# Multiple Extended Target Tracking Algorithm Based on Spatio-Temporal Correlation
## 4 Simulation Results and Analysis
### Simulation Experiment 1  
To verify the effectiveness of the proposed algorithm, two extended target cross motion scenes are constructed. The survival time of both extended target 1 and extended target 2 is 1\(\sim\)100 s, and there are no derived targets in the scenario. The intensity function of the newborn target is given by the following:  
\[\gamma_{t}(x)=0.1\mathcal{N}\Big{(}x;m_{\gamma,t}^{(1)},P_{\gamma,t}\Big{)}+ 0.1\mathcal{N}\Big{(}x;m_{\gamma,t}^{(2)},P_{\gamma,t}\Big{)} \tag{12}\]  
where \(m_{\gamma,t}^{(1)}=[250\) m, 250 m, 0 m/s, 0 m/s]T, \(m_{\gamma,t}^{(2)}=[-250\) m, \(-205\) m, 0 m/s, 0 m/s]T, \(P_{\gamma,t}=diag([100,100,25,25])\). The real tracks of the targets in the scene are shown in Figure 3(a), which shows that the tracks of the two extended targets cross at 56 s. Figure 3(b) shows the running results of the proposed algorithm under a single simulation. It can be seen from the figure that the state estimation of the target is also accurate when the extended target tracks cross.  
Figure 4(a) shows the OSPA distance comparison of different algorithms under 100 Monte Carlo simulations. It can be seen from the figure that the proposed algorithm OSPA distance is the minimum, even at the extended target track crossing moment. The OSPA distance gap between the algorithm, based on the directed graph partitioning of SNN, and the distance partitioning method is very small. Specifically, the OSPA distance of the directed SNN graph partition is significantly smaller in several adjacent moments when the targets cross. The comparison plot of OSPA distance verifies the effectiveness of the proposed algorithm.  
Figure 4(b) gives a comparison plot of the extended target number estimation. It can be seen from the figure that, since the two targets intersect at 56 s, the extended target at the current moment is close to the extended target at several adjacent moments. Thus, when the measurement set is partitioned by distance partition and directed graph SNN partition methods, measurements of different extended targets fall into the same set, resulting in the potential estimation error, and the potential error of graph partition method is smaller. The method proposed in this paper takes into account the correlation of the extended targets at adjacent times, so that it can achieve accurate potential estimation when the targets are close to each other or cross.  
Figure 6a,b shows the average number of partitions and the average running time of the measurement set at each time, respectively. It can be seen from the figures that distance partition has the highest average number of splits and the highest running time, because the distance partition needs to traverse multiple distance thresholds to find the best set of measurement partitions. The number of partitions of the directed graph SNN ranks second, and it first uses the DBSCAN algorithm to filter out part of the clutter, so the number of set partitions is smaller. The average number of partitions proposed in this paper is the lowest, which basically requires only one partition of the measurement set. When the extended target tracks cross, the measurement distance is close, and the number of distance division will be reduced at this time. At the same time, the running time of the algorithm reflects the number of partitions.  
Figure 4: (a) Real trajectory of the targets in Scenario 1. (b) Measurement values, true target trajectories, and estimated trajectories in Scenario 1.  
Figure 5: (a) Measurement values, true target trajectories, and estimated trajectories in Scenario 1.  
Figure 6: (a) Comparison of the number of measurement set partitions in Scenario 1. (b) Comparison of running time of each algorithm for Scenario 1.