Complex-Domain Super MDS: A New Framework for Wireless Localization With Hybrid Information

We revisit the super multidimensional scaling (SMDS) wireless localization algorithm first proposed a decade ago, recasting it onto the complex-domain. Under this new formulation, the edge kernel, which carries both angle and distance information simultaneously and plays a central role in the SMDS algorithm, becomes a complex-valued rank-one matrix, resulting in a new complex-domain SMDS framework, which yields several advantages over the original, including the elimination of redundancy, the enhancement of conditions to handle information erasure, and the possibility of designing several algorithmic variations that offer different complexity/performance improvements. To cite some concrete results, it is shown, for instance, that a distance-based localization system with 20 targets employing one of the new algorithms dubbed complex-domain SMDS (CD-SDMDS) outperforms the original SMDS at a tenth of the computational cost, and that the handling of missing information via matrix completion is superior in CD-SMDS compared to SMDS. If the same network collects also anchor-to-target angle information, it is furthermore shown that localization is achieved with nearly $20\times $ lower complexity and still higher accuracy using another new algorithm dubbed Turbo MRC-SMDS, and over $25\times $ faster using yet another method dubbed Iterative MRC-SMDS, with only a slight degradation.