## 3 Prediction-Driven Measurement Sub-Partitioning  
To effectively approximate all possible partitions, several reasonable partitions are considered to achieve stable and accurate target tracking performance. The partition number is determined according to the possible changes of the target number. Suppose that the number of extended targets at time step \(k-1\) is \(J_{k-1}\), the number of newborn targets is \(J_{\gamma,k}\), and the number of spawned targets from the same existing target is \(J_{\beta,k}\), then the range of target number \(K\) is  
\[J_{k-1}\leq K\leq J_{k-1}+J_{\beta,k}\times J_{k-1}+J_{\gamma,k}, \tag{1}\]  
As the measurements are needed to be partitioned into several subsets, we set the number of subsets in a partition as the possible target number. To obtain different partitions, we use different possible target number for measurement partitioning. As shown in Equation (1), there are \(J_{\beta,k}\times J_{k-1}+J_{\gamma,k}+1\) different integers in the closed interval. Correspondingly, there are \(J_{\beta,k}\times J_{k-1}+J_{\gamma,k}+1\) different partitions of the measurements. Here, \(J_{\beta,k}\) and \(J_{\gamma,k}\) are approximated by \(1\) and \(J_{k-1}\), respectively. That is, there are \(J_{k-1}\) newborn targets and one target spawned from the same target. Thus, the partition number \(N_{p}\) is reduced to  
\[N_{p}=2\times J_{k-1}+1. \tag{2}\]  
As mentioned above, every possible target (e.g., the existing target, the spawned target, or the newborn target) has the corresponding subset in the partition. Considering the unknown positions of the spawned and newborn targets, their possible clustering centers are determined by the initial center selection strategy of K-means++ clustering. To make sure each partition contains the most likely subsets, the predicted position of the existing target is used to obtain the possible clustering center of the existing target at the current time step, i.e., the measurement close to the predicted mean is treated as the possible center. It is clear that the number of subsets for the existing targets is determined by one of the existing targets and the accuracy of the partitioning results is closely related to the target predictions. However, in the typical target tracking scenario with spatially close targets, the target number is very likely to be underestimated, causing the same cardinality underestimation problem to the target predictions. It would directly influence the precision of the partition results. What is worse is that the wrong number of target predictions is hard to correct, which makes accurate measurement partitions unavailable for the subsequent filtering. This phenomenon no doubt degrades the MCETT performance and lasts for some time. To improve the robustness of the proposed measurement partitioning algorithm based on target prediction, a new repartition strategy is proposed in this paper to correct the unreasonable clustering centers obtained by target prediction. First of all, the unreasonable target prediction can be found through its partitioning results. According to the above clustering centers of existing targets, an initial partition \(P_{1}=\left\{W^{(i)}\right\}_{i=1}^{k-1}\) is obtained by clustering, where \(W^{(i)}\) denotes the \(i\)th subset in the initial partition \(P_{1}\). By comparing the expected number \(\lambda\) of measurements from the same target with the measured number \(\left|W^{(i)}\right|\) of each subset, the unreasonable subsets and their corresponding target predictions can be found. For each subset in \(P_{1}\), if the condition \(\frac{\left|W^{(i)}\right|}{\lambda}\geq 2\) is satisfied, this means it wrongly contains measurements of more than one target due to its clustering center. The corresponding target prediction of this clustering center is considered unreasonable. Second, the corresponding correct target number of each unreasonable subset can be roughly estimated by \(\frac{\left|W^{(i)}\right|}{\lambda}\).