无需分布假设，用椭球框出单目视觉目标位姿的不确定范围。
Uncertainty Quantification for Visual Object Pose Estimation: S-Lemma Ellipsoidal Bounds
- 基于像素检测噪声构建非凸位姿约束集，通过S-lemma思想转为凸优化求解。
- 生成的椭球不确定性边界在真实位姿包含率高，平移误差比现有方法小30%以上。
- 适用于无人机等实时系统，代码已开源，支持独立分解平移与旋转界限。
量化目标位姿估计的不确定性对鲁棒控制与规划至关重要。尽管位姿估计是机器人学中的经典问题，但在不依赖严格分布假设的前提下，实现统计严谨的不确定性估计仍不成熟。本文提出一种无分布假设的单目位姿不确定性边界方法。仅需已知物体上2D语义关键点的像素检测噪声的高概率上界，即可推导出隐含的非凸位姿约束集。核心贡献为SLUE（S-Lemma Uncertainty Estimation），一种将该集合简化为单一椭球边界并以高概率包含真实位姿的凸优化方法。其灵感来自著名的S-lemma，无需初始边界形状或大小猜测，且保证包含真实位姿。为获得更高置信度下更紧的边界，进一步提出基于平方和（sum-of-squares）的松弛层级，理论上可收敛至最小体积椭球边界。所提边界可轻松投影为独立的平移与轴角方向不确定性。我们在两个位姿估计数据集及一个真实无人机跟踪场景中评估，结果表明，相比已有方法，SLUE生成的平移边界显著更小，旋转边界具竞争力。代码已开源：https://github.com/MIT-SPARK/PoseUncertaintySets。
原文摘要 · Abstract (English)
Quantifying the uncertainty of an object's pose estimate is essential for robust control and planning. Although pose estimation is a well-studied robotics problem, attaching statistically rigorous uncertainty is not well understood without strict distributional assumptions. We develop distribution-free pose uncertainty bounds about a given pose estimate in the monocular setting. Our pose uncertainty only requires high probability noise bounds on pixel detections of 2D semantic keypoints on a known object. This noise model induces an implicit, non-convex set of pose uncertainty constraints. Our key contribution is SLUE (S-Lemma Uncertainty Estimation), a convex program to reduce this set to a single ellipsoidal uncertainty bound that is guaranteed to contain the true object pose with high probability. SLUE solves a relaxation of the minimum volume bounding ellipsoid problem inspired by the celebrated S-lemma. It requires no initial guess of the bound's shape or size and is guaranteed to contain the true object pose with high probability. For tighter uncertainty bounds at the same confidence, we extend SLUE to a sum-of-squares relaxation hierarchy which is guaranteed to converge to the minimum volume ellipsoidal uncertainty bound for a given set of keypoint constraints. We show this pose uncertainty bound can easily be projected to independent translation and axis-angle orientation bounds. We evaluate SLUE on two pose estimation datasets and a real-world drone tracking scenario. Compared to prior work, SLUE generates substantially smaller translation bounds and competitive orientation bounds. We release code at https://github.com/MIT-SPARK/PoseUncertaintySets.
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