Observability Conditions and Filter Design for Visual Pose Estimation via Dual Quaternions

TL;DR

This paper introduces a dual quaternion framework and observability analysis for 6-DOF visual pose estimation, improving robustness and accuracy over traditional methods, and develops a Kalman filter for better state estimation.

Contribution

It provides a novel dual quaternion-based approach with a Lie algebraic observability analysis and a Kalman filter that handles measurement dropouts and noise effectively.

Findings

Enhanced pose estimation accuracy in simulations.

Improved robustness to occlusions and measurement noise.

Theoretical conditions for local observability under different sensing modalities.

Abstract

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.