A noise subspace approach for localization

Abstract

Wireless sensor networks are becoming increasingly popular due to their low cost and wide applicability to support a large number of diverse application areas. Localization of sensor nodes is a fundamental requirement that makes the sensor data meaningful. Energy and cost constraints only allow to equip a few nodes with a GPS device and to localize the remaining nodes with the help of these known locations and a pair-wise range measurements. Multidimensional scaling is an attractive localization technique due to a closed-form solution. It however requires pairwise measurements between all nodes to obtain the unknown node coordinates. In this thesis we investigate the feasibility of an analytical solution when some of the dissimilarity measurements are missing. We propose a least squares method to obtain unknown node positions by projecting the squared distance matrix onto the noise subspace of the weight matrix. We evaluate the proposed method for fully connected, and partially connected networks. We show that the proposed method determines the absolute node locations for a fully connected sensor network. For partially connected networks, though it is infeasible to obtain the global node locations using our method, yet we present scenarios where relative node locations can be obtained. }