Algorithm 1 Labelling Particles and Targets

Initialization: the initialization particles are labelled with zeros, and maximum label is set to $r=0$.

Prediction: labels of the prediction particles are $l_{k|k-1}^i,i=1,\cdots ,v_{k|k-1}$, where $l_{k|k-1}^i=l_{k-1|k-1}^i,i=1,\cdots ,v_{k-1|k-1}$ and $l_{k|k-1}^i=0,i=v_{k-1|k-1}+1,\cdots ,v_{k|k-1}$.

Correction: labels of the posterior particles are $l_{k|k}^i=l_{k|k-1}^i,i=1,\cdots ,v_{k|k}$, and the resampling technique doesn’t change the labels of particles.

Trajectory extraction: ${\widehat{N}}_{k|k}$ targets are extracted from the posterior PHD. The label of target $x_k^{(n)}$ can be determined by $\arg \underset{l}{\max }\left|\left\{l_{k|k}^i|l_{k|k}^i=l,x_{k|k}^i\in x_k^{(n)},i=1,\cdots ,v_{k|k}\right\}\right|,n=1,\cdots ,{\widehat{N}}_{k|k}$, where $\left|X\right|$ represents the cardinality of set $X$.

For each target $x_k^{(n)}$, if its label is zero, then $r=r+1$, set its label to $r$, and set $l_{k|k}^i|l_{k|k}^i=0,x_{k|k}^i\in x_k^{(n)},i=1,\cdots ,v_{k|k}$ to $r$.

If there are multiple targets with the same label $l$, the optimal successor can be selected by Equation (10), and for other target similar operation will be performed like the scene that the label of target is zero.