MDS-based localization with known anchor locations and missing tag-to-tag distances

Abstract

Multidimensional Scaling (MDS) can be used to localize a set of nodes (tags) by evaluating their distances from another set of nodes having known location (anchors). Node localization with MDS generally requires that the proximity graph be fully connected. This implies that matrices generated from tag-anchor ranging for which tag-to-tag distances are missing can not be used directly with the MDS algorithm without the use of estimates for the missing data. These estimates, however, unavoidably introduce some approximations in the localization process, which can become relatively large depending on the number of missing measurements and the amount of noise in the pair-wise distance measurements. This paper proposes a specialized form of the anchored MDS algorithm that undermines missing tag-to-tag distances in the connectivity matrix. We show that decoupling tag-to-tag interactions in the Scaling by MAjorizing a COmplicated Function (SMACOF) algorithm can undermine the effects of missing tag-to-tag distances and produce tag configurations that are inferred directly from only anchor-tag pairwise distances.