## 2 The Measurement Partitioning Problem
### The Target Measurement Partitioning Algorithm Based on Target Predictions  
In addition to the distance-based measurement partitioning algorithms, predicted components are used to partition the measurement set in the prediction partition and EM partition in the random matrix framework of extended target tracking [37]. In prediction partition, the predicted mean of the GIW component is treated as the centroid of the elliptic target. The extension estimate \(\hat{X}_{k+1|k}^{(j)}\) (i.e., a symmetric positive definite matrix used to represent the elliptical shape of \(j\)th elliptic extended target) of the component is used to accurately partition the measurements, i.e., the measurements satisfying \(\left(z_{k}^{(i)}-m_{k+1|k}^{(j),d}\right)^{T}\left(\hat{X}_{k+1|k}^{(j)} \right)^{-1}\left(z_{k}^{(i)}-m_{k+1|k}^{(j),d}\right)<\Delta_{d}(p)\) are put into the same subset, where \(m_{k+1|k}^{(j),d}\) denotes the first \(d\) components of the predicted mean of \(j\)th GIW component, \(z_{k}^{(i)}\) is the \(i\)th measurement at time \(k\), \(\Delta_{d}(p)\) is determined according to the inverse \(\chi^{2}\) distribution with \(d\) degree of freedom, and \(p\) is the probability and equal to 0.99. For other measurements that are not included in any subsets of the predicted components, each of them is treated as an individual subset. However, the use of extension estimate limits the application of prediction partition to the tracking of extended targets with different shapes. It is also difficult to track ellipsoid targets with different sizes. To better partition the measurements when elliptic targets have different sizes and a diverse number of measurements, EM partition was proposed based on the Expectation Maximization algorithm for Gaussian mixtures. The predicted components are used to initialize the Gaussian mixtures. Both of the above algorithms only generate one accurate partition for the subsequent filtering, which can achieve good tracking performances when the target predictions are accurate in some cases. However, they are sensitive to the target predictions. When the target prediction is erroneous (i.e., the discrepancy between the predicted mean of the GIW component and the true target centroid is considerable), this partition is very likely to contain the non-information subsets, which directly causes the degradation of the target tracking performance. Thus, the alternative partitions should be considered to guarantee the stability of target tracking. Another problem of these partition algorithms is that they cannot handle well the measurement partitioning for tracking closely spaced extended targets in missed detection environments, which is very likely to cause the underestimation of the target number. Moreover, once the target number is underestimated, it further makes the target predictions erroneous, inevitably making the subsequent partition results unreasonable. Worst of all, only one partition is used in the partitioning algorithms. These subsets can directly influence the tracing performance and cause poor estimate performance of target number and state. To sum up, the key to achieving good tracking performance is to obtain the partitions that are closest to the true partition, and the number of partitions is the main factor affecting the averaged computation time. As for the distance-based measurement partitioning algorithms, there is still a large part of partitions that contain unreasonable subsets, which contributes little to tracking performance and leads to a heavy computational burden. In contrast, the measurement partitioning algorithms based on predictions aim to obtain one relatively accurate partition by utilizing predictive information, which greatly reduces the partition number. However, the accuracy of this partition can not be guaranteed, making the target tracking performance unstable. Both of these measurement partitioning algorithms cannot handle well the tracking scenario where extended targets are spatially close to each other.