Autonomous mobile robots have been widely studied not only as advanced facilities for industrial and daily life automation, but also as a testbed in robotics competitions for extending the frontier of current artificial intelligence. In many of such contests, the robot is supposed to navigate on the ground with a grid layout. Based on this observation, we present a localization error correction method by exploring the geometric feature of the tile patterns. On top of the classical inertia-based positioning, our approach employs three fiber-optic sensors that are assembled under the bottom of the robot, presenting an equilateral triangle layout. The sensor apparatus, together with the proposed supporting algorithm, are designed to detect a line's direction (vertical or horizontal) by monitoring the grid crossing events. As a result, the line coordinate information can be fused to rectify the cumulative localization deviation from inertia positioning. The proposed method is analyzed theoretically in terms of its error bound and also has been implemented and tested on a customary developed two-wheel autonomous mobile robot.