## 4 Discussion
### Explanation of the Simulation Results  
In the case simulation analysis of this paper, we conduct a comprehensive simulation study. For different variable conditions such as different sensor speeds, target speeds and target initial positions, the corresponding detection probability change curves under the two working modes of fully-passive and multi-base are calculated and given in detail. However, there are two issues that need further clarification. (1) The calculation of the detection probability is based on ideal conditions. Specifically, the calculation of the detection probability is closely related to various parameters of the sonar equation. However, we assume that the relevant sonar equation parameters are constant or model calculated values, which exposes certain limitations. In a real marine environment, the background noise NL of the marine environment varies due to changes  
Figure 17: Relationship curve between the signal excess and confidence level. in hydrological conditions. In addition, in this paper, the transmission loss (TL) is obtained through empirical formulas, which also results in certain errors. In the next step of our research, we plan to add a certain disturbance to the NL value to reflect the changing characteristics of the marine environment, and use models such as the Bellhop sound field to calculate the TL value to more accurately reflect the influence of hydrological conditions, sea surface and seabed characteristics, and other factors on the propagation of underwater acoustic signals. (2) The simulation results under different experimental conditions are the means of multiple Monte Carlo results, which indicates that the simulation results have certain statistical significance. To further determine whether the mean of the detection probability has statistical significance and improve the reliability of the simulation results, we take the instantaneous detection probability results in Figure 11 as an example (in this example, the sonar is working in multi-base mode, the sonar search speed is \(v_{2}\), and the time point \(T\) is 50 min), and the one-sample \(t\)-test method is used in significance testing to test whether the mean of sonar detection probability significantly differs from the assumed random horizontal probability value. We design a significance test method according to the following steps:  
1. Clarifying the basic setting of hypothesis testing
2. Null hypothesis (\(H_{0}\)): The mean probability of sonar detection is equal to the random horizontal probability value, i.e., \(H_{0}:Pd=0.5\). 3. Alternative hypothesis (\(H_{1}\)): It is bilateral test, the mean of sonar detection probability significantly differs from the random horizontal probability value, i.e., \(H_{1}:Pd\
eq 0.5\). 4. Data preparation  
We use the Monte Carlo method to generate multiple sonar detection probabilities that meet the conditions, \(Pd_{1},Pd_{2},\ldots,Pd_{n}(Pd_{n}\in[0,1])\). These detection probability data are independent and the sample mean is approximately normally distributed. 1. Calculation of the test statistic (t-value) and \(p\)-value
2. Calculate the sample mean: \(\bar{P}d=\frac{1}{n}\sum_{i=1}^{n}Pd_{i}\). According to the simulation results in Figure 11, the mean of instantaneous detection probability is 0.5870. 3. Calculate the standard deviation of the sample: \(s=\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(Pd_{i}-\bar{P}d)^{2}}\). The standard deviation of instantaneous detection probability is 0.3040. 4. Calculate the t-statistic: \(t=\frac{Pd-0.5}{s/\sqrt{n}}\). By calculation, the t-statistic is 28.6285. 5. Calculate the \(p\)-value. By calculation, the \(p\)-value is \(2.5574\times 10^{-173}\), which is almost zero. 6. Determining statistical significance  
The calculated \(p\)-value is compared with the significance level \(\alpha\) (usually taken as 0.05): (1) If \(p\leq\alpha\), the null hypothesis is rejected, indicating that the mean of detection probability is significantly different from 0.5 (statistically significant).