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Estimating the positions of sensor nodes is a fundamental and crucial problem in wireless sensor networks. In this paper, three novel subspace methods for node localization in a fully connected network are devised with the use of range measurements. Biases and mean square errors of the sensor node position estimates are also derived. Computer simulations are included to contrast the performance of the proposed algorithms with the conventional subspace positioning method, namely, classical multidimensional scaling, as well as Cramer-Rao lower bound.