Maximum entropy-based semi-definite programming for wireless sensor network localization

Localization in wireless sensor networks means determination of sensor nodes coordination, and this can be done using the known positions of some other nodes (called anchors) and given distance measurements. Practically, these distance measurements may be corrupted by noise and this may cause errors in estimating the nodes' locations. In addition, when some connections do not have line-of-sight (LOS) links, localization accuracy degrades significantly. Furthermore, in some cases, there is an uncertainty in anchor position and this degrades the accuracy of the localization. In this paper, we propose a new class of convex relaxations for wireless sensor network localization based on the principle of maximum entropy for both LOS and non-LOS environments. Moreover, unlike maximum likelihood (ML) formulation, this class is independent from noise probability density function. In this paper, we propose a localization method in the presence of anchor position uncertainty which is independent from knowing the covariance of uncertainty in anchor positions, while in the ML-based approaches, knowing the covariance matrix is necessary. Simulation results confirm that the proposed convex relaxations can provide more accuracy in comparison with ML-based semidefinite programming methods.