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An unmanned aerial vehicle (UAV) is tasked to explore an unknown environment and to map the features it finds, but must do so without the use of infrastructure-based localisation systems such as GPS, or any a priori terrain data. The UAV navigates using a statistical estimation technique known as simultaneous localisation and mapping (SLAM) which allows for the simultaneous estimation of the location of the UAV as well as the location of the features it sees. SLAM offers a unique approach to vehicle localisation with potential applications including planetary exploration, or when GPS is denied (for example under intentional GPS jamming, or applications where GPS signals cannot be reached), but more importantly can be used to augment already existing systems to improve robustness to navigation failure. One key requirement for SLAM to work is that it must reobserve features, and this has two effects: firstly, the improvement of the location estimate of the feature; and secondly, the improvement of the location estimate of the platform because of the statistical correlations that link the platform to the feature. So our UAV has two options; should it explore more unknown terrain to find new features, or should it revisit known features to improve localisation quality. These options are instantiated into the online path planner for the UAV. We present the SLAM algorithm and evaluate two important properties about the algorithm which assist in developing a path planning module for the UAV. The first of these is the use of the probabilistic measure of "entropy" as an information-based measure of the certainty in the map and vehicle locations, and is used as a utility function for planning the UAVs trajectory and determining the order in which features in the map are observed. The second is an observability analysis of SLAM which presents the unobservable states which are dependent on vehicle maneuvers. The analysis dictates the type of manoeuvres required by the UAV while- - observing features in order to maintain accurate statistical estimates of the map and vehicle location. This has the effect of reducing the action space that the path planner needs to search over. Using these two properties, we demonstrate an online path planner that intelligently plans the vehicle's trajectory while exploring unknown terrain in order to maximise the quality of both the map and vehicle location. Results of the online path planning algorithm are presented using a 6-DoF simulator of our UAV. The results show that the vehicle localisation errors are constrained and that the number of features and the size of the map steadily grows during the flight.