Algorithm 3 Refined PHD Filter

Initialization: suppose prior PHD at time 0 is Equation (3), $l_{0|0}^i=0,i=1,\cdots ,v_{0|0}$, and $r=0$.

Prediction: the predicted PHD at time $k$ is Equation (5), and labels of the prediction particles are $l_{k|k-1}^i=l_{k-1|k-1}^i,i=1,\cdots ,v_{k-1|k-1}$ and $l_{k|k-1}^i=0,i=v_{k-1|k-1}+1,\cdots ,v_{k|k-1}$.

Correction: the posterior particle weights at time $k$ are calculated by Equation (7), and $l_{k|k}^i=l_{k|k-1}^i,i=1,\cdots ,v_{k|k}$.

Revision of Posterior Weights: execute revision of posterior weights introduced in Section 3.3, the revised weights are still represented as $w_{k|k}^i$, and the posterior PHD at time $k$ is Equation (6).

State estimation: ${\widehat{N}}_{k|k}\approx round\left({\displaystyle \sum _{i=1}^{v_{k|k}}{w}_{k|k}^i}\right)$, resample with no change of particle labels, and ${\widehat{N}}_{k|k}$ targets are extracted by k-means clustering: $x_k^{(n)},n=1,\cdots ,{\widehat{N}}_{k|k}$.

Trajectory extraction: determine the label of target $x_k^{(n)}$ and corresponding particles according to Section 3.2.

Survival Probability Calculation: calculate survival probability of individual target according to Section 3.1.

Target Confirmation: calculate test statistic $\underset{k}{sum}{L^{\prime }}_{l,k}$, and for individual target, add it to the confirmation set, discard it, or make no decision according to Section 3.4.