## 5 Performance Analysis
### Validations of Unknown Detection Probability  
Figures 3-8 show the performance comparisons between the GCI-IGGM-PMBM filter and other multitarget tracking filters based on unknown detection probability. Figure 3a-d present the position estimations of the BGM-PMBM, IGGM-PHD, BGGIW-PMBM, and IGGM-PMBM filters, respectively. Overall, the trajectories of these filters mainly abided by the true trajectories, and the tracking estimations were accurate. Several different demonstrations in terms of the details are shown in Figure 3. Trajectory 2 (T2) and Trajectory 12 (T12) presented relatively large position errors for the BGM-PMBM filter, as shown in Figure 3a. T2 offset its trajectory from the initial tracking step and accumulated this error, whereas T12 presented poor turning performance for its bearing sets with a small turn rate. T1 and T3 for the IGGM-PHD filter presented relatively large errors, as shown in Figure 3b, especially for T3. T5 and T12 for the BGGIW-PMBM filter presented poor tracing performance; its computational burden was relatively high, and it took no account of bearing or turn rate in its designs. The IGGM-PMBM filter presented relatively superior tracking behaviors compared to the three other filters, as can be seen from the simulation results for several factors. For example, the IGGM-PMBM filter could work at an arbitrary turn rate. Performing the distributed fusion strategy using the global distributions of gamma, inverse gamma, and PMBM components, other than MB components, could substantially save energy. The actual but unknown detection probabilities were set to \(p_{D}=0.7\), \(p_{D}=0.9\), and \(p_{D}=0.96\). The clutter rate was \(\lambda_{c}=10\), and the anchor rate was \(\gamma_{0}=0.1\). The OSPA distances for different \(p_{D}\) were relatively high for the periods of 26-34 s, 46-53 s, 68-74 s, and 88-92 s, as shown in Figure 4a-c, which represent the intersecting points of these trajectories. The lowest OSPA distances for GCI-IGGM-PMBM at the initial trajectories prove that its HTC exchange strategy was applicable and accurate in the tracking initialization step. The distance error was relatively high at a lower detection probability; for example, the error for \(p_{D}=0.7\) was much higher than that for \(p_{D}=0.96\), and the error was highest for \(p_{D}=0.7\). The cardinality estimations for the periods of intersecting points, i.e., at 26-34 s, 46-53 s, 68-74 s, and 88-92 s, exhibited great deviation from the true trajectories shown in Figure 5. With an increase in the detection probability, the tracking performance improved. The cardinality estimations of GCI-IGGM-PMBM followed the true trajectory with relatively high accuracy. The detection probability plays an important role in multitarget tracking performance. For the processing period, 100 s in our simulations, the detection probability was changing and adaptive. The estimations of average OSPA error, cardinality, and \(p_{D}\) are shown in Figure 6. The value \(p_{D,k}\) was \(p_{D}=0.95\) at \(k\in(0,17]\), \(p_{D}=0.9\) at \(k\in(17,37]\), \(p_{D}=0.85\) at \(k\in(37,48]\), \(p_{D}=0.8\) at \(k\in(48,71]\), \(p_{D}=0.85\) at \(k\in(71,82]\), and \(p_{D}=0.7\) at \(k\in(82,100]\). Overall, the estimations for OSPA error, cardinality, and detection probability mainly abided by the true values, and tracking estimations were accurate, as shown in Figure 6. On the other hand, abrupt changes occurred at the change junctions of the detection probability, e.g., at 17-18 s, 37-38 s, 48-49 s, 71-72 s, and 82-83 s. All filters containing the GCI