Because i) Unscented Kalman Filters (UKFs) are composed by real algebra multiplications by scalar and additions, and ii) these operations are not closed under the set of unit quaternions, defining UKFs for unit quaternion systems is not straightforward. In this work, all the UKFs and Square-Root Unscented Kalman Filters (SRUKFs) for quaternion systems proposed in literature are studied in detail. First, we show that a considerable amount of these algorithms do not guarantee the quaternion norm to be unity at every step. Second, we propose two new algorithms, the Quaternionic Additive Unscented Kalman Filter (QuAdUKF), and a SRUKF variant of the QuAdUKF. The QuAdUKF is able to i) be particularized into new UKFs for quaternionic systems, and ii) to generalize all the UKFs for quaternionic systems of the literature preserving the unit quaternion norm at every step. The SRUKF variant of the QuAdUKF has better properties in comparison with all the SRUKFs for quaternion systems of the literature. Numerical simulations of spacecraft attitude filtering illustrates the theoretical results.