# Intelligent Simulation Technology Based on RCS Imaging
## 2 Target Drone Simulation Principle
### Variable Principle of Corner Reflector
When a plane wave is at an infinite position, all three reflected echoes have equal phases. Therefore, when the RCS value is calculated using the PO method, an angular reflector can be equivalent to a plane of some dimension through the vertex and orthogonal to the direction of incident, which is the \"equivalent aperture\". The incident direction of the electromagnetic wave \(\rm n=(l,m,n)=(\cos\alpha,\cos\beta,\cos\gamma)=(\sin\theta\cos\varphi,\sin \theta\sin\varphi,\cos\theta)\). Figure 1 shows the schematic diagram of the triple-bounce of the corner reflector. The expression of the incident magnetic field \(H_{i}\) is  
\[H_{i}=\hat{\alpha}H_{0}\exp(jk\hat{r}\cdot r^{\prime}) \tag{4}\]  
Figure 1: Schematic diagram of the triple-bounce of the corner reflector. where \(\hat{\hat{a}}\) is the unit vector representing the magnetic field direction, while \(\hat{\hat{\varLambda}}\) and \(r^{\prime}\) are the unit and distance vectors from the incident point to the origin, \(H_{0}\) is the amplitude, and d is the distance vector from the incident point to the origin. Let \(\hat{\varLambda}\), \(\hat{\varLambda}\), \(\hat{\varLambda}\) and \(\hat{\varLambda}\) be the unit vectors along the X, Y and Z axes, respectively. Subsequently, the unit vectors \(\hat{\varLambda}\) and \(\hat{\varLambda}\) can be obtained as follows:  
\[\hat{\varLambda}=A_{x}\cdot\hat{\varLambda}+A_{y}\cdot\hat{\varLambda}+A_{z} \cdot\hat{\varLambda} \tag{5}\]  
\[ \begin{array}{l}A_{x}=-\cos(90-\eta)\cos\varphi\cos\theta-\sin(90-\eta)\sin ]\varphi\\ A_{y}=-\cos(90-\eta)\cos\theta\sin\varphi+\sin(90-\eta)\cos\varphi\\ A_{z}=\cos(90-\eta)\sin\theta\end{array} \]  
where \(\eta\) is the polarization angle of the electric field at the incident point, e.g., vertical polarization means that this angle is \(0^{\circ}\). Therefore, the three reflections of incident electromagnetic waves on the corner reflector can be obtained from (5) as  
\[H_{i}\big{|}_{I\to m}=\left\{\hat{\varLambda}-2(\hat{\varLambda}\cdot\hat{ \varLambda}_{i})\hat{\varLambda}_{l}-2(\hat{\varLambda}\cdot\hat{\varLambda} _{m})\hat{\varLambda}_{m}^{\prime}\right\}\cdot H_{0}\exp\left\{jk\Big{[}\hat{ \varLambda}-2(\hat{\varLambda}\cdot\hat{\varLambda}_{i})\hat{\varLambda}_{l }-2(\hat{\varLambda}\cdot\hat{\varLambda}_{m}^{\prime})\hat{\varLambda}_{m} \Big{]}\cdot r^{\prime}\right\} \tag{6}\]  
where \(\hat{\varLambda}_{i}\) and \(\hat{\varLambda}_{m}^{\prime}\) are the normal vectors of the reflection surfaces \(l\) and \(m\), respectively. The total reflected magnetic field \(H_{s}\) is composed of a combination of the re-radiation of the aforementioned incident magnetic field. There are six combinations, namely, \(H_{i}|_{l\to m-n}^{3}\), \(H_{i}|_{l\to m-n}^{3}\), \(H_{i}|_{n\to l\to m}^{3}\), \(H_{i}|_{n\to m-l\to l}^{3}\), \(H_{i}|_{m\to n-l\to n}^{3}\) and \(H_{i}|_{m\to l\to n}^{3}\). After putting (6) into (4), \(H_{s}\) reflected three times on the corner reflector can be obtained as follows:  
\[H_{s}=\sum_{l,m,n=1}^{3}H_{s}|_{l\to m-n}^{3}=\sum_{l,m,n=1}^{3}\frac{jk}{4 \pi}\frac{\exp(-jkr)}{r}\int_{Sm}2(\hat{\varLambda}_{n}^{\prime}\times H_{i} \big{|}_{l\to m\to n})\,\times\,\widetilde{r}\exp(jk\widetilde{r} \cdot r^{\prime})ds_{n}^{\prime} \tag{7}\]  
By substituting (7) into (1), the RCS value of the incident point can be obtained as follows:  
\[\sigma=\lim_{R\to\infty}4\pi R^{2}\frac{\big{|}H_{s}\big{|}^{2}}{\big{|}H_{i} \big{|}^{2}}=\lim_{R\to\infty}\frac{H_{s}|_{l\to m-n}^{3}\big{|}^{2}}{H_{0}} \tag{8}\]  
In order to simplify the RCS calculation of complex structures, the RCS of the variable corner reflector can be calculated only by obtaining the shape of the \"equivalent aperture\". Subsequently, the shape can be integrated to obtain its area \(A_{eq}\), which is determined by regional projection. Firstly, the reflector structure has multiple scattering centers. Therefore, the RCS of target scattering center is required.