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

• URL: http://arxiv.org/abs/2605.02054v1
• Date: Sun, 03 May 2026 20:59:58 GMT
• Title: Observability Conditions and Filter Design for Visual Pose Estimation via Dual Quaternions
• Abstract summary: This paper presents a dual quaternion framework for 6-DOF visual target tracking.<n>It addresses key limitations of perspective-n-point (P$n$P) solvers: sensitivity to noise and outliers, and inability to propagate estimates.<n>Results are broadly applicable to visual-inertial navigation, simultaneous localization and mapping, and P$n$P solver development.
• Score: 1.9336815376402718
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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