Algorithm 2 Particle Filter Update with a Received Communication
1: function PF_Update($X_0,T,S,\theta ,z,D,X^r,{\Sigma }^r$)
2:    $particles\leftarrow X_0$	▹ Initialize particles
3:    $w\leftarrow 1/\left|particles\right|$	▹ Initialize particle weights
4:    for $t=0$ to T do
5:        $particles\leftarrow$move_particles($S,\theta ,t,M$)
6:        $\mathcal{Z}\leftarrow$BathymetryMap($particles$)
7:        $w_{bathy}\leftarrow$pdf${}_{alt}$ ($z-\mathcal{Z},{\mu }_{alt},{\sigma }_{alt}$)
8:        $w_{comms}\leftarrow$pdf${}_{coms}$($particles+D,X^r,{\Sigma }^r)$)
9:        $w\leftarrow w\times w_{bathy}\times w_{comms}$
10:        $w\leftarrow w/\sum \left(w\right)$
11:    $X\leftarrow \sum (weights\times particles)$
12:    $\Sigma \leftarrow Covariance\left(particles\right)$
return $X,\Sigma$