Localization of constituent nodes is of fundamental importance in many wireless sensor networks (WSNs) related applications. Existing research has mainly investigated the problem of localization in static WSNs, where the localization is performed mainly at the time of the node deployment. In contrast, it is important to keep track of the current locations of the nodes by invoking the localization algorithm periodically in mobile nodes. The high computation cost associated with most existing localization algorithms makes them less practical to use in resource constrained mobile sensor networks (MSNs). Additionally, these existing techniques often fail in hostile environments where some of the nodes may be compromised by adversaries, and used to transmit misleading information aimed at preventing accurate localization of the remaining sensors. In this paper, we build on our earlier work to propose an iterative gradient descent based technique with low computational complexity to securely localize nodes in MSNs. The proposed algorithm combines iterative gradient descent with selective pruning of inconsistent measurements to achieve a high localization accuracy. Simulation results demonstrate that the proposed algorithm can find a map of relative locations of the MSN even when some nodes are compromised and transmit false information.