Sparse recovery formulation for secure distance-based localization in the presence of cheating anchors

Secure localization in the presence of cheating anchors is a critical issue in wireless sensor networks, where compromised anchors attempt to falsify the measured distances in the location references. In this study, such misbehaviors of unfaithful anchors are modeled as unknown perturbations to the measured distances. By exploiting the sparsity of malicious anchors, the secure localization problem is formulated as a sparse signal recovery problem whose objective is to concurrently locate the sensors and identify the malicious anchors. Under the above formulation, the upper bound for the number of tolerable malicious anchors is obtained and the localization error bound is also provided. A gradient projection algorithm with variable step size is proposed to solve the sparse recovery problem. To further improve the localization accuracy, another modified gradient projection algorithm is presented. Simulation results show that the proposed algorithms can identify the unfaithful anchors with high probability and achieve good localization accuracy.