A two-stage fastmap-MDS approach for node localization in sensor networks

Given a set of pairwise distance estimates between nodes, it is often of interest to generate a map of node locations. This is an old problem that has attracted renewed interest in the signal processing community, due to the recent emergence of wireless sensor networks and ad-hoc networks. Sensor maps are useful for estimating the spatial distribution of measured phenomena, as well as for routing purposes. Both centralized and decentralized solutions have been developed, along with ways to cope with missing data, accounting for the reliability of individual measurements, etc. We revisit the basic version of the problem, and propose a two-stage algorithm that combines algebraic initialization and gradient descent. In particular, we borrow an algebraic solution from the database literature and adapt it to the sensor network context, using a specific choice of anchor/pivot nodes. The resulting estimates are fed to gradient descent iteration. The overall algorithm offers better performance at lower complexity than existing centralized full-connectivity solutions. Also, its performance is relatively close to the corresponding Cramer-Rao bound, especially for small values of range error variance.