## 3 Case Simulation and Result Analysis
### Simulation and Results Analysis
#### 3.2.3 The Influence of Different Sonar Parameters and Target Parameters on Evaluation Indicators  
On the basis of the collaborative search efficiency evaluation model established in this paper, this section studies the influence of different sonar parameters and target parameters on the instantaneous detection probability and cumulative detection probability of the multi-sonar system under the fully-passive working mode and multi-base working mode through simulation calculations. The influence of sonar search speed on evaluation indicators  
Assuming that the search speeds of the three sonars are always the same and remain constant, the search speeds are set to \(v_{1}\), \(v_{2}\), \(v_{3}\), and the other parameters are the same as those in the previous text. The simulation results are shown in Figure 11.  
According to the simulation results, as the sonar search speed increases, its detection capability gradually weakens. This is because the increase in speed leads to an increase in the background noise level of the sonar, such as propeller noise and flow noise, which affects its detection capability. Owing to the increase in search speed, the round-trip search period of the sonar decreases, which is reflected in the instantaneous detection probability. The reduction in detection capability is reflected in the decrease in instantaneous detection probability, resulting in a decrease in the maximum cumulative detection probability. However, the increase in search speed allows the multi-sonar system to approach the target at a faster speed, so the growth rate of the cumulative detection probability in the beginning stage increases. Figure 10: The influence Schematic diagram of different sonar transceiver combinations on the cumulative detection probability of the Multi-sonar system under the multi-base working mode. The influence of the target escape speed on evaluation indicators  
We set the target escape velocities to \(V_{t}1\), \(V_{t}2\), \(V_{t}3\), and \(V_{t}1<V_{t}2<V_{t}3\), all other parameters are the same as those in the previous text. The simulation results are shown in Figure 12.  
According to the simulation results, it can be concluded that: (1) As the target escape speed increases, its radiated noise level increases, resulting in an increased probability of being detected. But at the same time, it also brings another problem: the increase in target escape speed leads to an increase in escape distance at the same time, resulting in an increase in the distance between the multi-sonar system and the target at certain moments, thus reducing the probability target detection. (2) During each round-trip search cycle, as time passes, a larger target escape speed will cause the multi-sonar system to approach the target at a relatively fast speed. Therefore, in the initial short period of time, a larger target escape speed corresponds to a relatively higher instantaneous detection probability, resulting in a relatively higher cumulative detection probability. (3) The influence of the target disappearance position on evaluation indicators  
Figure 11: The influence of different sonar search speeds on evaluation indicators. Figure 12: The influence of target escape speed on evaluation indicators. We set the target disappearance positions as \((0,0)\), \((0,a)\), \((0,-a)\), \((a,0)\), and \((-a,0)\), where \(a\) is a positive number greater than 0 and ensures that all 5 points are within the task area. The other parameters are the same as those in the previous text. The simulation results are shown in Figure 13.  
According to the simulation results, it can be concluded that changing the target disappearance position point can achieve a 'translation' of the instantaneous detection probability and cumulative detection probability on the time axis, because different target disappearance positions result in different times for the Multi-sonar system to approach the target.