Occupancy Grid Mapping

In an occupancy grid mapping scheme, the map is represented as a grid (like pixels in an image):

$$m\in {\mathbb{R}}^{n_h\times n_v}$$

• $n_h$ rows and $n_v$ columns

In a standard mapping problem, for the $i$-th grid cell, we assign a pdf $p(m_i)$.

• Free (no obstacle) means $m_i=0$
• Occupied means $m_i=0$

We then use a Bayes Filter to estimate its posterior:

$$p(m_i\mid z_{1:k},{\xi }_{1:k})$$

If we assume that each cell is independent, we have

$$p(m_i\mid z_{1:k},{\xi }_{1:k})=\prod _{i}p(m_i\mid z_{i:k},{\xi }_{1:k})$$

Since $m_i$ can either be $0$ (free) or $1$ (occupied), this is binary Bayes filter.