Definition

In occupancy-grid Mapping, we represent our map as a discretization of our world into a 2D (or 3D) grid, $\mathbf{m} := [\mathbf{m}_{ij}], 0 \le i\le H, 0 \le j \le W$, where $H$ represents the height of the grid and $W$ the width. We say $\mathbf{m}_{ij},\,(i,j) ∈H \times W$ represents the probability that the cell $(i,j)$ is occupied. This can be represented similarly as in Feature-based mapping where we would like to compute at time $t$ the probability of our map given all our previous poses and observations $$p(\mathbf{m} \mid z_{[0,t]},x_{[0,t]})$$