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Sensor networks are highly susceptible to errors and malicious attacks. A host of nefarious attacks are targeted at preventing nodes from discovering their correct positions. In this work, we present a novel framework for position estimation in presence of malicious attacks on distance measurements of sensor networks. Additionally, we propose a practical randomized algorithm in the framework, which efficiently detects and rejects the corrupted measurements. The algorithm searches for an agreeable solution starting from randomly sampled minimal subsets of data; it subsequently enhances its estimate by augmenting consistent data points to the best random sample. The performance of the proposed algorithm is evaluated and compared to state-of-the-art robust positioning algorithms, both for independent and colluding attackers. While our method performs the same or better compared with the other algorithms on independent attacks, it is significantly more robust against collusion attacks, in terms of both the position estimation error and attack diagnosis and isolation. Moreover, the algorithm has a shorter runtime due to its randomized nature.