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.
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