N-Dimensional Distributed Network Localization with Noisy Range Measurements and Arbitrary Anchor Placement

This work presents a distributed algorithm for node localization problems in static sensor networks in n- dimensions. We focus on networks in which n + 1 nodes with known locations (anchors) are arbitrarily placed among all other nodes with unknown locations. In the noiseless case, barycentric coordinates computed from range measurements are used to transform the non-convex node localization problem into a standard linear system of equations. Meanwhile, adding independent zero mean Gaussian noise to range measurements turns all barycentric coordinates to dependent random variables with no known standard distribution which may not even be identically distributed. Relying on online optimization methods, we provide a distributed online gradient descent algorithm to solve the noisy range-only localization problem. Finally, comparisons among simple barycentric coordinate averaging, a centralized gradient descent formulation and our distributed algorithm are provided.