## 3 Prediction-Driven Measurement Sub-Partitioning
Accordingly, the lower bound is \(K_{L}=J_{k-1}^{*}=J_{k-1}-N+\sum\limits_{i=1}^{N}n_{i}\) and the upper bound is \(K_{U}=J_{k-1}^{*}+J_{\beta,k}\times J_{k-1}^{*}+J_{\gamma,k}\). Step 8. \(C^{K-I_{k-1}}\) and \(C^{K}\) are merged into \(C^{K}=C^{K-I_{k-1}}\cup C^{I_```
0:\(Z_{k}\): the set of measurements; \(N_{z,k}\): the number of measurements; \(X_{S,k|k-1}\): predictions for existing targets; \(J_{k-1}\): the number of targets at time \(k-1\); \(\lambda\): the expected number of measurements from one target; \(f_{pre}\left(X,Z\right)\): a function using target predictions to obtain clustering centers; \(f_{initialP}\left(K,C,Z\right)\): K-means clustering function with only one iteration; \(f_{alter}\left(n,c,Z\right)\): a function to compute alternative clustering centers; \(f_{K}\left(K,Z\right)\): K-means++'s initial clustering center selection function; \(f_{P}\left(K,C,Z\right)\): K-means clustering function;
0: partitions \(\left\{P_{k}\right\}_{K=K_{L}}^{K_{U}}\)
1:\(K_{L}=J_{k-1}\), \(K_{U}=J_{k-1}+J_{\beta,k}\times J_{k-1}+J_{\gamma,k}\);
2: Obtain \(C^{k_{-1}}:\left\{c_{i}\right\}_{i=1}^{k_{-1}}=f_{pre}\left(X_{S,k|k-1},Z_{k}\right)\);
3:if\(N_{z,k}/\lambda-J_{k-1}\geq 1\)then
4: First partitioning: \(\left\{W^{\left(i\right)}\right\}_{i=1}^{k-1}=f_{initialP}\left(J_{k-1},C^{k_{ -1}},Z_{k}\right)\);
5:\(J_{k-1}^{*}=J_{k-1}\);
6:for\(i=1:j\)do
7:if\(\frac{\left|W^{\left(i\right)}\right|}{\lambda}\)then
8:\(n_{i}\leftarrow\) ROUND \(\left(\frac{\left|W^{\left(i\right)}\right|}{\lambda}\right)\);
9: Find alternative centers: \(C^{i}_{n_{i}}=f_{alter}\left(n_{i},c_{i},Z_{k}\right)\);
10: Delete the center \(c_{i}\) in \(C^{k_{-1}}\)
11: Augment the new centers: \(C^{k_{-1}}=C^{k_{-1}}\cup C^{i}_{n_{i}}\);
12:\(J_{k-1}^{*}=J_{k-1}^{*}-1+n_{i}\);
13:endif
14:endfor
15:\(K_{L}=J_{k-1}^{*}\),\(K_{U}=J_{k-1}^{*}+J_{\beta,k}\times J_{k-1}^{*}+J_{\gamma,k}\);
16:endif
17:while\(K_{L}\leq K\leq K_{U}\)do
18: Obtain \(C^{K-k_{-1}}\): \(\left\{c_{i}\right\}_{i=I_{k-1}^{*}+1}^{K}=f_{K}\left(K-J_{k-1},Z_{k}\right)\);
19: Obtain the whole clustering center set \(C^{K}\): \(C^{K}=C^{k_{-1}}\cup C^{K-k_{-1}}\);
20: Measurements partitioning: \(P_{K}=\left\{W^{\left(i\right)}\right\}_{i=1}^{K}=f_{P}\left(K,C^{K},Z_{k}\right)\);
21:\(K=K+1\);
22:endwhile
```

**Algorithm 1** Prediction-driven measurement sub-partitioning algorithm. **Remark 1**. : _The above algorithm flexibly utilizes predictions of existing targets to obtain more accurate measurement partitioning results. Moreover, the unreasonable target predictions are replaced by more reasonable alternative points, which fits well in the tracking scenarios with extended targets spatially close (e.g., targets with tracks-crossed) when the number of targets is underestimated. Note that this strategy aims to make the use of target predictions more robust, which does not add extra partitions to improve the accuracy of partitions. Due to its concise mathematical forms and favorable properties, PMS can be easily integrated into the framework of ET-PHD filter, achieving higher tracking performance._

## 4 A Target Tracking Approach Based on Prediction-Driven Measurement Sub-Partitioning

As mentioned above, the proposed prediction-driven measurement sub-partitioning algorithm can be integrated into various filters to track multiple extended targets due to its concise mathematical forms and favorable properties. Thus, a multiple extended target tracking approach based on PMS is proposed. Based on the assumption of the measurement model that measurements are distributed around a target reference point approximately, the target state vector \(x_{k}^{(i)}=[m_{k}^{(i)},x_{k}^{*}]^{\mathrm{T}}\) consists of only the target position \(m_{k}^{(i)}\) and velocity \(x_{k}^{*}\) without any parameter of target's size and shape. Note that this is the basic structure of the target state vector, in which the parameters for spatial extent can be included according to other models of target extension.