Algorithm 1. The robust SMC-PHD filter.

Step 1 Prediction for $i=1,2,\dots ,L_{k-1}$     $x_k^{(i)}\sim q_k(\cdot \left|x_{k-1}^{(i)},Z_k\right.),{\omega }_{k\left|k-1\right.}^{(i)}\sim {\omega }_{k-1}^{(i)}\frac{p_{S,k}{f}_{k\left|k-1\right.}(x_k^{(i)}\left|x_{k-1}^{(i)}\right.)}{q_k(x_k^{(i)}\left|x_{k-1}^{(i)},Z_k\right.)}$     $\begin{array}{l}{\upsilon }_{k\left|k-1\right.}^{(i)}=\rho ({\upsilon }_{k-1}^{(i)}-d-1)+d+1,V_{k\left|k-1\right.}^{(i)}=\rho V_{k-1}^{(i)}\\ {\alpha }_{k\left|k-1\right.}^{(i)}=\rho {\alpha }_{k-1}^{(i)},{\beta }_{k\left|k-1\right.}^{(i)}=\rho {\beta }_{k-1}^{(i)}\end{array}$ end for for $i=L_{k-1}+1,L_{k-1}+2,\dots ,L_{k-1}+J_k$     $x_k^{(i)}\sim p_k(\cdot \left|Z_k\right.),{\omega }_{k\left|k-1\right.}^{(i)}\sim \frac{1}{J_k}\frac{{\gamma }_k(x_k^{(i)})}{p_k(x_k^{(i)}\left|Z_k\right.)}$     ${\upsilon }_{k\left|k-1\right.}^{(i)}={\upsilon }_{\gamma ,k}^{(i)},V_{k\left|k-1\right.}^{(i)}=V_{\gamma ,k}^{(i)}$     ${\alpha }_{k\left|k-1\right.}^{(i)}={\alpha }_{\gamma ,k}^{(i)},{\beta }_{k\left|k-1\right.}^{(i)}={\beta }_{\gamma ,k}^{(i)}$ end for

Step 2 Update For $i=1,2,\dots ,L_{k-1}+J_k$         $\begin{array}{l}{R}_k^{(i)}=V_{k\left|k-1\right.}^{(i)}/({\upsilon }_{k\left|k-1\right.}^{(i)}-d-1),{\nu }_k^{(i)}={\alpha }_{k\left|k-1\right.}^{(i)}/{\beta }_{k\left|k-1\right.}^{(i)}\\ g_k(z\left|{\ddot{x}}_k^{(i)}\right.)=\mathrm{St}(z;h(x_k^{(i)}),R_k^{(i)},{\nu }_k^{(i)})\end{array}$         $\begin{array}{l}{g}_k^p({\ddot{x}}_k^{(i)})=\frac{p_{D,k}{g}_k(z_k^p\left|{\ddot{x}}_k^{(i)}\right.)}{{\kappa }_k(z_k^p)+C_k(z_k^p)}\\ C_k(z_k^p)={\displaystyle \sum _{j=1}^{L_{k-1}+J_k}{p}_{D,k}{g}_k(z_k^p\left|{\ddot{x}}_k^{(i)}\right.){\omega }_{k\left|k-1\right.}^{(i)}}\end{array}$         $I=\left\{1,\dots ,\left|Z_k\right|\right\},J=\left\{p=1,\dots ,\left|Z_k\right|\left|g_k^p({\ddot{x}}_k^{(i)})\ge \sigma \right.\right\}$         $l=\underset{p\in I}{\arg \max }{g}_k^p({\ddot{x}}_k^{(i)}),q=\underset{p\in I}{\arg \min }{g}_k^p({\ddot{x}}_k^{(i)})$         ${\tilde{g}}_k^p({\ddot{x}}_k^{(i)})=\left\{\begin{array}{c}{g}_k^p({\ddot{x}}_k^{(i)}),p=l or p\notin J\\ g_k^q({\ddot{x}}_k^{(i)}),p\ne l \& p\in J\end{array}\right.$         ${\omega }_k^{(i)}=(1-p_{D,k}){\omega }_{k\left|k-1\right.}^{(i)}+{\displaystyle \sum _{p=1}^{\left|Z_k\right|}{\tilde{g}}_k^p({\ddot{x}}_k^{(i)})}{\omega }_{k\left|k-1\right.}^{(i)}$ Perform iteration initialization, set the iteration number $\tau$, and update the parameters of measurement noise by Equations (49)–(60). end for

Step 3 Resampling Step 4 State extraction     Step 3 and step 4 are the same as that in the standard SMC-PHD filter.