Observability Conditions and Filter Design for Visual Pose Estimation via Dual Quaternions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910187689869312 |
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| author | Andrews, Nicholas B. Morgansen, Kristi A. |
| author_facet | Andrews, Nicholas B. Morgansen, Kristi A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02054 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Observability Conditions and Filter Design for Visual Pose Estimation via Dual Quaternions Andrews, Nicholas B. Morgansen, Kristi A. Systems and Control Computer Vision and Pattern Recognition Robotics 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. |
| title | Observability Conditions and Filter Design for Visual Pose Estimation via Dual Quaternions |
| topic | Systems and Control Computer Vision and Pattern Recognition Robotics |
| url | https://arxiv.org/abs/2605.02054 |