Unscented and square‐root unscented Kalman filters for quaternionic systems

Summary Proper construction of an unscented Kalman filter (UKF) for unit quaternionic systems is not straightforward due to the incompatibility between the algebraic properties of the unit quaternions and the common real vector space operations (additions and scalar multiplications) needed in the steps of a filter algorithm. This work studies, in detail, all UKFs and square‐root UKFs for quaternionic systems proposed in the literature. First, we classify the algorithms according to the preservation of the unity norm of the quaternion variables. Second, we propose two new algorithms: the quaternionic additive unscented Kalman filter (QuAdUKF) and a square‐root variant of it. The QuAdUKF encompasses all known UKFs for quaternionic systems of the literature preserving, in all steps, the norm of the unit quaternion variables. Besides, it can also yield new UKFs with this norm preservation property. The QuAdUKF's square‐root variant has better properties in comparison with all the square‐root UKFs for quaternionic systems of the literature. Numerical experiments for a spacecraft attitude estimation problem illustrate the theoretical results.