Indoor wireless localization via convex feasibility problem

Node localization in wireless sensor networks (WSNs) aims to determine unknown target position given anchors´ known positions and available relative pairwise measurements among directly-connected neighboring nodes. From this point of view, WSNs can be divided into two groups based on collaboration between targets: cooperative networks in which the measurements between the targets are also used for positioning procedure, and non-cooperative networks in which only measurements between pairs of anchor nodes and target nodes are utilized. Obtaining a good estimation of where targets are located at is critical in sensor network applications such as monitoring, geographic routing, and industrial manufacturing. Since the positions of the targets are unknown and only local distance information is given, we need to find true positions from these local distance measurements. Maximum likelihood estimation is one of the state-of-art method for this problem, which is non-convex and consumes much effort to solve. Moreover, the quality of obtained solution is highly dependent on the chosen search methods and the used initial points. In this paper, we formulate the non-cooperative sensor network localization as a convex feasibility problem where the unknown node belongs to a sufficient intersection set of a family of closed convex sets, then apply a projection method to find the solutions. This approach leads us to the use of different algorithm which is fast, robust and convergent. With an appropriate step-size sequence, estimated sensor locations will converge to the global optimal solution in a finite number of steps, as shown by the numerical results. The proposed approach has good stability, robustness and lower complexity, which is effective for the localization problems with small sensor size constraints.