## 3 Prediction-Driven Measurement Sub-Partitioning
The true tracks (i.e., black solid lines) and measurements with clutter (i.e., black dots) are illustrated in Figure 8. The tracks of these targets are paralleled all the time, which is a typical scenario and brings a huge challenge for MCETT. Both of two extended targets were born at \(k=1\) s and died at \(k=100\) s. The targets' birth intensity is

\[D_{b}(x)=0.1\mathcal{N}(x;m_{b}^{(1)},P_{b})+0.1\mathcal{N}(x;m_{b}^{(2)},P_{ b}) \tag{37}\]

Figure 6: The comparison of four approaches in partitioning number. Figure 7: The comparison of four approaches in computation time (seconds). where \(m_{b}^{(1)}=[250,250,0,0]^{T}\), \(m_{b}^{(2)}=[250,180,0,0]^{T}\), and \(P_{b}=\text{diag}\left([100,100,25,25]\right)\). The other simulation parameters are the same as those of the extended targets in Scenario A. As is shown in Figure 9, PMS has much better performance than DP, SP, and PP in the target number estimation. Especially compared with PP, the estimate of the target number in PMS is more accurate. This is because PP directly fixes the predicted mean as the centroid of a target, which is likely to cause the non-information subsets. Unlike PP, PMS only uses the predicted mean of a target to find its possible centroid, which is more flexible and improves the accuracy of partition results. Besides, Figure 9 also implies that the strategy used in PMS is more effective than that of SP, in which K-means++ clustering is utilized to repartition the unreasonable subsets. Although SP can, to some extent, handle the partitioning problem in DP due to the dense distribution of measurements, the degradation of target number estimation performance still cannot be avoided, i.e., relatively accurate partitioning results are not available in some cases. This lies in the loss function of K-means++ clustering, which is very likely to obtain inaccurate repartitioning results. However, in PMS, the unreasonable target prediction is reasonably replaced by the alternative points so that measurements are divided into two subsets rather than one subset, which contributes to better target number estimation performance. Figure 10 shows the OSPA distance of the compared approaches. In this figure, PMS has much better tracking performance than DP, SP, and PP. This reflects that the strategy of predicted position is

Figure 8: True tracks and measurements with clutter. Green square is the beginning point of the track; red circle is the end point of the track. Figure 9: The comparison of four approaches in target number estimation. more reliable than K-means++ in SP. This figure also illustrates that the predictive information (instead of the distance information) is more appropriate to be utilized for measurements partitioning, because the distance information is very likely to wrongly divide the measurements from more than one target into one subset in closely spaced target tracking. The comparison of partitioning number is shown in Figure 4:0 Compared with DP and SP, PMS uses fewer partitions, which can greatly reduce the computational burden. Combined with the comparison results of the estimation performance of the target number and state in Figure 10, it can be seen that the tracking performance by PMS does not degrade due to the reduction of the partition number. This is because the strategy in PMS is useful to obtain relatively accurate partitioning results. Besides, from Figure 11, PP has the lowest number of partitioning, only one partition. However, its tracking performance is worse than PMS because PP may obtain non-information partitions, which undoubtedly causes an inaccurate estimation of target number and state. Thus, we conclude that the good tracking performance depends on the accurate measurements partitioning, instead of merely the number of partitions. The computation time of these four algorithms is given in Figure 4:1 Combined with the partition number results from Figure 11, we can see that partition number is the main factor affecting the computational time. The computational time increases with the increase of partition number.