Algorithm 1. Pruning and merging for the proposed algorithm.

Step 1. Pruning

Given the updated multi-target density ${\pi }_k(x_k,b_k)={\{r_k^{(i)},p_k^{(i)}(x_k,b_k)\}}_{i=1}^{M_k}$ at time step $k$, and two truncation thresholds $P_r$ and $T_w$.

Set $I=\{i|r_k^{(i)}\ge P_r\}$.

for $i=1,\cdots ,|I|$

Set $J^{(i)}=\{j|w_k^{(i,j)}\ge T_w\}$.

end

Step 2. Merging

Given a merging threshold $U_m$, and a maximum allowable number of Gaussian components $J_{\max }$.

for $i=1,\cdots ,|I|$

Set $a^{(i)}=0$.

if $|J^{(i)}|>0$

$a^{(i)}=a^{(i)}+1$.

$n=\arg \underset{j\in J^{(i)}}{\max }{w}_k^{(i,j)}$.

$A=\{j\in J^{(i)}|(m_k^{(i,j)}-m_k^{(i,n)}){}^T(P_k^{(i,j)}){}^{-1}(m_k^{(i,j)}-m_k^{(i,n)})\le U_m\}$.

${\tilde{w}}_k^{(i,a^{(i)})}={\displaystyle \sum _{j\in A}{w}_k^{(i,j)}}$.

${\tilde{m}}_k^{(i,a^{(i)})}=\frac{{\displaystyle \sum _{j\in A}{w}_k^{(i,j)}{m}_k^{(i,j)}}}{{\tilde{w}}_k^{(i,a^{(i)})}}$.

${\tilde{P}}_k^{(i,a^{(i)})}=\frac{{\displaystyle \sum _{j\in A}{w}_k^{(i,j)}[P_k^{(i,j)}+({\tilde{m}}_k^{(i,a^{(i)})}-m_k^{(i,j)})({\tilde{m}}_k^{(i,a^{(i)})}-m_k^{(i,j)}){}^T]}}{{\tilde{w}}_k^{(i,a^{(i)})}}$.

${\tilde{\widehat{m}}}_k^{(i,a^{(i)})}=\frac{{\displaystyle \sum _{j\in A}{\widehat{m}}_k^{(i,j)}}}{|A|}$.

${\tilde{\widehat{P}}}_k^{(i,a^{(i)})}=\frac{{\displaystyle \sum _{j\in A}{\widehat{P}}_k^{(i,j)}}}{|A|}$.

$J^{(i)}=J^{(i)}A$.

end

if $a^{(i)}>J_{\max }$

Discard $a^{(i)}-J_{\max }$ Gaussian components with lowest weights.

end

end

Step 3. Output results

Output ${\{r_k^{(i)},\{{\tilde{w}}_k^{(i,j)},{\tilde{m}}_k^{(i,j)},{\tilde{\widehat{m}}}_k^{(i,j)},{\tilde{P}}_k^{(i,j)},{\tilde{\widehat{P}}}_k^{(i,j)}\}{}_{j=1}^{{\tilde{a}}^{(i)}}\}}_{i\in I}$ with ${\tilde{a}}^{(i)}=\min (J_{\max ,}{a}^{(i)})$.