Algorithm 1.

Measurement Update

1:	/* sample M particles from importance function */
2:	${\tilde{x}}_t^i~\pi \left(x_t\mid Y_{1:t}\right),i=1,\dots ,M$.
3:	/* compute particle weights */
4:	${\tilde{w}}_t^i\propto \frac{p_{\theta }\left(y_t\mid {\tilde{x}}_t^i\right)}{{\sum }_{j=1}^M{p}_{\theta }\left(y_t\mid {\tilde{x}}_t^j\right)},i,j=1,\dots ,M$.
5:	/* normalize the weights */
6:	$w_t^i=\frac{{\tilde{w}}_t^i}{{\sum }_{j=1}^M{\tilde{w}}_t^j},i,j=1,\dots ,M$.
7:	/* calculate the filtered distribution */
8:	${\mu }_t={\sum }_{j=1}^M{w}_t^j{\tilde{x}}_t^j$,
9:	${\Sigma }_t={\sum }_{j=1}^M{w}_t^j\left({\mu }_t-{\tilde{x}}_t^j\right){\left({\mu }_t-{\tilde{x}}_t^j\right)}^T$.