## 4 Simulation Verification
The scattered sound field of all the plate elements in the bright area is summed to obtain the approximate value of the scattered sound field of the target, and the plate elements with different orientations are transformed uniformly to some determined plane by coordinate transformation; consequently, we can ascertain:  
\[I=\sum\limits_{i=1}^{N}\sum\limits_{j=1}^{M}\left[V(\theta_{ij}^{\prime})w^{ \prime}\sum\limits_{n=1}^{K}\frac{\mathrm{e}^{2\mathrm{i}k_{0}(x_{n}u_{ij}^{ \prime}+y_{n}v_{ij})}(p_{n-1}-p_{n})}{(u_{ij}^{\prime}+p_{n-1}v_{ij}^{\prime}) (u_{ij}^{\prime}+p_{n}v_{ij}^{\prime})}\right]\Bigg{|}_{sij} \tag{21}\]  
where \(x_{n}\)',\(y_{n}\)' is the coordinate of the vertex of the (_i,j_)th plate after transformation to the 2D plane, \(V(\theta_{ij})\) is the local surface reflection coefficient of the (_i,j_)th plate, and \(\theta_{ij}\)' is the angle between the normal and incident sound lines of the (_i,j_)th plate. In the later specific calculations, the triangular plate element is adopted; therefore, \(K=3\) after a simulated Doppler frequency shift. Figure 9 shows the benchmark submarine target echo. We can see the relationship between the target intensity of each part of the submarine (transom, enclosure, and bow), obtained by matching the filtering gain with the angle. The target intensity of the submarine is more significant when the angle is 0\({}^{\circ}\)-90\({}^{\circ}\), because the frontal scattering area of the submarine is large, and the structure is simple; the phase cancellation is less. If the angle is closer to 90\({}^{\circ}\), the time delay difference of the target echoes in each part of the submarine are smaller. Figure 10 shows the torpedo and target movement posture. As the fixed advance angle guidance method is less difficult in engineering practice, and can make the torpedo attack end effective, it is an ideal guidance method for an active acoustic homing torpedo. The attack posture of the torpedo can be set using the fixed advance angle guidance method; \(O\) point is the active acoustic homing torpedo initial position, \(A_{0}\) point is the target initial position, the distance \(r_{0}\) between the torpedo and the target is 500 m, the orientation \(\theta\) of the target initially located in the torpedo is 45\({}^{\circ}\), the torpedo speed \(v_{t}\) is 50 km, and the torpedo fixed advance angle \(\alpha\) is 5\({}^{\circ}\). Since the torpedo usually attacks from a certain angle behind the side of the target, we can set the initial enemy side angle \(\Phi\) to 135\({}^{\circ}\). When the target is a submarine or a homing acoustic decoy, the target velocity \(v_{m}\) is 15 km, the submarine is 60 m, and the homing acoustic decoy line array is 40 m. Ten suspended acoustic decoys are deployed at point \(O\); when the targets are suspended acoustic decoys, the deployment scatter error is 40 m [25]. The operating frequency of the torpedo transmitting signal was set to be 30 kHz and bandwidth to be 0.8 kHz. The signal period was 1 s, the time width was 62.5 ms, the sound source level 220 dB, the noise level 60 dB, the receiving directivity index 17 dB, and the detection index 12 dB. When the acoustic signal propagates in the ocean channel, the surface and bottom reflections produce multipath scattering [26; 27; 28; 29]. Moreover, the sound velocity gradient causes the refraction of acoustic waves, which tend to refract toward the lower sound velocity region, leading to the propagation of the acoustic signal curve. This paper applies [PERSON]'s depth-dependent sound velocity profiles derived from summertime temperature, pressure, and salinity data in the North Atlantic off the coasts of Britain and Ireland [30]. Figure 11 shows the sound speed profile data. The refraction and reflection of the acoustic signal cause the acoustic signal to propagate in different channels, causing the attenuation of the single-channel acoustic signal amplitude and the superposition of the different  
Figure 10: The torpedo and the target movement posture. Figure 9: The benchmark submarine target echo.