Localization of distributed wireless sensor networks using Two Sage SDP optimization

In many applications of wireless sensor network (WSN), the location of sensors is a necessity to evaluate the sensed data and it is not energy and cost efficient to equip all sensors with global positioning systems. In WSN localization, some sensors (called anchors) are aware of their location. Then, the distance measurements between sensors and anchors are used to localize the whole network. WSN localization is a non-convex optimization, however, relaxation techniques such as semi-definite programming (SDP) are used to relax the optimization. To solve this problem, all constraints should be considered simultaneously and the solution complexity order is O n2 where n is the number of sensors. The complexity of SDP prevents solving large size problems. Therefore, it is necessary to reduce the problem size in large and distributed WSNs. In this paper, we propose a two stage optimization to reduce the solution time, while provide better accuracy compared with original SDP method. We first select some sensors that have the maximum connection with anchors and perform the localization. Then, we select some of these sensors as virtual anchors. By adding the virtual anchors, we decrease the number of constraints. We propose an algorithm to select virtual anchors so that the total solution complexity and time decrease considerably, while improving the localization accuracy.