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We report a decentralized extended information filter (DEIF) algorithm designed for single-beacon cooperative acoustic navigation of one or more client underwater vehicles. In single-beacon cooperative acoustic navigation, ranges and state information from a single reference source (the server) are used to improve localization and navigation of an underwater vehicle (the client). The ranges and state information are obtained using underwater acoustic modems and a synchronous-clock time-of-flight paradigm. Apart from the server's acoustic data broadcasts, the client has no access to the server's position or sensor measurements. We show that at the instance of each range measurement update, the DEIF algorithm yields identical results for the current vehicle state estimate as the corresponding centralized extended information filter (CEIF), which fully tracks the joint probability distribution between the server and client. We compare the state estimation results of the DEIF algorithm with that of a CEIF and three other filters reported in the literature. The evaluation is performed using both simulated data and an experimental dataset comprised of one surface craft and two autonomous underwater vehicles.