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PnP problem is well researched in many fields, such as computer vision. It is considered the fundamental method to solve the key problems of robot SLAM. However, in pedestrian visual localization, uncalibrated PnP (UPnP), specifically PnP with unknown focal length (PnPf) is more suitable for solving the problem. Recently, a few researchers proposed some methods to alleviate this problem. However, the localization accuracy of the existing methods is not satisfied when image pixel noise is larger. In other words, RANSAC should be running before solving the PnPf problem to get less noisy input, which means the localization delay increases inevitably. In this paper, we propose a more robust method for solving the PnPf problem without the help of RANSAC based on Gro&#x0308;bner basis and convex optimization. We build a Gro&#x0308;bner basis solver on the offline stage with one instance in the prime field. Then, we substitute the coefficients with real value and find multiple solutions on the online stage. Finally, we construct a convex optimization program to seek the final robust solution to PnPf problem. The other purpose of this paper is to provide a second-level localization experience for the end-user. The simulation result shows that our method can give a localization solution, which is more reliable than benchmark methods by both synthetic and real data verified.

A Robust Visual Localization Method With Unknown Focal Length Camera