Range-Only Node Localization: The Arbitrary Anchor Case In D-Dimensions

This work is situated at the intersection of two large fields of research the Localization problem and applications in Wireless Networks. We are interested in providing good estimations for network node locations in a defined space based on sensor measurements. Many methods have being created for the localization problem, in special we have the classical Triangulation and Trilateration procedures and MultiDimensional Scaling. A more recent method, DILOC, utilizes barycentric coordinates in order to simplify part of the non-linearities inherent to this problem. Except for Triangulation in which we require angle measurements between nodes, the other cited methodologies require, typically only, range measurements. Off course, there exists variants which allow the use of range and angle measurements. We specialize our interest in range only methods utilizing barycentric coordinates by first providing a novel way to compute barycentric coordinates for any possible node-neighbor spatial configuration in any given dimension. Which, we use as basis for our experiments with averaging processes and the development of our centralized and distributed gradient descent algorithms. Our distributed algorithm is able to receive range measurements with noise of uncharacterized distributions as it inputs. Using simulations in Matlab, we provide comparisons of our algorithms with Matlab\u27s MDS function. Lastly, we show our efforts on providing a physical network implementation utilizing existing small form factor computers, wireless communication modules and range sensors