Large Scale Sensor Network Localization

There have been wide application of sensor network localization techniques in wireless network, environmental monitoring, Global Positioning System (GPS), habitant monitoring and so on. The essential techniques include Multidimensional Scaling (MDS), Semidefinite (Conic) Programming (SDP) and their variants. When we are given the information about the pairwise dissimilarity measures (for example, Euclidean distances), MDS provides very efficient algorithm for reconstruction of the sensor locations up to rotation and reflection, even for large scale problems. When the dissimilarity matrix is very sparse and has low dimension, traditional SDP provides an efficient solution. However, for large scale problems with sparse dissimilarity measures, SDP usually slow down dramatically and do not have any practical value. This paper discusses the mathematical formulation of sensor network localization and the related problems and provides an efficient large scale solution under the assumption that the number of anchors is large enough and the anchors is evenly distributed in the whole graph. We also provide several simulation studies to support our proposed method.