# Fine Recognition of MEO SAR Ship Targets Based on a Multi-Level Focusing-Classification Strategy
## 2 Signal Modeling and Characteristic Analysis of MEO SAR Ships
### MEO SAR Image Defocusing Caused by Ship Sailing  
The translational motions of a ship mainly refer to its sailing movements. Specifically, the average speed of bulk carriers is about 10.9 knots, while the average speed of container ships is 13.9 knots, and that of tankers is approximately 11.5 knots. In contrast, military ships typically maintain a speed of around 30 knots. The translational motions can be decomposed into velocity along the azimuth direction and velocity along the range direction. The range velocity primarily causes azimuthal displacement in the SAR image, while the azimuth velocity mainly leads to defocusing. The latter has a more significant impact on target recognition. The greater the azimuth velocity of a ship, the more pronounced the defocusing of its image. This section focuses on analyzing the effects of azimuth velocity on the SAR image.  
The azimuth FM rate of the SAR signal for a static target is  
\[K_{a}=\frac{2v^{2}}{\lambda R} \tag{3}\]  
in which \(v\) is the satellite equivalent velocity and \(R\) is the shortest slant range. Let \(\Delta v_{g}\) denote the target azimuth velocity. Taking into account the satellite-ground geometry, the azimuth FM error induced by \(\Delta v_{g}\) can be written as  
\[\Delta K_{a}=\frac{4v\Delta v_{g}}{\lambda R}\sqrt{\frac{H+R_{e}}{R_{e}}} \tag{4}\]  
where \(H\) is the orbit height, while \(R_{e}\) is the Earth's radius. Let \(T_{s}\) be the synthetic aperture time. The maximum quadratic phase error caused by \(\Delta K_{a}\) is  
\[\varphi_{\text{max}}=\pi\Delta K_{a}\bigg{(}\frac{T_{s}}{2}\bigg{)}^{2} \tag{5}\]  
Figure 2 shows the maximum quadratic phase error with different target azimuth velocities. Compared with LEO SAR, MEO SAR exhibits a multiplicative increase in phase errors. Set the azimuth velocities of the point target to 0 m/s, 5 m/s, 10 m/s, and 15 m/s, respectively, with the range velocity fixed at 0 m/s. Perform echo simulation and imaging processing on the point target under two orbital altitude conditions. The final SAR images are shown in Figure 3.  
\begin{table}
\begin{tabular}{c c c} \hline
**Parameters** & **MEO SAR** & **LEO SAR** \\ \hline Wavelength (m) & 0.03 & 0.03 \\ Bandwidth (MHz) & 300 & 300 \\ Orbit height (km) & 7500 & 600 \\ Look angle (\({}^{\circ}\)) & 15 & 15 \\ \hline \end{tabular}
\end{table}
Table 1: Simulation parameters of MEO SAR and LEO SAR.  
The range velocity of the point target is set to 10 m/s, and the azimuth velocity is set to 0 m/s. Perform echo simulation and imaging processing on the point target with MEO SAR and LEO SAR parameters, respectively. The imaging results are shown in Figure 4. It can be seen that, for both the MEO and LEO SAR systems, the range velocity has nearly no influence on the focusing result.  
Figure 4: Imaging results of a point target for LEO SAR and MEO SAR with a range velocity of 10 m/s: (a) LEO SAR; (b) MEO SAR.  
Figure 3: Imaging results of a point target for LEO SAR and MEO SAR with different azimuth velocities: (a) 0 m/s; (b) 5 m/s; (c) 10 m/s; (d) 15 m/s.  
Figure 2: Maximum quadratic phase error caused by target azimuth velocity for LEO SAR and MEO SAR.  
From the imaging results it can be observed that, compared to LEO SAR, the defocusing of moving point targets in MEO SAR is more severe under the same velocity conditions. In the LEO SAR images, targets with velocities below 15 m/s can still be visually distinguished, whereas in the MEO SAR images, the shape characteristics of the point targets are completely lost. Azimuthal defocusing causes the point targets to appear as straight lines, making it difficult to directly identify targets under such conditions.