## 4 Simulation and Analysis
### Simulation Experiment 3  
In this simulation experiment, the motion mode of the target is set as the barrel roll maneuvering with a high overload, which is one of the most commonly used tactical maneuvers in the BVR air combat. Set \(n_{xt}=\sin\theta_{t}\), \(n_{yt}=5\cos(0.25t)+cos\theta_{t}\), and \(n_{zt}=5\sin(0.25t)\). It should be noted that the initial altitude of both the target and the UCAV is set as 6 km in this experiment, and other simulation settings remain unchanged. Then the simulation results are shown in Figures 14-16. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(I_{e}\)(rad) & \(I_{d}\)(s) & \(I_{c}\) \\ \hline PID method & 0.0912 & 7.55 & 2.1901 \\ AFC method & 0.0587 & 24.50 & 2.1628 \\ The proposed method & 0.0195 & 94.70 & 2.0539 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparisons of quantitative evaluation indexes of the three methods. Figure 13: The actual control overloads of the UCAV during the process of attack guidance. It can be seen from Figure 14 that the target performs periodic overload maneuver on both horizontal and vertical directions to form a three-dimensional barrel roll trajectory, which significantly improves the difficulty of aiming. The three methods can generate the correct attack guidance which is  
Figure 16: The actual control overloads of the UCAV during the process of attack guidance. Figure 14: Attack guidance trajectories for the barrel roll maneuvering of the target. Figure 15: The aiming error angles of the UCAV during the process of attack guidance. also approximately the barrel roll trajectory following the target maneuver. As shown in Figure 15, the aiming error angle generated by the proposed method can be rapidly converged to the vicinity of zero and the oscillation amplitude is very small. In contrast, due to the large maneuver magnitude of the target, the aiming error angle generated by the other two methods is large. In Figure 16, the three methods generate periodic control overload on both horizontal and vertical directions. Besides, the difference of control overload of the three methods is small, in other words, under the approximate control overload condition, the proposed method can generate the attack guidance trajectory with the highest precision and the best stability. Comparisons of quantitative evaluation indexes of the three methods in simulation experiment 3 are shown in Table 4.  
It can be seen from the data in Table 4 that the proposed method has significant superiority over the other methods in terms of evaluation indexes of \(I_{e}\) and \(I_{d}\). Specifically, the proposed method can provide the UCAV with a high-precision aiming time of about 106 seconds during the attack guidance when the target doing a large overload maneuver, while the other methods are nearly zero. Besides, its control overload cost is also slightly less than that of the other methods. From the perspective of the engineering application, the timeliness of the proposed method is analyzed below. In this study, the timeliness is evaluated by the average calculation time in a single step, which is the average CPU time required to solve the current control overload in each step over the whole process. A comparison of the timeliness of the three methods in simulation experiment 3 is shown in Table 5.  
From the data in Table 5, it can be seen that the proposed method is more time-consuming than the other two methods due to the complexity of the algorithm itself. However, the computation efficiency in a single step of about 0.46 milliseconds can still fully meet the requirements of the airborne computer for the timeliness of fire control computation. Specifically, the timeliness will be further improved, when running on the airborne computers with higher computational performance. Therefore, the proposed method also has the capability of on-line application in terms of timeliness. Based on the above simulation experiment results, the accuracy of models, and the effectiveness and superiority of the proposed method are verified convincingly.