# Tracking Extended Targets: Novel TPMB Filter Driven by Model and Data Collaboration
## 5 Simulation Results and Discussions
### Simulation 1  
For Simulation 1, we set up a challenging experiment to demonstrate the tracking error of target trajectories and the precision of extended state tracking under a fixed clutter rate, 10, by four filters. The parameters of target trajectories are shown in Table 2. Note that the targets in three different motion states appear at different locations within the detection area at the 10 th s, 20 th s, and 30 th s. With a total of 100 steps run, each trajectory initialized from the starting point to the midway step, with the remaining steps generated forwards and backwards. In this scenario, we concentrate on estimating trajectories and compare the estimated extended states against the actual values. Among the various performance metrics for tra \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **Prior Target State** & **First Stage** & **Second Stage** & **Third Stage** \\ \hline
1 & (15, 2.1, 17, 2.5)T & 20–40 s & 40–63 s & — \\
2 & (150, \(-\)1.5, 200, \(-\)1)T & 10–40 s & 25–75 s & — \\
3 & (150, 0, 18, 2)T & 35–55 s & 55–90 s & 90–100 s \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of target trajectories in Simulation 1.  
jectory estimation, we employ the Linear Programming (LP) and the Gaussian Wasserstein Distance (GWD) metric \(d(\cdot,\cdot)\)[27]. We set the cut-off distance to 20, establish the order \(p=1\), and set the track switch cost to 2 in order to apply these metrics at each time step. The target trajectories are shown in Figure 2. We know that the available measurement information contains both real targets and random clutter. From this figure, we observe three trajectories. Clearly, the three targets have nonlinear motion states, performing CV and CT motions in stages within the detection area and the model has different angular velocities during CT motion. During three stages, the respective motion states are designated as CV, CT, and CV in turn, where the turning velocity is given before the scenario. The clutter obeys Poisson distribution, and the measurement noise and covariance are unknown to the filter. In Figure 2(a), it is evident that the filters proposed in this paper offer excellent extended state estimation and stable tracking performance for elliptical extended targets. In Figure 2(b), we note that the cardinality statistics change as time progresses. Obviously, all algorithms perform well in the potential estimation. The TPMB-BP, TPMB-GBP, IMM-TPMB-GBP-CKF algorithms, and the algorithm discussed in this paper all closely approximate the true number of targets, while the classical GGIW-TPMB algorithm underestimates the number of highly maneuverable targets; significant deviations in the potential estimation by the GGIW-TPMB algorithm from the true values are evident at the 30 th s, 40 th s, and 65 th s. The TPMB-BP and TPMB-GBP algorithms have a faster computation speed compared to IMM-TPMB-BP-CKF, and both algorithms essentially provide similar estimates of target potential. Notably, the standard filters are affected by multiple measurements from random clutter, resulting in some positional estimation biases. The filters proposed in this paper effectively eliminate the impact of unknown noise on tracking performance, providing accurate estimates. Figure 3: Target extended state estimation at the 40 th s and cardinality statistics for 5 filters. Figure 2: Tracks of 3-target estimates. The track error of the trajectory in Scenario 1 under the LP metric is presented in Table 3. For the extended target, the cost of state error dominates the overall LP estimation error. When the targets are in the same clutter, the measurement errors increase. For the most advanced TPMB-BP filter, we improved its correlation process and obtained the Gate-control BP association method that reduces the LP measurement error with adaptive gating. Among the five filters, the IMM-TPMB-GBP-ASCKF filter, with its superior noise adaptability, achieves the lowest LP metric. All five filters perform well when tracking targets at adequate intervals.