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We consider cooperative positioning using acoustic range measurements for underwater sensor networks, including networks formed by autonomous unmanned underwater vehicles (UUVs). Severe multipath scattering from the seabed and ocean surface can result in inaccurate range measurements. In an inhomogeneous medium, such as sea water, the direct path is not necessarily the strongest path or the first arrival. Hence, the range measurements based on the first or strongest arrival could be significantly biased. We introduce herein a new centralized cooperative positioning algorithm, referred to as the weighted Gerchberg-Saxton algorithm (WGSA), for underwater sensor networks. We assume that for each acoustic ranging channel, multiple range measurements corresponding to several propagation paths, one of which is the direct path, are available for cooperative positioning. Since it is unknown a priori which path is the direct path, we must identify it first. We show that WGSA can be used to automatically identify the direct path. We also show using numerical examples that WGSA is an effective and efficient approach to cooperative positioning in underwater sensor networks.