This paper presents a vision-based indoor positioning system of a small robotic vehicle utilizing knowledge of the building floorplan. Using images taken by a monocular camera rigidly mounted onto the deck of the vehicle, the localization system obtains initial geometry of the environment and camera motion by running Structure from Motion. The localization system resolves the scale ambiguity present in the data by associating planar structures in the 3D point cloud with walls of the building. In order to extract the planes, we developed a Scale Invariant Planar RANSAC (SIPR) algorithm which handles situations of scale ambiguity in the point cloud data. Our Wall Plane Fusion algorithm forms correspondences between walls and computed planes, and the best such correspondence is used as an external constraint to the Bundle Adjustment algorithm which is run on the Structure from Motion data. A necessary condition for providing a global positioning solution is that one wall be in view. This paper provides results in both simulated and real-world scenarios.