Definition

In feature-based Mapping, we would like to estimate a set of discrete landmarks (or features) in the environment given sensor observations and robot motion. For some $N\in\mathbb{N}$, let $\mathbf{m} := \{\mathbf{m}_{i}\}^{N}_{i=1},\,\mathbf{m}_{i}\in\mathbb{R}^{d},i=1,\dots,N$ be the set of landmark locations. Then, the goal is to estimate $\mathbf{m}$, the set of landmark positions at time $t$, given our sensor observations $z_{[0,t]}$, and robot poses $x_{[0,t]}$. This can represented as a posterior: $$p(\mathbf{m} \mid z_{[0,t]},x_{[0,t]})$$