## 3 Scenario Setting and Experimental Metrics
### MDF-Clustering Algorithm Evaluation Index  
The evaluation of the algorithm's effectiveness involves comparing the results of the other four algorithms in three scenarios with different false alarm rates using three evaluation methods.  
(1) The average number of frames required for target stabilization initialization  
One of the evaluation methods employed to assess the algorithm's performance involves calculating the average number of frames required for target stabilization and initialization. This metric is crucial as it reflects the efficiency of the target tracking algorithm by indicating the time needed for the algorithm to achieve a stable state from the initialization of tracking. A lower value suggests that the algorithm can quickly and accurately lock on and track the target stably, demonstrating the responsiveness of the algorithm. The average number of frames for stable initialization is calculated using the following formula:  
\[\overline{f_{s}}=\frac{\sum_{q=3}^{Q}\overline{f_{sq}}}{Q} \tag{26}\]  
(2) Average occupancy rate of false trajectories  
The average false track occupancy is a metric used to assess the ratio of false tracks detected to all tracks detected by the target tracking algorithm. A lower value suggests that the algorithm is successful in differentiating between actual targets and noise, resulting in a lower false alarm rate and ensuring the accuracy and reliability of the generated results. The formula for calculating this metric is as follows:  
\[F_{pq}\triangleq\frac{\frac{\sum_{i=1}^{N}F_{i}}{\sum_{i=1}^{N}R_{i}}}{N} \tag{27}\]  
The false trajectory occupancy rate \(F_{pq}\) is calculated under various false alarm rates \(q\), with \(F_{i}\) representing the false trajectory and \(R_{i}\) representing the actual trajectory of simulations at a specific false alarm rate. The variable N denotes the total number of simulation runs at this false alarm rate.  
\[F_{P}\triangleq\frac{\sum_{q=3}^{Q}F_{pq}}{Q-3} \tag{28}\]  
\(F_{P}\) represents the average false track occupancy and \(Q\) represents the maximum false alarm rate.  
(3) Average Initialization Rate of Correct Trajectory  
The average initialization rate of correct trajectory measures the ability of the target tracking algorithm to accurately identify and start tracking the real target at the initial stage. This index reflects the algorithm's capability to identify and initiate tracking of the actual target. A higher value indicates a more accurate tracking of the target in the initialization phase. The formula for this is:  
\[D_{pq}\triangleq\frac{\frac{\sum_{i=1}^{N}T_{i}}{T_{All}}}{N} \tag{29}\]  
\(D_{pq}\) represents the correct trajectory initialisation rate at different false alarm rates \(q\), \(T_{i}\), \(T_{All}\) represent the number of accurate trajectories initialized and the total number of actual target trajectories for the \(i\)th simulation at a given false alarm rate, respectively, and \(N\) represents the total number of times the simulation has been performed at that false alarm rate.  
\[D_{P}\triangleq\frac{\sum_{q=3}^{Q}D_{pq}}{Q-3} \tag{30}\]\(D_{P}\) represents the average false track occupancy and \(Q\) represents the maximum false alarm rate.  
(4) Trajectory leakage rate  
The miss rate is the proportion of targets that should be detected by the system but are not detected. This metric reflects the tracking system's inability to detect targets, and its formula is as follows:  
\[R_{m}=\frac{N_{non\_det}}{N_{all\_tr}} \tag{31}\]  
\(R_{m}\) represents the missed batch rate of the trajectory, \(N_{non\_det}\) represents the number of undetected targets, and \(N_{all\_tr}\) represents the total number of valid targets.