Euclidean Distance Matrix Optimization for Sensor Network Localization *

Abstract

Sensor Network Localization (SNL) is a general framework that generates a set of embedding points in a low-dimensional space so as to preserve given distance information as much as possible. Typical applications include source localization in two or three dimensional space,molecular conformation in three dimensions, graph embedding and data visualization. There are three main difficulties in solving SNL:(i) low-dimensional embedding that gives rise to non-convexity of the problem,coupled with infinitely many local minima;(ii) a large number of lower and upper bounds for certain distances used to improve the embedding quality; and (iii) non-differentiability of some loss functions used to model SNL. There exist a few promising approaches including co-ordinates minimization and semi-definite programming. This survey mainly focus on a recently established approach: Euclidean Distance Matrix (EDM) Optimization. We will give a short but essential introduction how this approach is theoretically well-developed and demonstrate how EDM optimization nicely handles those difficulties through a few widely used loss functions. We also show how regularization terms can be naturally incorporated into EDM optimization. Numerical examples are used to demonstrate the potential of EDM optimization in tackling large scale problems and effect of regularizations.