# Joint Probabilistic Hypergraph Matching Labeled Multi-Bernoulli Filter for Rigid Target Tracking
## 4 Simulation
### Scenario 1
Firstly, the effect of measurement errors on tracking performance is analyzed. The OSPA and clear mot metrics of these filters with different measurement errors are shown in Figure 10 and Table 3 respectively. From Figure 10, when targets maneuvering during the interval 20 s-40 s, the OSPA of three filters increases, the reason is the mismatch between actual motion model and dynamic motion model. When targets born or die, the number of targets will change, these filters will take some time to obtain the true number of targets, then the OSPA distance increase. The performance of JPHGM-LMB degrades with increasing measurement error and these filters achieves almost similar performance when \(\sigma_{m}=0.4\) m. However, JPHGM-LMB outperforms other filters, because JPHGM-LMB takes both kinematic and structure information into account and missed detections are considered. In JPHGM-LMB, the hypergraph is introduced to represent the structure of predictions and measurements, then the problem of data association can be formulated as a hypergraph matching problem, it becomes more challenge to obtain the correct matching results as measurement errors increases. Moreover, the structure of targets will be deformed because unreliable measurements are used to update the states of targets. From Table 3, JPHGM-LMB achieves larger MOTA values than other filters, it means that JPHGM-LMB obtains higher quality trajectories than other filters, it further validates the superiority of JPHGM-LMB. Figure 9: True trajectories in scenario 2. Secondly, the effect of occlusions are considered, it can not be avoided in practice applications, for example, the car may be partly covered by pedestrians or other barriers. In order to simulate occlusions, the 4 th scattering centers of two rigid targets are occluded during several time steps for simplicity. The beginning of the occlusion is at \(k=32\) s (targets are maneuvering), the duration of occlusion is \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & **MOTP** & **Miss Rate** & **False Positive Rate** & **Mismatches** & **MOTA** \\ \hline \multirow{3}{*}{\(\sigma_{m}=0.1\) m} & LMB & 0.6266 & 7.5\% & 6.62\% & 50.66 & 73.28\% \\  & HGM-LMB & 0.4698 & 4.29\% & 3.05\% & 27.98 & 85.74\% \\  & JPHGM-LMB & **0.4053** & **3.23**\% & **2.54**\% & **23.52** & **88.41**\% \\ \hline \multirow{3}{*}{\(\sigma_{m}=0.2\) m} & LMB & 1.009 & 10.56\% & 9.18\% & 60.58 & 63.9\% \\  & HGM-LMB & 0.9432 & 8.41\% & 6.94\% & 58.7 & 70.13\% \\  & JPHGM-LMB & **0.7436** & **5.03**\% & **4.27**\% & **48.82** & **78.61**\% \\ \hline \multirow{3}{*}{\(\sigma_{m}=0.3\) m} & LMB & 1.11 & 12.54\% & 11.12\% & 63.52 & 60.61\% \\  & HGM-LMB & 1.01 & 11.3\% & 9.33\% & 59.36 & 63.25\% \\ \cline{1-1}  & JPHGM-LMB & **0.8985** & **9.45**\% & **7.64**\% & **52.08** & **68.79**\% \\ \hline \multirow{3}{*}{\(\sigma_{m}=0.4\) m} & LMB & 1.1745 & 14.75\% & 13.82\% & 66.1 & 56.44\% \\ \cline{1-1}  & HGM-LMB & 1.0519 & 14.45\% & 12.32\% & 65.14 & 58.78\% \\ \cline{1-1}  & JPHGM-LMB & **1.016** & **13.96**\% & **12.2**\% & **57.48** & **60.54**\% \\ \hline \hline \end{tabular}  
* MOTP is the multiple object tracking precision and MOTA is the multiple object tracking accuracy.  
\end{table} 
Table 3: Clear mot metrics of filters with different measurement errors. denoted by \(\beta\). The OSPA and clear mot metrics of these filters with different occlusion time steps are shown in Figure 11 and Table 4 respectively.