A barycentric coordinate based approach to three-dimensional distributed localization for wireless sensor networks

This paper introduces a new range-based distributed localization algorithm for wireless sensor networks in the three-dimensional space. To overcome the difficulty in computing the barycentric coordinates of a node with respect to its neighbors in 3D, a new scheme is developed for this purpose by using the fact that a congruent framework of the subnetwork consisting of the node and its neighbors has the same barycentric coordinates. A multidimensional scaling (MDS) method is used to calculate the coordinates of the congruent framework, which can provide a solution for each subnetwork with not only exact range measurements but also noisy range measurements. Thus, a linear equation related to a signed Laplacian is obtained to describe the geometric constraints of the whole network. We then show a globally convergent and linear iterative algorithm called MDS-DILOC for each node to locate itself in the three-dimensional space by solving the linear equation. Simulation is carried out to demonstrate the validity of MDS-DILOC.