In this paper, we propose a new robot localization method for wireless sensor networks (WSNs). The proposed localization method, finite memory filtering based localization (FMFL), considers the refined measurement estimates pose of a mobile robot, unlike existing estimators that use an infinite impulse response (IIR) structure. We design an estimator to minimize the Frobenius norm of the gain matrices to give it high robustness. The method shows excellent performance in environments, where noise information is unknown and in which sudden disturbances are inserted. Moreover, even when the observation is temporarily impossible due to the non-line-of-sight (NLOS) situation or the temporary failure of sensors, the proposed localization scheme still ensures high robustness, unlike existing methods. The performance of the proposed method is experimentally compared with existing methods in a harsh environment.