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Mobile locationing using time difference of arrival (TDOA) measurements has received considerable attention over the last few years. The classical two-step approach consists of acquiring TDOA measurements followed by a separate computation of the mobile position. This approach suffers from issues such as high outlier probabilities in the TDOA measurement acquisition. The paper presents an approach to estimating the mobile's position in one single step, improving the performance of the classical approach. Numerical simulations show the gain in terms of outlier probability and positioning accuracy.