estimation. It formulates the pose estimation problem as a low-rank homogeneous system in which the solution lies on its one-dimensional (1D) null space. Outlier correspondences are those rows of the linear system that perturb the null space and are progressively detected by projecting them on an iteratively estimated solution of the null space. Although REPP$n$P is very fast and accurate, it suffers from a severe limitation that it cannot handle more than approximately $50\%$ of outliers.

In this paper, we propose a robust 1-point RANSAC-based P$n$P method named R1PP$n$P. We first present an optimal iterative process as the core P$n$P algorithm of R1PP$n$P. The core algorithm takes a random 3D-2D correspondence as the control point. To address outliers, we propose a soft weight assignment method according to reprojection errors to distinguish inliers and outliers, and integrate it into the core algorithm. The weight factors associated with outliers decrease significantly during the iteration to reduce the impact of outliers. Finally, we employ the 1-point RANSAC scheme to try different control points for the core P$n$P algorithm. By using this combination of the RANSAC scheme and the soft weight assignment, the algorithm is capable of eliminating outliers when the selected control point 