## 3 Prediction-Driven Measurement Sub-Partitioning
\[m_{k|k}^{(j)}=m_{k|k-1}^{(j)}+\mathrm{K}_{k}^{(j)}\left(\left[ \begin{array}{c}z_{ 1}\\ \vdots\\ z_{|W|}\end{array} \right]-H_{K}m_{k|k-1}^{(j)}\right) \tag{24}\]

\[P_{k|k}^{(j)}=(\mathrm{I}-\mathrm{K}_{k}^{(j)}H_{K})P_{k|k-1}^{(j)} \tag{25}\]

\[\mathrm{K}_{k}^{(j)}=P_{k|k-1}^{(j)}H_{K}^{\mathrm{T}}(R_{K}+H_{K}P_{k|k-1}^{( j)}H_{K}^{\mathrm{T}})^{-1} \tag{26}\]

where \(K_{k}^{(j)}\) denotes the matrix of Kalman filter gain. To sum up, the proposed multiple close-spaced extended target tracking approach is summarized as follows. Step 1. Calculate the predicted intensity:

\[m_{k-1}^{(j)}\to m_{k|k-1}^{(j)},P_{k-1}^{(j)}\to P_{k|k-1}^{(j)},\omega_{k-1} ^{(j)}\to\omega_{k|k-1}^{(j)} \tag{27}\]

Step 2. Determine the range of K value:

\[J_{k-1}+J_{\beta,k}\times J_{k-1}+J_{\gamma,k}\to K_{U} \tag{28}\]

\[J_{k-1}\to K_{L} \tag{29}\]

Step 3. Select the initial clustering centers \(C^{k_{-1}}\) by using the predictive information and obtain the first partition \(P_{1}\) based on the above centers:

\[m_{S,k|k-1}^{(j)}\to c_{j}\in C^{k_{-1}} \tag{30}\]

\[Z_{k}\to P_{1}=\left\{W^{(i)}\right\}_{i=1}^{k_{-1}} \tag{31}\]

Step 4. Partition measurements: If \(\frac{N_{k,k}}{\lambda}-J_{k-1}\geq 1\), it implies that the target number has been underestimated. Then, execute PMS to find the alternative initial centers of the estimated subsets in \(P_{1}\), which contributes to more accurate partitioning results when extended targets cross each other. \[\mathrm{PMS}\to P=\left\{P_{1},P_{2},\cdots\right\} \tag{32}\]

If this judgment condition is not satisfied, PMS directly uses the predictions of existing targets to obtain the clustering centers and partition the measurement set. Step 5. Update the predicted intensity:

\[m_{k|k-1}^{(j)}\to m_{k|k}^{(j)},P_{k|k-1}^{(j)}\to P_{k|k}^{(j)},\omega_{k|k -1}^{(j)}\to\omega_{k|k}^{(j)} \tag{33}\]

## 5 Simulation Results and Performance Evaluation

In this section, the effectiveness of the proposed MCETT approach based on prediction-driven measurement sub-partitioning (PMS) for tracking of closely spaced targets is illustrated by comparing the proposed MCETT approach with the existing MCETT approaches based on different measurements partitioning strategies:

1. PP: The MCETT approach using the measurement partitioning of the work in [37]. 2. SP: The MCETT approach using the measurement partitioning of the work in [27]. 3. DP: The MCETT approach using the distance-based partitioning. To better illustrate the tracking performance of multiple extended targets, a typical simulation scenario is considered: (A) Tracking of extended targets with typical tracks, which contains the crossing targets, spawned targets, and newborn targets. To further illustrate the tracking performance of closely spaced targets, two more specific simulation scenarios of MCETT are considered: (B) Tracking of extended targets with paralleled tracks; (C) Tracking of extended targets with crossed tracks. In each simulation scenario, there is a stationary sensor platform and multiple moving extended targets and approaches are initialized with the same target state and number without further information. Moreover, there are clutter measurements distributed randomly, and the measurements of each target may be not detected by the sensor at per time step. Both of these bring great difficulties to accurately track multiple extended targets. We calculate the performance in the computational burden, target number estimation, and optimal sub-pattern assignment (OSPA) distance [41]. Note that the OSPA distance is chosen as the measure to evaluate the tracking performance. The computation time and partition number of measurements are jointly used to reflect the computational burden of the algorithm in simulations. The computational complexities for these approaches are compared in the CPU running time and simulations are implemented by MATLAB on Intel(R) Core(TM) i3-2130, 3.40 GHz, and 4 GB RAM. The detailed discussions and analysis are as follows.