{x2}\), receive the scene echo simultaneously. The moving target velocity is decomposed into the radial velocity \(V_{r}\) and the azimuth velocity \(V_{a}\). Ideally, that is, the two receiving apertures are absolutely the same, and the total antenna length is \(D_{a}\), so the phase center spacing between beams can be written as \(d=D_{a}/2\). Assuming that the azimuth moment equals zero, the coordinate of the entire antenna phase center in the azimuth-slant range plane is \((0,0)\), and the actual phase center coordinates of each sub-beam are \((\Delta x_{m},0)\), where \(\Delta x_{m}=(m-\dfrac{3}{2})d,m=1,2\). After compensating for a constant phase, the \(m\_\)th channel's echo can be equivalent to the echo spontaneously sent and received at the equivalent phase center (EPC). Then, the coordinate of the equivalent phase center \((R_{c1},R_{c2})\) of the \(m\_\)th channel is \((x_{m},0)\), where:  
\[x_{m}=(m-\dfrac{3}{2})d/2,m=1,2. \tag{1}\]  
\[B=x_{2}-x_{1}=d/2, \tag{2}\]  
where \(B\) represents the effective along-track interferometric baseline. Specifically for GF-3 ATI mode, \(D_{a}=15\) m. Therefore, GF-3 ATI mode has a 3.75 m along-track interferometric baseline. The two equivalent single-channel echo signals are denoted by \(s_{1}(\tau,\eta)\) and \(s_{2}(\tau,\eta)\), respectively. According to [14; 15; 16], \(s_{2}(\tau,\eta)\) can be obtained by \(s_{1}(\tau,\eta)\) through a certain time shift and phase shift. For a stationary target, the relationship between \(s_{1}(\tau,\eta)\) and \(s_{2}(\tau,\eta)\) can be expressed as follows:  
Figure 1: Geometric model in the azimuth-slant range plane. \[s_{2}(\tau,\eta)\approx s_{1}(\tau,\eta+\Delta\eta_{21}), \tag{3}\]  
\[S_{2}(\tau,f_{a})\approx S_{1}(\tau,f_{a})e^{i2\pi\Delta\eta_{21}f_{a}}, \tag{4}\]  
where \(\Delta\eta_{21}=(x_{2}-x_{1})/v_{s}\). It is reported that the radial velocity of a moving target can be directly calculated by the interferometric phase [17; 18; 19]. After matching, the interferometric phase between channels can be expressed as follows:  
\[\phi_{21}=arg(s_{1}(\tau,\eta+\Delta\eta_{21})\cdot s_{2}^{*}(\tau,\eta)) \approx-\frac{4\pi B}{\lambda V_{s}}\cdot V_{r}. \tag{5}\]  
As described in Equation (5), the two images' interferometric phases are proportional to the radial velocity \(V_{r}\) of the target at the corresponding position, and the interferometric phase for a stationary target is zero. Yet, it should be pointed out that the radial velocity \(V_{r}\) does not reflect the real ocean current. Since the SAR imaging mode of the sea surface is extremely complicated and \(V_{r}\) includes the components in the LOS velocity of the sea surface scatterer of different scales in the sea surface scattering unit, then \(V_{r}\) can be derived as,  
\[V_{r}=v_{c}+v_{w}+v_{o}+v_{b}, \tag{6}\]  
where \(\theta\) is the radar incident angle, \(v_{c}\) represents the contribution of the ocean current, \(v_{w}\) represents the contribution of the sea surface wind, \(v_{o}\) represents the contribution of the large-scale wave orbital velocity, and \(v_{b}\) denotes the contribution of the phase velocities of the Bragg-resonant wave components.