## 1 Introduction
Research Question 1: Evaluation of Collaborative Detection Efficiency of Multi-Sonar Systems in Real-Time Situation-Changing Environments_  
The collaborative search based on multi-sonar system is a dynamic process with real-time changes in relative position due to the mobility of the sonar and the target, and the efficiency evaluation model needs to adapt to the complex dynamic changes of the scene. Traditional efficiency evaluation methods are not suitable for this problem, because most traditional methods are limited to static modeling, which lacks dynamic analysis and adaptive adjustment capability, and cannot cope with the dynamic situations with real-time changes. In the process of multi-sonar collaborative search, due to the uncertainty of target motion, the relative position and situation between the sonar and the target are changing in real time, resulting in a real-time change of the sonar detection probability. This is an efficiency evaluation problem under uncertain target situation conditions, and it is difficult for us to establish a mathematical model that can accurately characterize the law of detection probability change. Therefore, traditional static modeling and evaluation methods have difficulty meeting the dynamic change requirements of the search process. To address this question, we discretize the sonar search path and target motion trajectory in time and space, and perform point-by-point deduction calculations. Through spatiotemporal discretization modeling and point-by-point dynamic deduction, the spatiotemporal interaction process between sonars and targets is accurately characterized, enhancing dynamic adaptability. To solve the problem of uncertain situations, we generate many target motion trajectories via the Monte Carlo method, and then transform uncertain situations into multiple relatively certain situations. _B. Research Question 2: Adaptive Fusion Method of Multi-Sonar Detection Information_  
In the search process, the detection capability of multi-sonar system is strongly correlated with the detection capability of each sonar platform. It is necessary to integrate the detection capability of each sonar platform to derive the overall detection capability. However, due to the real-time changes in the relative situation of the scene, the effective detection ability of each sonar platform also changes. We consider that sonar detection probability has a certain level of confidence, so multi-sonar detection information fusion is also in a \"dynamic\" state of change, that is, a high detection probability should be given high confidence and high weight. The traditional methods do not consider the 'dynamic' characteristics in the information fusion process. To address this issue, in this paper, we propose a multi-sensor detection information fusion method based on adaptive weight calculations. Among them, we use a linear function to calculate the confidence of the detection probability value, and normalize the confidence of multiple sonars before weighting them to obtain the overall detection probability. The accuracy of the fusion result is improved through adaptive weight allocation. In summary, we introduce the Monte Carlo sampling concept to establish a collaborative search efficiency evaluation model of multi-sonar system based on information fusion and dynamic deduction under uncertain target situations. We overcome the challenges posed by dynamicity in two ways. First, the dynamic change in the scenario can be accurately characterized by simulating the task process. Second, by a novel Monte Carlo-based searching strategy, the uncertainty of the target situations can be transformed into multiple relatively deterministic situations. Our proposed model is more in line with an actual scenario, and the efficiency evaluation results are more accurate and reliable. Our main innovations and contributions are summarized as follows.