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This paper describes an algorithm for distributed acoustic navigation for Autonomous Underwater Vehicles (AUVs). Whereas typical AUV navigation systems utilize pre-calibrated arrays of static transponders, our work seeks to create a fully mobile network of AUVs that perform acoustic ranging and data exchange with one another to achieve cooperative positioning for extended duration missions over large areas. The algorithm enumerates possible solutions for the AUV trajectory based on dead-reckoning and range-only measurements provided by acoustic modems that are mounted on each vehicle, and chooses the trajectory via minimization of a cost function based on these constraints. The resulting algorithm is computationally efficient, meets the strict bandwidth requirements of available AUV modems, and has potential to scale well to networks of large numbers of vehicles. The method has undergone extensive experimentation, and results from three different scenarios are reported in this paper, each of which utilizes MIT SCOUT Autonomous Surface Craft (ASC) as convenient platforms for testing. In the first experiment, we utilize three ASCs, each equipped with a Woods Hole acoustic modem, as surrogates for AUVs. In this scenario, two ASCs serve as Communication/Navigation Aids (CNAs) for a third ASC that computes its position based exclusively on GPS positions of the CNAs and acoustic range measurements between platforms. In the second scenario, an undersea glider is used in conjunction with two ASCs serving as CNAs. Finally, in the third experiment, a Bluefin12 AUV serves as the target vehicle. All three experiments demonstrate the successful operation of the technique with real ocean data.