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In this paper, we propose new approaches based on convex optimization to address the received signal strength (RSS)-based noncooperative and cooperative localization problems in wireless sensor networks (WSNs). By using an array of passive anchor nodes, we collect the noisy RSS measurements from radiating source nodes in WSNs, which we use to estimate the source positions. We derive the maximum likelihood (ML) estimator, since the ML-based solutions have particular importance due to their asymptotically optimal performance. However, the ML estimator requires the minimization of a nonconvex objective function that may have multiple local optima, thus making the search for the globally optimal solution hard. To overcome this difficulty, we derive a new nonconvex estimator, which tightly approximates the ML estimator for small noise. Then, the new estimator is relaxed by applying efficient convex …