## 5 The Simulation Validation and Results Analysis
### Performance of the Algorithm in a Complex Scenario
#### 5.3.1 Three UAVs Tracking One Moving Target  
In Scenario 3, a moving target \(T\) is continuously tracked by three UAVs \(A_{1}\), \(A_{2}\) and \(A_{3}\). The detailed initial settings of the UAVs are listed in Table 6. The initial position of target is (\(-800\), \(600\)) m. The position of the base station \(B\) is (\(-500\), \(-1000\)) m. The safety distance for collision avoidance is \(d_{\text{safe}}\) = 250 m. The other simulation conditions are same with Scenario 1. The snapshots, Figures 27-29, show the trajectories and communication topology of the UAVs at 10 s, 50 s and 100 s, respectively. In the tracking process, the MST communication topology is [\(A_{2}\rightarrow\)\(A_{3}\to A_{1}\to B\)]. With \(A_{3}\) and \(A_{1}\) acting as the relays, \(A_{2}\) gets close to the target to get better measurements and then circles it around. \(A_{1}\) automatically sets itself up as a relay for \(A_{3}\), so it is close enough to the base station. \(A_{3}\) takes advantage of the position of \(A_{1}\) to fly closer to \(A_{2}\) and acts as the relay for \(A_{2}\). Although \(A_{2}\) is too far from the base station, it still can send its measurements back to the base station successfully. The communication performances of \(A_{1}\), \(A_{2}\) and \(A_{3}\) are shown in Figure 30. The average transmission probability of \(A_{2}\) can be improved to about 0.5. By contrast, if \(A_{2}\) communicates with the base station directly without any relay, its average transmission probability is lower than 0.1. Thus, the communication performance of \(A_{2}\) is vastly improved with \(A_{3}\) and \(A_{1}\) acting as the relays. \begin{table}
\begin{tabular}{c c c} \hline \hline
**UAV \(A_{i}\)** & **Position (\(x_{i}\), \(y_{i}\))/(m)** & **Heading Angle \(\mathbf{\Psi_{j}/(^{\circ})}\)** \\ \hline \(A_{1}\) & (\(-400\), \(-900\)) & 10 \\ \(A_{2}\) & (\(-800\), \(300\)) & 0 \\ \(A_{3}\) & (\(-800\), \(0\)) & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The initial settings of three UAVs in Scenario 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Item** & **Group** & **Base Station** & \(A_{1}\) & \(A_{2}\) \\ \hline \multirow{2}{*}{Average estimation error for position (m)} & A & 0.4266 & 0.7203 & 1.1680 \\  & B & 0.5081 & 0.9029 & 0.7240 \\ \hline \multirow{2}{*}{Average transmission probability} & A & - & 0.7463 & 0.9818 \\  & B & - & 0.9209 & 0.6051 \\ \hline \multirow{2}{*}{Average trace of the FIM} & A & 27.4777 & 14.6744 & 13.0033 \\  & B & 15.5617 & 13.1899 & 14.2413 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of the average estimate errors, the average transmission probabilities, and the average trace of the FIM in Scenario 2 (Group A vs. Group B). Figure 27: Trajectories of UAVs and target at \(t=10\) s (Group A in Scenario 3). Figure 28: Trajectories of UAVs and target at \(t=50\) s (Group A in Scenario 3). Figure 30: The communication performances of \(A_{1}\), \(A_{2}\) and \(A_{3}\) (Scenario 3). Figure 29: Trajectories of UAVs and target at \(t=100\) s (Group A in Scenario 3). The trace of the FIM is shown in Figure 31. To establish a reliable multi-hops chain between \(A_{2}\) and the base station, \(A_{3}\) and \(A_{1}\) get close to the base station act as relays for \(A_{2}\). Hence, \(A_{3}\) and \(A_{1}\) have no information gathering, and their trace of FIM have no change in the long time. Figure 32 shows that the safety of the UAVs is guaranteed because the minimum distance between UAVs is always larger than the safety distance (\(d_{\text{safe}}=250\) m). In Scenario 3, the average estimate errors, the average transmission probabilities, the average trace of the FIM are shown in Table 7.  
It can be seen from Table 7 that, our algorithm integrates the communication and sensing objectives, so that the UAVs intelligently move to the locations that maximize both the information gained and the successful transmission probabilities in communication links with the base station. Thus, the base station can obtain a good estimate result of the target state.