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Localization is a crucial service for various applications in wireless sensor networks (WSNs). Although most researches assume stationary nodes, sensor mobility can enrich the application scenarios. Existing dynamic localization approaches require high seed density or incur a large communication overhead. In order to address these problems, we propose an efficient rang-free localization algorithm, EUL, which utilizes the relationship between neighboring nodes to estimate their possible location boundaries. Our algorithm not only allows all the nodes to remain static or move freely but also reduces the dependence on seeds, which achieves a uniform energy distribution to address the excessive energy drain around seeds and lengthen the network lifetime. We have evaluated EUL together with other major dynamic localization approaches. Simulation results show that EUL outperforms existing approaches in terms of accuracy under many different mobility conditions.