  Accurate and robust global localization is essential to robotics
applications. We propose a novel global localization method that employs the
map traversability as a hidden observation. The resulting map-corrected
odometry localization is able to provide an accurate belief tensor of the robot
state. Our method can be used for blind robots in dark or highly reflective
areas. In contrast to odometry drift in long-term, our method using only
odometry and the map converges in longterm. Our method can also be integrated
with other sensors to boost the localization performance. The algorithm does
not have any initial state assumption and tracks all possible robot states at
all times. Therefore, our method is global and is robust in the event of
ambiguous observations. We parallel each step of our algorithm such that it can
be performed in real-time (up to ~ 300 Hz) using GPU. We validate our algorithm
in different publicly available floor-plans and show that it is able to
converge to the ground truth fast while being robust to ambiguities.
