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Terrain Relative Navigation (TRN) has the potential to enable drift-free, low-cost navigation for a wide range of underwater vehicles. Current underwater TRN systems have demonstrated meter-level navigation accuracy by utilizing high-accuracy inertial navigation systems in combination with both low and high quality sonar sensors and bathymetry maps. No studies, however, have considered the application of underwater TRN to vehicles with non-inertial-grade navigation systems, an extension which would greatly increase its applicability. The use of low-grade motion sensors in TRN is problematic due to the presence of large errors which can cause highly inaccurate alignment of successive sonar pings. To address this, a TRN filter is developed in which information present in the terrain correlations is used to help identify and mitigate large motion sensor errors. The resulting filter consists of a tight coupling between TRN and the onboard navigation, yielding a significantly improved navigation solution. The development of this TRN system is detailed for an AUV with an Attitude, Heading and Reference System (AHRS)-based dead reckoning navigation, which has an observed accuracy of 5 - 25% distance traveled. Field trials in Monterey Bay, CA demonstrate the ability of the TRN filter to acheive 5 - 10m navigational precision. Field trials are also presented demonstrating successful real-time, closed-loop TRN on the AUV. For these trials, the combined TRN/AHRS system enabled the vehicle to fly to a known beacon location with ability comparable to an acoustic homing system. The presented results demonstrate that TRN technology can successfully be applied to non-inertial-grade vehicle platforms, greatly improving the navigation capabilities of such systems.