## 3 Case Simulation and Result Analysis
### Simulation and Results Analysis  
2.1 Simulation and Analysis of Collaborative Search Efficiency Evaluation of Multi-Sonar System Under Two Working Modes  
This section distinguishes between the fully-passive working mode and multi-base working mode of sonar, and evaluates the collaborative search efficiency. Among them, in the multi-base working mode, the second sonar works actively, and the first and third sonars work passively. From the analysis of Figure 7, it can be observed that the instantaneous detection probability curve shows a cyclic trend of increasing first and then decreasing, which is consistent with the scene of three sonars executing search tasks back and forth along designated search routes. The instantaneous detection probability of 2 nd sonar in the initial stage is almost zero, because the target is always within the blind zone range of 2 nd sonar at the beginning stage. Figure 5: Schematic diagram of the collaborative search efficiency evaluation model of multi-sonar system. Figure 6: Schematic diagram of the task scene. According to the analysis of Figure 8, in the fully passive working mode of the sonar, when the target passes through the detection blind zone of 2 nd sonar, the cumulative detection probability growth rate of 2 nd sonar for the target is relatively high. This is because at this stage, the target is closer to 2 nd sonar, and it has a slight \"search advantage\". The cumulative detection probability of 2 nd sonar in the initial stage is almost zero, which is consistent with the analysis above, because the target is always within the blind zone range of 2 nd sonar at the beginning stage. The measurement standard is the time required for the cumulative detection probability to reach 0.9. Table 1 lists the time required for the cumulative detection probability to reach 0.9 under different conditions. \begin{table}
\begin{tabular}{c c c} \hline  & \
\begin{tabular}{c} **Under Fully-Passive** \\ **Working Mode of** \\ **Sonar** \\ \end{tabular} &
\begin{tabular}{c} **Under Multi-Base** \\ **Working Mode of** \\ **Sonar** \\ \end{tabular} \\ \hline \hline The time required for the cumulative detection probability & & \\ of 1 st sonar to reach 0.9 & & 48 \\ The time required for the cumulative detection probability & & 56 \\ The time required for the cumulative detection probability & & 79 \\ of 3 rd sonar to reach 0.9 & & 49 \\ The time required for the cumulative detection probability & & 71 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Time required for cumulative detection probability to reach 0.9 under different conditions. Figure 7: Instantaneous detection probability curves under two working modes. By analyzing the data in Table 1, the following conclusions can be drawn:  
(1) The detection efficiency of the Multi-sonar system is greater than that of each sonar, which intuitively reflects the advantages of collaboration. (2) The detection efficiency of the Multi-sonar system in multi-base working mode is superior to that in fully-passive working mode. 2.2 The Influence of Different Sonar Transceiver Combinations on Evaluation Indicators Under the Multi-Base Working Mode  
On the basis of the collaborative search efficiency evaluation model established in this paper, this section studies the influence of different sonar transceiver combinations on the instantaneous detection probability and cumulative detection probability of the Multi-sonar system under the multi-base working mode through simulation calculations. The simulation results are shown in Figures 9 and 10. Figure 8: Cumulative detection probability curves under two working modes. Figure 9: The influence Schematic diagram of different sonar transceiver combinations on the instantaneous detection probability of the Multi-sonar system under the multi-base working mode.