Considering the inertial measurement unit (IMU) faults risk of an unmanned aerial vehicle (UAV), this paper provides an analysis of the error overboundings of position estimation in a tightly coupled IMU/global navigation satellite system (GNSS) integrated architecture under the IMU fault conditions using an error-state EKF-based approach and provides a comparison to a recently published EKF-based full state method. Simulation results show that both the error overboundings of the error-state and full-state EKFs can fit the state error against the IMU faults, but the error-state EKF is more suitable for UAV navigation system integrity assurance due to its higher calculation effciency. This study will be extended to the integrity monitoring of multisensor systems.