In this paper a dynamic model based control scheme is proposed for the stabilization of an underactuated underwater vehicle, in the presence of slowly varying, unknown disturbances. An Unscented Kalman Filter (UKF), based on the vehicle's dynamic model, is applied for the sensor fusion process to provide an estimation of the full state vector of the system. External disturbances and unmodeled phenomena are included in the dynamic model as zero-mean Gaussian white noise processes. The estimation of the state vector is used as feedback for the proposed control scheme, which stabilizes the vehicle to the desired position and orientation. The proposed methodology is experimentally implemented using a 3-DOF underactuated vehicle. The efficiency of the methodology under various environmental conditions is demonstrated by simulation results. The overall system can be used for inspection tasks of sea platforms, e.g. during the inspection of a ship hull for possible damage tracking.