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We transform the 3D underwater sensor network (USN) localization problem into its 2D counterpart by employing sensor depth information and a simple projection technique. We first prove that a nondegenerative projection preserves network localizability. We then prove that given a network and a constant k, all of the geometric k-lateration localization methods are equivalent. Based on these results, we design a purely distributed bilateration localization scheme for 3D USNs termed as underwater sensor positioning (USP). Through extensive simulations, we show that USP has the following nice features: (1) improved localization capabilities over existing 3D methods, (2) low storage and computation requirements, (3) predictable and balanced communication overhead, and (4) robustness to errors from the underwater environment.