Precision Quaternion Estimation With Partially Norm-Constrained Unscented Kalman Filtering

Accurate orientation estimation is a key challenge in dynamics and control, particularly for rigid body motion. Quaternions are commonly used to represent rotations due to their computational efficiency, but they must always maintain a unit norm to function correctly. If this constraint is not enforced properly, it can lead to significant errors in orientation estimation. This article proposes an unscented Kalman filter that ensures the quaternion parameters, a subvector within the state vector, adhere to the unit norm constraint. The proposed method provides a closed-form solution without dividing the state vector into constrained and unconstrained vectors. In simulation studies under high-noise conditions, the filter demonstrates significantly improved performance compared to standard unscented and pseudo-unscented Kalman filters, enhancing accuracy during both transient and steady-state phases. These results highlight the importance of enforcing quaternion constraints to reduce mean square error and improve convergence.