## 3 Data Analyses
### Design of the Evaluation Model  
Utilizing \(L_{air}\), \(B_{air}\), and \(H_{air}\) in the GPS/BD data of the carrier, cartesian coordinates \(X_{air\_CGCS}\), \(Y_{air\_CGCS}\), and \(Z_{air\_CGCS}\) of the carrier in the CGCS2000 coordinate system were obtained via coordinate transformation.  
Similarly, from \(L_{aim}\), \(B_{aim}\), and \(H_{aim}\) in the GPS/BD data of the target aircraft, the cartesian coordinates \(X_{aim\_CGCS}\), \(Y_{aim\_CGCS}\), and \(Z_{aim\_CGCS}\) of the target position in the CGCS2000 coordinate system were obtained.  
Next, the position of the target in the launch coordinate system at moment \(t_{F}\), when the \"simulated launch\" instruction was issued by the carrier to the pod, was calculated. The launch coordinate system was defined with the launch point being origin \(O_{F}\). Furthermore, the \(OX_{F}\) axis was in the horizontal plane crossing the origin and pointing to the north direction; meanwhile, the \(OY_{F}\) axis was in the vertical plane of the \(OX_{F}\) axis, perpendicular to the \(OX_{F}\) axis, and the upward direction was assigned as positive. Additionally, the \(OZ_{F}\) axis complied with the right-hand rule to form the coordinate system with the two axes defined above.  
Using the longitude \(L_{aim\_rad}\), latitude \(B_{aim\_rad}\), and altitude \(H_{aim\_rad}\) of the target aircraft measured by the airborne radar, the cartesian coordinates \(X_{aim\_rad}\_CGCS}\), \(Y_{aim\_rad}\_CGCS}\), and \(Z_{aim\_rad\_CGCS}\) of the target in the CGCS2000 system were obtained by coordinate transformation.  
By using the output longitude \(L_{air\_INS}\), latitude \(B_{air\_INS}\), and altitude \(H_{air\_INS}\) of the main inertial navigation system of the carrier, its cartesian coordinates \(X_{air\_INS\_CCS}\), \(Y_{air\_INS\_CSCSC}\), and \(Z_{air\_INS\_CSCSC}\) in the CGCS2000 system were obtained by coordinate transformation. Then, the position measurement of the target aircraft in the launch coordinate system of the carrier could be calculated as follows:  
\[\begin{bmatrix}X_{aim\_radr}F\\ Y_{aim\_radr}F\\ Z_{aim\_radr}F\end{bmatrix}=\begin{bmatrix}-cosL_{air}sinB_{air}&-sinL_{air} sinB_{air}&cosB_{air}\\ cosL_{air}cosB_{air}&sinL_{air}cosB_{air}&sinB_{air}\\ -sinL_{air}&cosL_{air}&0\end{bmatrix}\cdot\begin{bmatrix}X_{aim\_radr}\_CGCS -X_{air\_INS\_CSCSC}\\ Y_{aim\_radr}\_CGCS -Y_{air\_INS\_CSCSC}\\ Z_{aim\_radr}\_CGCS -Z_{air\_INS\_CSCSCSC}\end{bmatrix} \tag{1}\]  
The position error of the target aircraft measured by the airborne radar was then obtained.  
\[\begin{bmatrix}\Delta X\\ \Delta Y\\ \Delta Z\end{bmatrix}=\begin{bmatrix}X_{airF}\\ Y_{airF}\\ Z_{airF}\end{bmatrix}-\begin{bmatrix}X_{aim\_radr}F\\ Y_{aim\_radr}F\\ Z_{aim\_radr}F\end{bmatrix} \tag{2}\]  
Next, the spatial pitch angle \(\varphi_{YG}\) and course angle \(\varphi_{ZG}\) of the line-of-sight vector between the carrier aircraft and target in the carrier's launch coordinate system could becalculated utilizing the measurement data from the airborne radar. Consequently, the angle measurement error of the airborne radar could be acquired as follows:  
\[\Delta\varphi_{\text{Y}RAD} =\varphi_{\text{Y}G}-\varphi_{\text{Y}R} \tag{3}\] \[=arctan\Big{(}\frac{\varphi_{\text{int},\,rate\,F}}{X_{\text{int}, \,rate\,F}}\Big{)}-arctan\Big{(}\frac{Z_{\text{int},\,rate\,F}}{X_{\text{int} \,rate\,F}}\Big{)}\]  
\[\Delta\varphi_{ZRAD} =\varphi_{\text{Z}G}-\varphi_{\text{Z}R} \tag{4}\] \[=arctan(\frac{Y_{\text{int},\,rate\,F}}{(X^{2}_{\text{int},\,rate \,F}+Y^{2}_{\text{int},\,rate\,F})^{\frac{1}{2}}})-arcsin(\frac{Y_{\text{int}, \,rate\,F}}{(X^{2}_{\text{int},\,rate\,F}+Y^{2}_{\text{int},\,rate\,F}+Z^{2}_{ \text{int},\,rate\,F})^{\frac{1}{2}}})\]  
Finally, the position and angle information of the target measured by the pod was compared to that measured by the airborne radar, and the accuracy of the measurement from the seeker to the target was obtained.