# First Retrieval of Sea Surface Currents Using L-Band SAR in Satellite Formation
## 4 Data Processing
### Cross-Track Baseline Component Phase Removal  
The LuTan-1 InSAR system operates in a unique double-helix formation during flight, resulting in temporally varying cross-track baseline components. These variations introduce flat Earth and height phase errors in ocean surface velocity measurements [36]. Before removing the cross-track phase component, a multi-looking process is applied to the interferogram to reduce the phase noise and improve phase accuracy, albeit at the expense of spatial resolution. This study employed a \(64\times 64\) window size for the multi-looking operation, resulting in an approximate spatial resolution of 89.6 m in the azimuth direction and 106.8 m in the range direction. To obtain accurate ocean surface velocity measurements, it is necessary to correct for the interferometric phase induced by the cross baseline. This study employed a two-step strategy. In the first step, the theoretical cross-track baseline phase was computed based on satellite navigation system positioning and external sea surface height data and then subtracted from the co-registered interferometric phase. This step is commonly referred to as the orbit-based method. However, owing to limitations in the measurement accuracy of hardware systems, the navigation data from many satellites are not sufficiently precise, as observed in various SAR systems such as RADARSAT-1 [37], RADARSAT-2 [38], JERS-1 [39], Sentinel-1 [40], ALOS [41], and Gaofen-3 [42,43]. Consequently, residual cross-baseline phases may remain, leading to inaccuracies in the subsequent inversion of sea surface currents. Given that the phase information induced by sea surface currents is typically small, achieving a high level of precision in cross-baseline phase removal is essential. In the second step, a parameterized model-based approach was proposed to mitigate these residual components further. This method is effective and easy to implement. Unlike the commonly used polynomial fitting methods [44, 45, 46, 47, 48, 49], the proposed approach has a clear physical interpretation. Figure 8 shows a schematic of the imaging geometries of the hybrid interferometric SAR systems. The \(xyz\) coordinate system originates at the position of the leading antenna \(A_{1}\) at time \(t\), with the \(x\)-axis aligned with the flight direction, the \(z\)-axis vertically oriented upward from the Earth's center to the satellite's position, and the \(y\)-axis defined by the right-hand rule. Variables \(B_{x}\), \(B_{y}\), and \(B_{z}\) denote the baseline vector components along the \(x\), \(y\), and \(z\) axes, respectively. \(R_{1}\) and \(R_{2}\) are the respective distances from antennas \(A_{1}\) and \(A_{2}\) to the oceanic scatterers. Further, \(\triangle t\) is the time delay. In Figure 8, when antenna  
Figure 7: (**a**) Correlation coefficient between primary and secondary images. (**b**) Interferometric phase diagram. The red box in the left column indicates the area corresponding to the interference fringes on the right. pointing errors are disregarded, \(B_{x}\) is equal to zero, leading to a distance difference \(\triangle R\) between \(A_{2}(t+\triangle t)\) and \(A_{1}(t)\) relative to the same oceanic target, as shown by (13). \[ \begin{split}\Delta R&=R_{2}(t+\Delta t)-R_{1}(t)\\ &=v_{\tau}\Delta t-B_{y}\sin\theta_{L}+B_{z}\cos\theta_{L}\end{split}  \tag{13}\]  
where \(\theta_{L}\) denotes the look angle. Consequently, we can obtain  
\[\phi=-\frac{4\pi}{\lambda}\big{(}v_{\tau}\Delta t-B_{y}\sin\theta_{L}+B_{z} \cos\theta_{L}\big{)}. \tag{14}\]  
\[v_{\tau}=-\frac{1}{\Delta t}\bigg{(}\frac{\lambda}{4\pi}\phi-B_{y}\sin\theta_{L }+B_{z}\cos\theta_{L}\bigg{)} \tag{15}\]  
where \(\big{(}B_{z}\cos\theta_{L}-B_{y}\sin\theta_{L}\big{)}\) is the cross-track baseline component that contributes to distortions in the radial velocity measurements. \(B_{y}\) and \(B_{z}\) can be computed from the satellite's orbital data files.