Spatial Geometry Theory-Based Algorithm for Accurate Positioning With Single Vision Beacon

Quick response (QR) code is one of the most popular beacons for indoor positioning. Existing QR code-based algorithms typically require several QR codes for precise positioning, which may need intense QR code deployment or have limited coverage. This paper proposes a visual positioning algorithm based on feature points and triangular structures on a QR code (V-FTQ), which can achieve precise position and orientation estimation using only a monocular camera and a single QR code beacon. In the considered system, a few QR codes are placed on the ceiling, and a user holds a camera in hand to capture the QR code for positioning. In particular, we first propose an efficient matching mechanism to match the feature points of the captured QR beacon to their projections in the image plane of the camera. Then, based on the geometry relations between the feature points and their projections, V-FTQ can calculate the coordinates of the feature points in the camera coordinate. Finally, the orientation and position of the user are estimated based on linear algebra and spatial geometry. Moreover, since V-FTQ may have a few ambiguous solutions, a singular solution elimination scheme is further proposed based on plane geometry and linear programming, which can effectively eliminate the incorrect solutions. Both simulation and experimental results demonstrate that V-FTQ can achieve a positioning accuracy within 10 cm with only one captured beacon, outperforming baseline algorithms in terms of precision and robustness to noise. Note to Practitioners—Existing positioning algorithms typically require multiple beacons for accurate positioning, which may limit its coverage or require dense beacon deployment. The paper proposes a novel positioning algorithm that achieves 3D orientation and position estimation with only a single beacon and a single camera. We applied the proposed method to the mobile phone and developed an APP for actual positioning tests. Experimental results verify that the positioning scheme reduces both the number of beacons required and the cost of the positioning system, making it suitable for the automatic navigation of robots and other applications in industrial automation.