Since the global positioning system (GPS) is not applicable underwater, source localization using wireless sensor networks (WSNs) is gaining popularity in oceanographic applications. Unlike terrestrial WSNs (TWSNs) which use electromagnetic signaling, underwater WSNs (UWSNs) require underwater acoustic (UWA) signaling. Received signal strength (RSS)-based source localization is considered in this paper due to its practical simplicity and the constraint of low-cost sensor devices, but this area received little attention so far because of the complicated UWA transmission loss (TL) phenomena. In this paper, we address this issue and propose two novel semidefinite programming (SDP) approaches which can be solved more efficiently. The numerical results validate our proposed SDP solvers in underwater environments, and indicate that the placement
of the anchor nodes influences the RSS-based localization accuracy similarly as in the terrestrial counterpart. We also highlight that adopting traditional terrestrial RSS-based localization methods will fail in underwater scenarios.