Algorithm 2.

Time Update

1:	/* sample M particles */
2:	${\tilde{x}}_t^i={\mu }_t,i=1,\dots ,M$.
3:	/* propagate particles through the motion model */ ${\tilde{x}}_{t+1}^i=f_t\left({\tilde{x}}_t^i,w_t,\theta \right),i=1,2,\dots ,M$.
4:	/* calculate the predicted distribution */
5:	${\tilde{\mu }}_{t+1}={\sum }_{j=1}^M{w}_{t+1}^j{\tilde{x}}_{t+1}^j$,
6:	${\tilde{\Sigma }}_{t+1}={\sum }_{j=1}^M{w}_{t+1}^j\left({\mu }_{t+1}-{\tilde{x}}_{t+1}^j\right){\left({\mu }_{t+1}-{\tilde{x}}_{t+1}^j\right)}^T$.