Time-varying, smooth trajectory estimation is of great interest to the vision
community for accurate and well behaving 3D systems. In this paper, we propose
a novel principal component local regression filter acting directly on the
Riemannian manifold of unit dual quaternions $\mathbb{D} \mathbb{H}_1$. We use
a numerically stable Lie algebra of the dual quaternions together with $\exp$
and $\log$ operators to locally linearize the 6D pose space. Unlike state of
the art path smoothing methods which either operate on $SO\left(3\right)$ of
rotation matrices or the hypersphere $\mathbb{H}_1$ of quaternions, we treat
the orientation and translation jointly on the dual quaternion quadric in the
7-dimensional real projective space $\mathbb{R}\mathbb{P}^7$. We provide an
outlier-robust IRLS algorithm for generic pose filtering exploiting this
manifold structure. Besides our theoretical analysis, our experiments on
synthetic and real data show the practical advantages of the manifold aware
filtering on pose tracking and smoothing.

本文提出了一种基于双四元数 Riemann 流形的新型主成分局部回归滤波器，并在 7 维实射影空间中，共同处理旋转和平移，利用此流形结构提供一种异常鲁棒的通用姿势过滤 IRLS 算法，从理论和实验上表明了该流形感知滤波对姿态跟踪和平滑处理的实际优势。