# Multiple Extended Target Tracking Algorithm Based on Spatio-Temporal Correlation
## 4 Simulation Results and Analysis
### Simulation Experiment 4  
The purpose of this experiment is to verify the filtering performance of the proposed algorithm in the variable velocity case in case of variable velocity. We consider adding a constant turn (CT) model, i.e.,  
Figure 11: (**a**) Comparison of CSPA errors for Scenario 3 (**b**) Comparison of target number estimation in Scenario 3.  
Figure 12: (**a**) Comparison of measurement set partition number in Scenario 3. (**b**) Comparison of running times of each algorithms for Scenario 3.  
Figure 10: (**a**) Real target trajectory for Scenario 3. (**b**) Measurement values, true target trajectories, and estimated trajectories in Scenario 3.  
\[\mathbf{F}=\begin{bmatrix}1&\sin(T_{\mathrm{s}}\omega)/\omega&0&-(1-\cos(T_{ \mathrm{s}}\omega))/\omega\\ 0&\cos(T_{\mathrm{s}}\omega)&0&-\sin(T_{\mathrm{s}}\omega)\\ 0&(1-\cos(T_{\mathrm{s}}\omega))/\omega&1&\sin(T_{\mathrm{s}}\omega)/\omega\\ 0&\sin(T_{\mathrm{s}}\omega)&0&\cos(T_{\mathrm{s}}\omega)\end{bmatrix} \tag{15}\]  
\[\mathbf{Q}_{\mathrm{CT}}=q_{\tau_{2}}\begin{bmatrix}T_{\mathrm{s}}^{4}/4&T_{ \mathrm{s}}^{3}/2&0&0\\ T_{\mathrm{s}}^{3}/2&T_{\mathrm{s}}^{2}&0&0\\ 0&0&T_{\mathrm{s}}^{4}/4&T_{\mathrm{s}}^{3}/2\\ 0&0&T_{\mathrm{s}}^{3}/2&T_{\mathrm{s}}^{2}\end{bmatrix} \tag{16}\]  
where \(q_{\tau_{2}}=0.0016\), \(\omega\) denotes the rotational angular velocity,and \(T_{\mathrm{s}}\) denotes the sampling period.  
The strength function of the newborn target is given by the following:  
\[\begin{split}\gamma_{t}(x)&=0.1\mathcal{N}\Big{(}x;m_{ \gamma,t}^{(1)},P_{\gamma,t}\Big{)}+0.1\mathcal{N}\Big{(}x;m_{\gamma,t}^{(2)}, P_{\gamma,t}\Big{)}\\ &+0.1\mathcal{N}\Big{(}x;m_{\gamma,t}^{(3)},P_{\gamma,t}\Big{)}\end{split} \tag{17}\]  
where  
\[m_{\gamma,t}^{(1)} =[-1300\;\mathrm{m},\,5\,\mathrm{m}/\mathrm{s},\,500\;\mathrm{m}, -5\,\mathrm{m}/\mathrm{s}]^{\top} \tag{18}\] \[m_{\gamma,t}^{(2)} =[50\;\mathrm{m},\,8\,\mathrm{m}/\mathrm{s},\,50\;\mathrm{m},\,8 \,\mathrm{m}/\mathrm{s}]^{\top}\] (19) \[m_{\gamma,t}^{(3)} =[-550\;\mathrm{m},-6\,\mathrm{m}/\mathrm{s},-650\;\mathrm{m},\, 6\,\mathrm{m}/\mathrm{s}]^{\top} \tag{20}\]  
The motion model for Scenario 4 is shown in Table 2.  
Figure 12(a) shows the real tracks of multiple extended targets in Scenario 4. Figure 12(b) shows the OSPA distance comparison of the three partition methods in scenario 4. It can be seen from the figure that the proposed method has the smallest OSPA distance. However, at the 1 st-5 th seconds, the OSPA distance becomes larger, which is because there are newborn targets. Figure 13(a),b shows the average number of partitions and the average running time of the three methods. The proposed method has the lowest number of partitions and running time. The reason is that the proposed method not only makes full use of the prior information, but also converts point target tracking into extended target tracking. Figure 13(c) shows the comparison of target number estimation. As can be seen from the figure, the cardinality estimation of the proposed algorithm is significantly better than the other two algorithms.  
From the simulation results, we can see that the performance of the proposed algorithm is still better than the other two comparison methods in the variable velocity scenario with a CT model.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Target** & **Dynamic Models** & **Model Duration Time** & **Birth Time** & **Death Time** \\ \hline \multirow{2}{*}{1} & CV & 1–10 s, 60–70 s, 87–100 s & \multirow{2}{*}{1 s} & \multirow{2}{*}{100 s} \\  & CT & 11–59 s, 71–86 s & & \\ \hline \multirow{2}{*}{2} & CV & 1–10 s, 60–70 s, 87–100 s & \multirow{2}{*}{1 s} & \multirow{2}{*}{100 s} \\  & CT & 11–59 s, 71–86 s & & \\ \hline \multirow{2}{*}{3} & CV & 1–10 s, 60–70 s, 87–100 s & \multirow{2}{*}{1 s} & \multirow{2}{*}{100 s} \\  & CT & 11–59 s, 71–86 s & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Trajectory configurations in Scenario 4.