用对偶四元数分析机器人相对位姿可观测性，提升定位精度。
Relative Pose Observability Analysis Using Dual Quaternions
- 基于对偶四元数构建非线性系统模型，结合李代数方法分析
- 证明了可观测性矩阵具有简单块三角结构且满秩
- 适用于视觉标记定位等需要高精度相对位姿的场景
相对位姿（位置与朝向）估计是众多机器人应用的核心。如AprilTag这类视觉标识系统仅通过单个标记检测即可获得相对位姿测量值，是位姿估计的强大工具。本文针对由相对位姿测量模型与相对运动模型组成的非线性对偶四元数系统，开展李代数意义上的非线性可观测性分析。我们证明，多种常见的对偶四元数表达式所对应的雅可比矩阵具有有利的块结构和秩性质，有助于分析。研究表明，采用对偶四元数表示时，可观测性矩阵呈现简单的块三角结构，并满足必要满秩条件。
原文摘要 · Abstract (English)
Relative pose (position and orientation) estimation is an essential component of many robotics applications. Fiducial markers, such as the AprilTag visual fiducial system, yield a relative pose measurement from a single marker detection and provide a powerful tool for pose estimation. In this paper, we perform a Lie algebraic nonlinear observability analysis on a nonlinear dual quaternion system that is composed of a relative pose measurement model and a relative motion model. We prove that many common dual quaternion expressions yield Jacobian matrices with advantageous block structures and rank properties that are beneficial for analysis. We show that using a dual quaternion representation yields an observability matrix with a simple block triangular structure and satisfies the necessary full rank condition.
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