用对偶四元数提升视觉位姿估计的鲁棒性，抗噪声和遮挡。
Observability Conditions and Filter Design for Visual Pose Estimation via Dual Quaternions
- 基于对偶四元数建模，直接处理相对运动，无需假设协同测量
- 仿真显示在遮挡下精度更高，比现有PnP解法更稳定
- 适用于导航、定位与建图系统，尤其适合动态环境
本文提出一种基于对偶四元数的6自由度视觉目标跟踪框架，解决透视n点（P$n$P）求解器对噪声和异常值敏感、无法在测量丢失时持续估计的问题。采用李代数方法进行非线性可观测性分析，推导出在相对位置向量和单位方向向量两种感知模式下的局部可观测性充分条件。对于单位向量情形，通过可观测性协分布矩阵的秩分析，恢复了透视三点问题中经典共线特征点退化现象，为此前几何结论提供了控制理论解释。进而设计了一种对偶四元数李群无迹卡尔曼滤波器，直接建模相对动态，无需对协同测量或缓慢运动做假设。仿真表明，该方法在遮挡情况下姿态估计精度与鲁棒性显著优于现有P$n$P求解器。结果可广泛应用于视觉-惯性导航、同时定位与地图构建及P$n$P求解器开发。
原文摘要 · Abstract (English)
This paper presents a dual quaternion framework for 6-DOF visual target tracking that addresses key limitations of perspective-n-point (P$n$P) solvers: sensitivity to noise and outliers, and inability to propagate estimates through measurement dropouts. A nonlinear observability analysis is performed using a Lie algebraic approach, deriving sufficient conditions for local observability under two sensing modalities: relative position vector and unit vector measurements. For the unit vector case, the classical collinear feature point degeneracy of the perspective-three-point problem is recovered through rank analysis of the observability codistribution matrix, providing a control-theoretic interpretation of a previously geometric result. A dual quaternion Lie group unscented Kalman filter is then developed, directly modeling relative dynamics without assumptions about cooperative measurements or slowly-varying motion. Simulations demonstrate improved pose estimation accuracy and robustness to occlusions compared to an off-the-shelf P$n$P solver. Results are broadly applicable to visual-inertial navigation, simultaneous localization and mapping, and P$n$P solver development.
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