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Recently, ocean exploration has increased considerably through the use of autonomous underwater vehicles (AUV). A key enabling technology is the precision of the AUV navigation capability. In this paper, we focus on understanding the limitation of the AUV navigation system. That is, what are the observable error-states for different maneuvering types of the AUV? Since analyzing the performance of an underwater navigation system is highly complex, to answer the above question, current approaches use simulations. This, of course, limits the conclusions to the emulated type of vehicle used and to the simulation setup. For this reason, we take a different approach and analyze the system observability for different types of vehicle dynamics by finding the set of observable and unobservable states. To that end, we apply the observability Gramian approach, previously used only for terrestrial applications. We demonstrate our analysis for an underwater inertial navigation system aided by a Doppler velocity logger or by a pressure sensor. The result is a first prediction of the performance of an AUV standing, rotating at a position and turning at a constant speed. Our conclusions of the observable and unobservable navigation error states for different dynamics are supported by extensive numerical simulation. [ABSTRACT FROM AUTHOR]