# Markov and Gaussian Localization

## Mobile Robot Localization: Markov and Gaussian

Mobile robot localilzation is the problem of determining the pose of a robot relative to a given map of the environment. It is also refered to as position estimation.

### Markov Localization

Probabilistic localization algorithms are variants of the Bayes filter. Markov localization is just a different name for the Bayes filter applied to the mobile robot localization problem.

    \begin{algorithm}
\caption{Markov localization}
\begin{algorithmic}
\PROCEDURE{MarkovLocalization}{$bel(x_{t-1}), u_t, z_t, m$}
\FORALL{$x_t$}
\STATE $\bar{bel}(x_t) = \int p(x_t | u_t, x_{t-1}, m) bel(x_{t-1}) \,d x_{t-1}$
\STATE $bel(x_t) = \eta p(z_t | x_t, m) \bar{bel}(x_t)$
\ENDFOR
\RETURN $bel(x_t)$
\ENDPROCEDURE
\end{algorithmic}
\end{algorithm}