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}