Robust Multidimensional Similarity Analysis for IoT Localization With SαS Distributed Errors

Subspace location estimators are a class of range-based source localization (SL) methods built upon the multidimensional similarity (MDS) theory. Since they are computationally lightweight while maintaining a reasonably good level of positioning accuracy, these techniques can be well-suited for the context of Internet of Things (IoT), where precise localization is necessary but the on-device computational resources turn out to be relatively limited. MDS analysis (MDSA), in signal processing terms, is the statistical process of disentangling the signal subspace components from their disturbance counterparts for an observed MDS matrix that measures the similarity among multiple source-sensor coordinate differences. A prominent drawback of traditional MDSA schemes devised under the assumption of Gaussian noise is their vulnerability to outliers in the available range-type data, which are frequently encountered in IoT SL applications due to adverse environmental factors like non line-of-sight signal propagation and interference. In this contribution, we use symmetric $\alpha $ -stable $(S \alpha S)$ distributions to systematically characterize the MDS matrix observation errors, thus accounting for the existence of outliers. To resist against $S \alpha S$ disturbances, we cast MDSA as an $\ell _{p}$ -norm-based robust low-rank approximation problem. We then develop a practical optimization solution by means of the alternating direction method of multipliers, for which we further conduct a theoretical analysis of convergence. Simulations and real-world experiments confirm the feasibility of our robust subspace positioning approach.