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

2026-05-03

AI Summary

This work proposes a dual quaternion-based 6-degree-of-freedom visual object tracking framework to address the sensitivity of conventional P$n$P methods to noise and outliers, as well as their difficulty in handling missing observations. By analyzing system observability through Lie algebra, the approach introduces a measurement model based on unit vectors and relative positions, and uniquely integrates Lie group unscented Kalman filtering with dual quaternions to achieve robust state estimation. The method provides a control-theoretic interpretation of the collinearity-induced degeneracy in P3P and is applicable to non-cooperative, non-smooth motion scenarios. Simulations demonstrate significant improvements over existing P$n$P solvers in both pose accuracy and robustness under occlusion, highlighting its suitability for applications such as visual-inertial navigation and SLAM.

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.

Problem

• visual pose estimation
• PnP solvers
• observability
• measurement dropouts
• noise sensitivity

Innovation

• dual quaternions
• observability analysis
• Lie group unscented Kalman filter
• visual pose estimation
• PnP solvers