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We study the problem of three-dimensional localization of the underwater mobile sensor networks using only range measurements without GPS devices. This problem is challenging because sensor nodes often drift with unknown water currents. Consequently, the moving direction and speed of a sensor node cannot be predicted. Moreover, the motion devices of the sensor nodes are not accurate in underwater environments. Therefore, we propose an adaptive localization scheme, ProLo, taking these uncertainties into consideration. This scheme applies the rigidity theory and maintains a virtual rigid structure through projection. We have proved the correctness of this three-dimensional localization scheme and also validated it using simulation. The results demonstrate that ProLo is promising for real mobile underwater sensor networks with various noises and errors.