Recently there has been increasing engineering activity in the deployment of Autonomous Underwater Vehicles (AUVs). Different types of AUVs are being used for applications ranging from ocean exploration to coastal tactical surveillance. These AUVs generally follow a predictable trajectory specified by the mission requirements. Inaccuracies in models for deriving position estimates and the drift caused by ocean currents, however, lead to uncertainty when estimating an AUV’s position. In this article, two forms of position uncertainty – internal and external – are studied, which are the position uncertainty associated with a particular AUV as seen by itself and that as seen by others, respectively. Then, a statistical model to estimate the internal uncertainty for a general AUV is proposed. Based on this model, a novel mathematical framework using Unscented Kalman Filtering is developed to estimate the external uncertainty. Finally, the benefits of this framework for several location-sensitive applications are shown via emulations.