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

arXiv: https://arxiv.org/abs/2605.02054 · HTML: https://mlsanity.com/paper/2605.02054/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 42 references that are in the map.
- First posted on arXiv 3 May 2026.

## Builds on (most cited first, 8 of 8)

- [Quaternion kinematics for the error-state Kalman filter](https://mlsanity.com/paper/1711.02508/) (2017)
- [An Efficient Algebraic Solution to the Perspective-Three-Point Problem](https://mlsanity.com/paper/1701.08237/) (2017)
- [On 'A Kalman Filter-Based Algorithm for IMU-Camera Calibration: Observability Analysis and Performance Evaluation'](https://mlsanity.com/paper/1311.4769/) (2013)
- [EKFPnP: Extended Kalman Filter for Camera Pose Estimation in a Sequence of Images](https://mlsanity.com/paper/1906.10324/) (2019)
- [Sensor Placement on a Cantilever Beam Using Observability Gramians](https://mlsanity.com/paper/2501.01726/) (2025)
- [Distributed Dual Quaternion Extended Kalman Filtering for Spacecraft Pose Estimation](https://mlsanity.com/paper/2411.19033/) (2024)
- [Relative Pose Observability Analysis Using Dual Quaternions](https://mlsanity.com/paper/2501.00657/) (2024)
- [Optimal Fiducial Marker Placement for Satellite Proximity Operations Using Observability Gramians](https://mlsanity.com/paper/2501.01704/) (2025)

## Abstract (arXiv)

This paper presents a dual quaternion framework for 6-DOF visual target tracking that addresses key limitations of perspective-n-point (PnP) 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 PnP solver. Results are broadly applicable to visual-inertial navigation, simultaneous localization and mapping, and PnP solver development.