## 5 The Simulation Validation and Results Analysis
### Comparative Simulations for Communication Optimization
#### 5.1.3 Monte-Carlo Simulations for Scenario 1  
Due to the acceleration noise in the target model and the measurement noise in the sensor model, the results of a single simulation are not sufficient to illustrate that the proposed method is effective. Hence, we run ten times Monte-Carlo simulations for Scenario 1 to further analyze the performance of the target state estimation in two cases. The statistical results--such as the average errors of the target state estimation (position, speed, movement direction)--the average transmission probabilities, the average trace of the FIM, are shown in Table 3.  
Figure 16: The trace of the FIM for \(A_{1}\), \(A_{2}\) and base station (Group B in Scenario 1).  
Figure 17: The distance between the UAVs during the simulation process (Group B in Scenario 1).  
\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 & 1.2778 & 3.4806 & 1.9570 \\  & B & 1.6287 & 2.4619 & 1.9565 \\ \hline \multirow{2}{*}{Average estimation error for speed (m/s)} & A & 0.2100 & 0.3110 & 0.2714 \\  & B & 0.2451 & 0.2931 & 0.2493 \\ \hline \multirow{2}{*}{Average estimation error for direction (\({}^{\circ}\))} & A & 1.2098 & 1.5951 & 1.3775 \\  & B & 1.2133 & 1.5253 & 1.3121 \\ \hline \multirow{2}{*}{Average transmission probability} & A & - & 0.8858 & 0.8056 \\  & B & - & 0.7359 & 0.6203 \\ \hline \multirow{2}{*}{Average trace of the FIM} & A & 72.4468 & 50.5545 & 55.9077 \\  & B & 46.2311 & 52.0081 & 60.4408 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of the average estimate errors, the average transmission probabilities, and the average trace of the FIM in Scenario 1 (Group A vs. Group B).  
* For the base station, the average errors in the estimation of the target state (position, speed, movement direction) in Group A are less than in Group B, and the average trace of the FIM in Group A is larger than in Group B. Thus, when communication optimization is considered, the global estimate results for the target state are more accurate and more effective. This is because our algorithm maximizes the information gain while considering communication reliability. The remote UAVs can successfully transmit their measurement packets back to the base station with other UAVs acting as communication relays. These measurements are used to improve the accuracy and effectiveness of the global estimate results.
* For \(A_{1}\) and \(A_{2}\), their target state estimate results in Group B are better than in Group A in terms of the average errors and the average trace of the FIM. The reason is that, in Group B, the algorithm only focuses on sensing optimization, and guides both \(A_{1}\) and \(A_{2}\) toward the target to maximize the information gain. However, \(A_{1}\) and \(A_{2}\) are outside the range for direct communication to the base station, and then the measurements obtained from \(A_{1}\) and \(A_{2}\) do not contribute to the global estimate results of the target state.
* In Group A, \(A_{2}\) has lower average estimate errors and larger the average trace of the FIM than \(A_{1}\). It implies that \(A_{2}\) has better sensing performance than \(A_{1}\). This is because \(A_{1}\) acts as a relay for \(A_{2}\) in a long time. To establish a multi-hops chain to get the measurement packets from \(A_{2}\) back to the base station, \(A_{1}\) orbits near the base station, and hence cannot get better sensing information from the target. These results illustrate how the proposed algorithm implements tradeoffs between communication performance and sensing utility.