This paper proposes a discrete-time linear parameter varying (LPV) unknown input observer (UIO) for the diagnosis of actuator faults and ice accretion in unmanned aerial vehicles (UAVs). The proposed approach, which is suited to an implementation on-board, exploits a complete 6-degrees of freedom (DOF) UAV model, which includes the coupled longitudinal/lateral dynamics and the impact of icing. The LPV formulation has the advantage of allowing the icing diagnosis scheme to be consistent with a wide range of operating conditions. The developed theory is supported by simulations illustrating the diagnosis of actuator faults and icing in a small UAV. The obtained results validate the effectiveness of the proposed approach. Keywords Unknown input observers (UIOs) • Linear parameter varying (LPV) systems • Icing diagnosis • Fault diagnosis • Unmanned aerial vehicles (UAVs) This work has been supported by the Research Council of Norway through the Centres of Excellence funding scheme (ref. 223254-AMOS). Damiano Rotondo is also supported by the ERCIM Alain Bensoussan Fellowship programme. This work has also been partially funded by the Spanish Government (MINECO) and FEDER through the project CICYT HARCRICS (ref. DPI2014-58104-R).