Localization is crucial to many applications in wireless sensor networks. In this article, we propose a range-free anchorbased localization algorithm for mobile wireless sensor networks that builds upon the Monte Carlo localization algorithm. We concentrate on improving the localization accuracy and efficiency by making better use of the information a sensor node gathers and by drawing the necessary location samples faster. To do so, we constrain the area from which samples are drawn by building a box that covers the region where anchors' radio ranges overlap. This box is the region of the deployment area where the sensor node is localized. Simulation results show that localization accuracy is improved by a minimum of 4% and by a maximum of 73% (average 30%), for varying node speeds when considering nodes with knowledge of at least three anchors. The coverage is also strongly affected by speed and its improvement ranges from 3% to 55% (average 22%). Finally, the processing time i...