# Relative Pose Observability Analysis Using Dual Quaternions

arXiv: https://arxiv.org/abs/2501.00657 · HTML: https://mlsanity.com/paper/2501.00657/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Dec 2024.

## Built on by (most cited first, 1 of 1)

- [Observability Conditions and Filter Design for Visual Pose Estimation via Dual Quaternions](https://mlsanity.com/paper/2605.02054/) (2026)

## Abstract (arXiv)

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.