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This paper reports the development and experimental evaluation of a state-of-the-art model-aided inertial navigation system (MA-INS) for underwater vehicles. Together with real-time sea current estimation, the output from an experimentally validated kinetic vehicle model is integrated in the navigation system to provide velocity aiding for the INS. Additional aiding sources include ultrashort base line (USBL) acoustic positioning, pressure readings, and measurements from a Doppler velocity log (DVL) with bottom track. The performance of the MA-INS is evaluated on data from a field-deployed autonomous underwater vehicle (AUV). Several scenarios are examined, including removal or dropouts of USBL and DVL. The presented results verify that with merely an addition of software and no added instrumentation, it is possible to significantly improve the precision and robustness of an INS by utilizing the physical insight provided by a kinetic vehicle model. To the best of our knowledge, this paper reports the first experimental evaluation and practical application of a MA-INS for underwater vehicle navigation. The proposed approach improves underwater navigation capabilities both for systems lacking conventional velocity measurements, and for systems where the need for redundancy and integrity is important, e.g., during sensor dropouts or failures, or in case of emergency navigation. The MA-INS also represents a feasible step toward the solution to several prospective challenges in underwater navigation, including improved navigation in the midwater zone and increased level of autonomy and robustness.