## 2 Methodology
### The Proposed Method of SRS Images Generation
#### 2.1.3 SRS Image Generation  
The generation process of the simulation ship mainly includes the steps shown in Figure 3. The red box in Figure 3 is the key to the whole generation process. The next section provides a detailed description of the parts in the red box. Figure 2: Selection of experimental scene: (**a**) experimental location, (**b**) experimental scene image. Calculate the Size of the Simulation Ships  
Figure 3 briefly illustrates the generation method of the simulated real ship image: the simulated ship is extracted from the simulated ship image and superimposed into the real experimental background scene to form the simulated real ship image. However, there is no clear explanation for the scale, pose, and superimposed position of the simulated ship in the simulated real ship image. The scale calculation method of the simulated ship in the simulated real ship image is as follows:  
\[(U_{j},V_{j})=\lambda_{j}\cdot(u_{j},v_{j}) \tag{5}\]  
where \((u_{j},v_{j})\) is the size of the simulated ship, \(\lambda_{j}\) is the scale factor, and \((U_{j},V_{j})\) is the ship image after the scale change. Calculate the Trajectory of Simulation Ships  
As shown in Figure 4, suppose the length and height of the bounding box of the simulation ship are \(h\) (pixel) and \(w\) (pixel), respectively. The distance between the center point of the bounding box and the four corners of the bounding box is \(L\). Here, set \(L\) as the size of the simulation ship. The size (pixel) of \(L\) is:  
\[L=\sqrt{\left(\frac{h}{2}\right)^{2}+\left(\frac{w}{2}\right)^{2}} \tag{6}\]  
Figure 4: Modeling of simulation ship in background scene. Figure 3: Key steps of SRS images generation. As shown in Figure 4, the length and height of the bounding box of the simulated ship are \(h\) (pixels) and \(w\) (pixels), respectively. The distance from the center of the bounding box to the four corners of the bounding box is \(L\). The center point of the simulated ship are the coordinates \((x_{1},y_{1})\) of the simulated ship in the background image. \(L\) is the size of the simulated ship (pixels). Sailing ships need to follow navigation rules, and they must navigate within the area marked by the buoy boats. Both lines connecting the position of the buoy boats refers to the red dashed line in Figure 4. Passing ships must navigate within the area enclosed by the two red dotted lines. We considered the posture of the simulated ship fixed due to the unchanged sailing direction. Next, we analyzed the trajectory of the simulated ship in the background image, as shown in Figure 5.  
\[\left[ \begin{array}{c}x^{\prime}\\ f^{\prime}(x^{\prime})\end{array} \right]=\left[ \begin{array}{cc}cos\theta& sin\theta\\ -sin\theta&cos\theta\end{array} \right]\left[ \begin{array}{c}x\\ f(x)\end{array} \right] \tag{7}\]  
\[f^{\prime}(x^{\prime})=-x\cdot sin\theta+f(x)\cdot sin\theta+\lambda\cdot \frac{1}{\sqrt{2\pi}\sigma}exp(-\frac{\left((x\cdot cos\theta+f(x)\cdot sin \theta)-\mu\right)^{2}}{2\sigma^{2}}) \tag{8}\]  
where \((x,f(x))\) is the coordinate of the simulation ship in the background image, and \((x^{\prime},f(x^{\prime}))\) is the coordinate of the simulation ship after the \(\theta\) degree rotation of the coordinate axis. The trajectories of the ships in the maritime scene are distributed around the \(X\)-axis. Firstly, we calculated the mean value of the ship's trajectory, and then the navigation coordinates of the SRS image were obtained by adding Gaussian distribution parameters. The trajectory of the simulation ships in the real scene can be calculated through this method. Figure 5: Trajectory of the generation of SRS images. On the basis of mean value of ship trajectory, Gaussian distribution parameters are added to obtain the navigation trajectory of the simulation ship of the SRS images.