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.
Reliable navigation in GPS-denied environments remains a fundamental challenge in robotics, aerospace, and autonomous vehicle applications. This paper presents a Dual Quaternion-Based Unscented Kalman Filter (DQUKF) equipped with a Visual Inertial Odometry (VIO) algorithm for accurate state estimation enabling navigation in GPS denied locations. The proposed framework formulates the DQUKF in an error state manner, where the nominal pose is represented by a unit dual quaternion and the local pose error is represented by a 6-dimensional twistor parameterization used for sigma point generation, covariance propagation, and measurement correction. In parallel, the VIO algorithm tracks features across image frames, synchronizes measurements between the IMU and camera, and provides visual constraints that complement inertial propagation. Simulation results on the EuRoC MAV dataset show that the proposed DQUKF converges under high initialization uncertainty and achieves a position RMSE of 0.2584~m in the difficult flight sequence, outperforming the benchmark filters.
This paper addresses the problem of estimating the relative pose (position and orientation) and velocity of a vehicle with respect to a moving target, where both are equipped with Inertial Measurement Units (IMUs), assuming the availability of relative position or bearing measurements. The body-target relative dynamics are formulated on SE2(3) and recast into a linear time-varying (LTV) model in the ambient space R15, on which a deterministic Riccati observer is designed. We analyze the uniform observability (UO) conditions required to guarantee global exponential convergence of the estimation error in the ambient space for both measurement cases. In the case of relative position measurements, UO requires only a persistence-of-excitation condition on the target acceleration, whereas for bearing measurements, additional conditions are required. Building on this, a nonlinear complementary filter on SO(3) is designed to provide a smooth estimate of the orientation component of the state with almost global asymptotic stability. Finally, simulation results are provided to validate the proposed solution.
This paper introduces the ensemble directional Kalman filter (EnDKF), an ensemble-based Kalman filtering approach for pose tracking that jointly estimates an object's position and attitude using ideas from directional statistics. The EnDKF integrates a unit-quaternion attitude representation to move beyond canonical Kalman filter mean and covariance assumptions that poorly capture directional uncertainty. Experiments on a synthetic constant-velocity constant-angular-velocity system and a digital-twin head-tracking scenario using the FoundationPose algorithm demonstrate a significant reduction in error as opposed to merely using measurements.