One-sentence summary

A novel scheme to use angle measurements between pairs of devices, exploiting trigonometric properties of inner angles to first denoise a measurement set, followed by a simple triangulation scheme for point reconstruction.

Abstract

Localization of a set of nodes is an important and a thoroughly researched problem in robotics and sensor networks. This paper is concerned with the theory of localization from inner-angle measurements. We focus on the challenging case where no anchor locations are known.

Inspired by Euclidean distance matrices, we investigate when a set of inner angles corresponds to a realizable point set. In particular, we find linear and non-linear constraints that are provably necessary, and we conjecture also sufficient for characterizing realizable angle sets. We confirm this in extensive numerical simulations, and we illustrate the use of these constraints for denoising angle measurements along with the reconstruction of a valid point set.

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