Underwater unmanned vehicles are complementary with human presence and manned vehicles for deeper and more complex environments. An autonomous underwater vechicle (AUV) has automation and long-range capacity compared to a cable-guided remotely operated vehicle (ROV). Navigation of AUVs is challenging due to the high absorption of radio-frequency signals underwater and the absence of a global navigation satellite system (GNSS). As a result, most navigation algorithms rely on inertial and acoustic signals; precise localization is then costly in addition to being independent from acoustic data communication. The purpose of this paper is to propose and analyze the performance of a novel low-cost simultaneous communication and localization algorithm. The considered scenario consists of an AUV that acoustically sends sensor or status data to a single fixed beacon. By estimating the Doppler shift and the range from this data exchange, the algorithm can provide a location estimate of the AUV. Using a robust state estimator, we analyze the algorithm over a survey path used for AUV mission planning both in numerical simulations and at-sea experiments.