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State estimation methods allow the vehicle position and velocity to be reconstructed by combining information from sensors and vehicle model. From a security point of view, position and velocity have to be known with a high level of confidence in order, for example, to avoid vehicle collision. In this paper, a confidence interval observer is developed to enclose positioning variables with some confidence degree (or integrity level). For this purpose, the algorithm is divided in two parts. First, a predictor, based on the vehicle dynamics, is derived to estimate bounds on state variables with lower bounded integrity. Then, at each measurement time, confidence intervals from the sensors are combined with union and intersection operations to satisfy the integrity level. The shortest non-empty intervals are chosen among the safe intervals. Finally, to quantify the reliability of estimation, a security measure is defined by the probability of having one faulty estimation in some period of time and is related to the integrity level objective. This method is illustrated with simulation tests based on an autonomous underwater vehicle described by a nonlinear model.