## 3 Status and Application
### Single-Pass Interference
#### 3.2.2 AT-InSAR
The radar echoes from the two forward beams and the radar echoes from the two backward beams are cross-correlated, generating a pair of interferograms. The phase of each interferogram provides a line-of-sight component of the Doppler surface velocity, and then the vector estimation is obtained by appropriately combining the separated interferograms. As shown in the right part of Figure 12, the radial velocity measurement of the target point in the forward beam is as follows:  
\[\hat{u}_{r}=\frac{V}{kB}\phi, \tag{8}\]  
Then,  
\[x_{\text{max}}=x_{0}+\frac{R}{V}u_{r}, \tag{9}\]  
Then, the phase at the point \(x_{\text{max}}\) is  
\[\phi(x_{\text{max}})=\frac{kB}{V}u_{r}=k\tau u_{r}, \tag{10}\]  
Herein, \(k\) represents the wave number, \(\tau\) represents the coherence time, and \(\tau=B/V\). From this, the radial velocity measurement formula can be derived. \(\hat{u}_{r}\) represents the estimated value of radial velocity. According to the geometric relationship, the radial velocities measured by the forward and backward beams can be used to calculate the two-dimensional ocean surface currents, which are the velocity components of the ocean surface currents along the track and perpendicular to the track, respectively:  
\[\hat{v}_{Ox}=\frac{\hat{u}_{r}^{+}}{2\sin\theta_{i}\sin\theta_{fore}}-\frac{ \hat{u}_{r}^{-}}{2\sin\theta_{i}\sin\theta_{aff}},\hat{v}_{Oy}=\frac{\hat{u}_ {r}^{+}}{2\sin\theta_{i}\cos\theta_{of}}+\frac{\hat{u}_{r}^{-}}{2\sin\theta_{ i}\cos\theta_{aft}} \tag{11}\]  
Among them, \(\theta_{fore}=\theta_{aft}=\theta_{ps}\) is called the projection squint angle. The variance of radial velocity can be obtained by measuring the radial velocity from the forward and backward wave beams:  
\[\sigma_{vx}^{2}=\frac{\sigma_{u_{r}^{+}}^{2}+\sigma_{u_{r}^{-}}^{2}}{\left(2 \sin\theta_{i}\sin\theta_{ps}\right)^{2}},\sigma_{vy}^{2}=\frac{\sigma_{u_{r} ^{+}}^{2}+\sigma_{u_{r}^{-}}^{2}}{\left(2\sin\theta_{i}\cos\theta_{ps}\right) ^{2}}, \tag{12}\]  
The derivation of the phase yields the overall variance of the velocity as follows:  
\[\sigma_{v}^{2}=\frac{\sigma_{\phi^{+}}^{2}+\sigma_{\phi^{-}}^{2}}{\left(k \tau\sin\theta_{i}\sin 2\theta_{ps}\right)^{2}} \tag{13}\]  
Figure 12: The observation geometry of the DBI method. At the International Geoscience and Remote Sensing Symposium (IGARSS) in 2011, [PERSON] introduced the Wavemill project. In November 2011, an airborne test was conducted to verify the feasibility of the squint InSAR method. Further potential was explored to optimize the system design [79]. Regarding the airborne test of the Wavemill project, [PERSON] et al. [80] presented the system parameters and processing algorithms of the airborne test at the EUSAR conference in 2012. The airborne test area was in Liverpool Bay and Anglesey, UK. The formation along track interference has the characteristics of flexible multi-baseline, mixed baseline, and multi-angle observation. It can measure ocean surface currents, sea surface wind fields, and ocean waves while also conducting elevation mapping of the sea surface. In June 2010, TanDEM-X (TDX) was launched into space. Together with TerraSAR-X (TSX), which was launched earlier, they formed a dual-star formation in a helix configuration. The main task of the TSX and TDX radar system formation was to map the global DEM. The working distance could be controlled within 150 to 400 m [63; 64; 81; 82]. In addition, the TSX and TDX radar system formation could provide a baseline along the flight path within a range of zero to a few kilometers, because TDX also had a dual-reception mode. After forming a dual-star formation with TSX, it could be equivalent to having four phase centers along the flight path for interferometric SAR with long and short baselines. The design of long and short baselines can effectively solve the phase ambiguity problem of high-speed scatterers [13]. The long baseline is sensitive to slow motion while the short baseline is sensitive to fast motion.