Algorithm 2 SMC Filter for BLE Localization

1:Instantiate For $i\in [1..N]$, sample $P_0^{\left(i\right)}\sim p\left(P_0\right)$ 2:Importance Sampling Update time index $t\leftarrow t+1$ For $i\in [1..N]$, sample ${\tilde{P}}_t^{(i)}\sim p(P_t|P_{t-1}^{(i)})$ For $i\in [1..N]$, evaluate to obtain the importance weights $w_t^{(i)}=p(D_t|{\tilde{P}}_t^{(i)})$ Normalize the importance weights ${\tilde{w}}_t^{\left(i\right)}=\frac{w_t^{\left(i\right)}}{{\sum }_{i=0}^N{w}_t^{\left(i\right)}}$ 3:Select Resample N particles as $P_t^{\left(i\right)}$ from the particles ${\tilde{P}}_t^{\left(i\right)}$ according to the importance weights. 4:Recurse with repeating 2.