Algorithm 2: Particle filtering for localization.
Initialization
1: $p_i^0\leftarrow {\mathcal{N}}_2(p,\sigma )\{i=1,\cdots ,n\}$	▹ Randomly initialization of particles from location p
2: ${\varphi }_i^0\leftarrow {\mathcal{N}}_2(p_i^0,\sigma )\{i=1,\cdots ,n\}$	▹ Initialization of distribution from the position $p_i^0$
3: $s_i^0\leftarrow [{\mathbf{x}}_{\mathbf{i}}^{\mathbf{0}};w_i^0;{\varphi }_i^0:i=1,\cdots ,n]$	▹ Initialization of samples within the uncertain location
Recursive loop for localization
4: while true do
5: k++
6: ENP = $\frac{1}{{\sum }_{i=1}^{n}lo{g}^2\left(w_i^k\right)}$	▹ Effective number of particles
7: if ENP < $\beta ·n$then	▹ Condition of particle population depletion ($0\le \beta \le 1$)
8:  ${\mathbf{s}}^{\mathbf{k}}$	← Resampling(${\mathbf{w}}^{\mathbf{k}}$)
9: end if
10: Prediction stage
11: ${\mathbf{x}}^{\mathbf{k}+\mathbf{1}}$←$h({\mathbf{x}}^{\mathbf{k}},\alpha )$	▹ Include action $\alpha$ (dead-reckoning displacements)
12: ${\mathbf{x}}^{\mathbf{k}+\mathbf{1}}$←${\mathbf{x}}^{\mathbf{k}+\mathbf{1}}$+$\alpha$·$\mathcal{N}(0,{\alpha }_u)$	▹ Include ramdom noise to the variable of interest
13: Update stage
14: ${\mathbf{w}}^{\mathbf{k}+\mathbf{1}}$=${\mathbf{w}}^{\mathbf{k}}·g(\gamma ,{\mathbf{x}}_{\mathbf{j}}^{\mathbf{k}})$	▹ Update with sensing $\gamma$
15: Normalization of the weights
16: for j← 1 to n do
17:  $w_j^{k+1}$=$\frac{w_j^{k+1}}{{\sum }_{i=1}^n{w}_i^{k+1}}$
18: end for
19: end while