# Tracking Extended Targets: Novel TPMB Filter Driven by Model and Data Collaboration
## 5 Simulation Results and Discussions
### Simulation 2  
For Scenario 2, to further validate the performance of the proposed algorithm, we designed a set of comparative experiments under the low clutter rate of 10 and the high clutter rate of 30, respectively. The parameters of target trajectories are shown in Table 4.  
Figure 4 shows that all five filters can converge to the actual number of targets. It was observed that as the clutter density increases, the state estimation error of each algorithm also increases. The reason for the increase in state estimation error in standard filters is due to the generation of random clutter by the filter and environment while tracking maneuvering targets. In contrast, the other four filters exhibit better robustness to the state transitions of targets, resulting in more accurate state estimations. More importantly, this \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & **Prior Target State** & **Motion** & **Lasting Time** & **Death Position** \\ \hline
1 & (100, \(-1.125\), \(66\), \(-0.55\))T & CV & (3,83) & (10,22) \\
2 & (138, \(-0.95\), \(152\), \(0.125\))T & CV & (3,83) & (62,162) \\
3 & (51, 0.75, 4, \(1.25\))T & CV & (6,86) & (111,104) \\
4 & (57, \(-0.225\), \(15\), \(0.55\))T & CT & (6,86) & (23,135) \\
5 & (133, \(-0.25\), \(41\), \(0.2\))T & CT & (9,89) & (33,141) \\
6 & (3, 0.175, 12, \(0.75\))T & CT & (9,89) & (33,112) \\
7 & (29, 1.5, 133, \(-0.75\))T & CT-CV & (12,92) & (170,115) \\
8 & (34, 0.6, 9, \(0.55\))T & CT-CV & (12,92) & (94,101) \\
9 & (21, 0.25, 16, \(0.6\))T & CT-CV & (15,95) & (112,116) \\
10 & (24, 0.125, 141, \(-0.75\))T & CT-CV & (15,95) & (35,53) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Averaged tracking errors for each filter. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Filter** & **Total** & **State** & **Miss** & **False** & **Switch** \\ \hline GGIW-TPMB & 52.65 & 43.41 & 11.41 & 17.39 & 0.158 \\ TPMB-BP & 44.35 & 38.75 & 6.27 & 13.74 & 0.076 \\ TPMB-GBP & 43.79 & 36.92 & 6.13 & 13.49 & 0.074 \\ IMM-TPMB-GBP-CKF & 40.12 & 34.14 & 5.84 & 14.01 & 0.097 \\ IMM-TPMB-GBP-ASCKF & **37.60** & **33.74** & **3.73** & **8.68** & **0.079** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean tracking errors for each filter. paper employs a method using interactive gating with GBP data association and an ASCKF that adapts the covariance matrix for unknown noise, addressing inaccuracies in state estimation under high clutter and unknown noise conditions. However, the cardinality estimated by standard filters is the least stable. During low clutter phases, false alarms occur due to the filter's inability to adaptively model estimates for non-linear targets. Since the targets maintain non-maneuverability, standard filters mix random clutter and unknown noise, leading to inaccurate state estimation. Conversely, at the 55 th s mark, there is a missed detection because two of the targets switch from CT to CV motion models, and the filters fail to immediately adapt to the motion changes. The IMM-TPMB-GBP-CKF, TPMB-GBP, and TPMB-BP algorithms exhibit lower state estimation errors and show stable performance throughout the detection period, though they also face the issues of increased estimation error with higher clutter rates. In contrast, the algorithm proposed in this work maintains low state estimation errors under both low and high clutter rates. It is less affected by increases in clutter and motion model transitions and controls the overestimation of target states under high clutter conditions. The GOSPA distances for the five filters are shown in Figure 5. As expected, throughout the detection period, the algorithm proposed in this paper consistently shows the lowest GOSPA distance. At the 10 th s, 20 th s, 45 th s, and 65 th s, the peaks in clutter density from the standard filter are caused by false alarms, mode transitions, and missed targets, involving both cardinality and location errors.