sQPEP: Global Optimal Solutions to Scaled Quadratic Pose Estimation Problems

State estimation encounters significant hurdles in scale ambiguity, both when assimilating data from scale-uninformed sources such as Structure from Motion (SfM) and when handling normalized point clouds, each scenario demanding robust solutions to achieve consistent scale and accurate estimation. Addressing this critical issue, we propose the Scaled Quadratic Pose Estimation Problem (sQPEP), a novel unified framework designed to enhance scale estimation in various state estimation algorithms. Our framework not only establishes a globally optimal solution strategy for the precise estimation of pose and scale factors but also systematically categorizes a broad spectrum of pose estimation challenges. This is crucial for advancing our theoretical understanding and the practical application of these solutions. The sQPEP framework consolidates a range of scale and pose estimation challenges into a unified theoretical paradigm, thereby refining the methodology for these estimations. By applying algebraic techniques, we have effectively bifurcated the problem into two distinct categories. Subsequently, we have deduced globally optimal solutions and unveiled two robust solvers. These solvers are proficient in generating 80 and 81 solutions for their respective problem classes, featuring elimination template dimensions of 664×744 and 521×602. Our method's efficacy has been rigorously confirmed through experimental validation, which demonstrates its consistent performance in degenerate conditions and its superior noise immunity. These results bolster the framework's applicability to intricate scenarios encountered in real-world settings. © 2025 IEEE.