In this work, we present an aided inertial navigation system for an autonomous underwater vehicle (AUV) using an unscented Kalman filter on manifolds (UKF-M). The inertial navigation estimate is aided by a Doppler velocity log (DVL), depth sensor, acoustic range and, while on the surface, GPS. The sensor model for each navigation sensor on the AUV is explicitly described, including compensation for lever arm offsets between the IMU and each sensor. Additionally, an outlier rejection step is proposed to reject measurement outliers that would degrade navigation performance. The UKF-M for AUV navigation is implemented for real-time navigation on the Virginia Tech 690 AUV and validated in the field. Finally, by post-processing the navigation sensor data, we show experimentally that the UKF-M is able to converge to the correct heading in the presence of arbitrarily large initial heading error.