In this paper, the problem of target localization in the presence of outlying sensors is tackled. This problem is important in practice because in many real-world applications the sensors might report irrelevant data unintentionally or maliciously. The problem is formulated by applying robust statistics techniques on squared range measurements and two different approaches to solve the problem are proposed. The first approach is computationally efficient; however, only the objective convergence is guaranteed theoretically. On the other hand, the whole-sequence convergence of the second approach is established. To enjoy the benefit of both approaches, they are integrated to develop a hybrid algorithm that offers computational efficiency and theoretical guarantees. The algorithms are evaluated for different simulated and real-world scenarios. The numerical results show that the proposed methods meet the Cr'amer-Rao lower bound (CRLB) for a sufficiently large number of measurements. When the number of the measurements is small, the proposed position estimator does not achieve CRLB though it still outperforms several existing localization methods.