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This paper reports the analytical development and preliminary experimental evaluation of a class of exact nonlinear full state model-based observers for underwater vehicle navigation. This class of observers exploits exact knowledge of the vehicle's nonlinear dynamics, the forces and moments acting on the vehicle, and disparate position and velocity measurements. The reported observer is novel in that it estimates the full state of the vehicle and employs Lyapunov techniques to show stability. The performance of the observer is evaluated using data from single degree-of-freedom experiments with a laboratory remotely operated vehicle. High-precision measurements from a 300kHz long baseline (LBL) acoustic positioning systems serve as the basis for evaluating the performance of the observer. Error in the observer position estimate possesses a significantly lower standard deviation than measurements from 12kHz LBL systems alone. The performance of the observer is compared to the extended Kalman filter (EKF) and the error in the position estimates of these two estimators found to be comparable. These experiments are, to the best of our knowledge, the first report of the experimental implementation of exact nonlinear dynamic model-based observers and their comparison to EKFs for underwater vehicle navigation.