Relative Pose Observability Analysis Using Dual Quaternions
Nicholas B. Andrews, Kristi A. Morgansen
TL;DR
The paper addresses local weak observability of a nonlinear relative pose system modeled with dual quaternions, using a single fiducial-marker measurement. It formulates a six-DOF relative-motion model and a relative pose measurement model in the dual-quaternion framework, then applies Lie-derivative based observability analysis to reveal a simple block-triangular observability structure. The main contributions are the first analytic nonlinear observability proof for a dual-quaternion system and the demonstration that a full-rank observability matrix can be achieved with a single marker, independent of the dynamics. This work provides a compact, efficient framework for relative navigation estimator design and informs practical implementation for satellite proximity operations and robotics where pose observability from relative measurements is critical.
Abstract
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.