Trustworthy Target Localization via ADMM in the Presence of Malicious Nodes

Similar to numerous problems that gain interest nowadays (like the ones arising in statistics and machine learning), target localization problem can be cast in the framework of convex optimization. Nevertheless, owing to recent eruption in both size and heterogeneity of modern wireless networks which exposes them to various security threats, it is increasingly important to be able to localize the target reliably (securely). On the one hand, the security feature precludes the direct use of most existing localization algorithms in modern networks, since these are vulnerable to malicious attacks (for instance, measurement spoofing). On the other hand, taking security menace into consideration often leads to an under-determined problem formulation which requires certain approximations/relaxations of the problem, resulting in insufficiently accurate solutions. This work argues that the alternating direction method of multipliers (ADMM) is a well tailored approach to combat the secure localization problem. The proposed solution is a decomposition-coordination scheme, where solutions to smaller local (sub-) problems are bound together to obtain a solution to a larger global problem. To this end, an equivalent reformulation of the (non-convex) maximum likelihood estimator (MLE) as a smooth constrained non-convex minimization problem is derived first, which gives rise to a simple iterative scheme that does not require further approximations nor convex relaxations. The performance of the proposed algorithm is corroborated through computer simulations and experimental measurements.