Convex Position Estimation in Wireless Sensor Networks

A method for estimating unknown node positions in a sensor network based exclusively on connectivity-induced constraints is described. Known peer-to-peer communication in the network is modeled as a set of geometric constraints on the node positions. The global solution of a feasibility problem for these constraints yields estimates for the unknown positions of the nodes in the network. Providing that the constraints are tight enough, simulation illustrates that this estimate becomes close to the actual node positions. Additionally, a method for placing rectangular bounds around the possible positions for all unknown nodes in the network is given. The area of the bounding rectangles decreases as additional or tighter constraints are included in the problem. Specific models are suggested and simulated for isotropic and directional communication, representative of broadcast-based and optical transmission respectively, though the methods presented are not limited to these simple cases.