Network localization from range measurements: algorithms and numerical experiments

The problem of estimating node positions in sensor networks and multi agent formations has been extensively studied in the last decade for the purpose of enabling self-configurable and autonomous systems. A typical scenario involves the nodes to estimate their locations using relative measurements from neighbors. When full relative positions (coordinates or, equivalently, range and angle) between pairs of nodes are available, the problem reduces to linear estimation. Contrary, when distance-only (range) measurements are available, the localization problem is strongly NP-hard, and convergence of general-purpose optimization techniques can no longer be guaranteed. In the present paper we analyze three ad-hoc numerical techniques for solving the network localization problem under range-only measurements, namely an iterative Least-Squares algorithm, a Trust-Region method, and a Global Continuation method based on Gaussian smoothing. The global convergence properties of these techniques are then tested through numerical simulations.