Markov Localization

A direct extension of the Bayes Filter, but using the map $m$ of the environment:

$Unknown environment 'algorithm'$

The initial belief reflects initial knowledge of the robot pose, and can be instantiated differently:

If the initial pose is known, $bel (x_{0})$ is a point-mass distribution such that:

$bel (x_{0}) = {\begin{cases} 1 & if x_{0} = {\bar{x}}_{0} 0 & otherwise \end{cases}$

However, point-mass distributions are discrete and do not have a density, so in most scenarios, a narrow Gaussian centered around ${\overset{―}{x}}_{0}$ is used instead.

If the initial pose is unknown, $bel (x_{0})$ is initialized with a uniform distribution over the space of all legal poses in the map.

Jethro's Braindump

Markov Localization

Markov Localization

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