Large Environment Indoor Localization Leveraging Semi-Tensor Product Compression Sensing

The sparsity of the localization problem makes the compression sensing (CS) theory suitable for indoor localization in wireless local area networks (WLANs). However, in practice, we find that the location errors and computing complexity increase significantly as the dimensionality of the sparse vector and measurement matrix are high in a large environment, so most CS-based localization techniques are accompanied by coarse localization and access point (AP) selection stages. Therefore, in this article, we first deduced the relationship between the number of APs and the dimensionality of the sparse vector theoretically to give the guideline that the number of subdatabases and APs should be obtained. Then an adaptive intuitionistic fuzzy C-ordered mean (AIFCOM) clustering is designed for the data with outliers in the environment with multipath effects. Finally, in the fine localization stage, we propose a semi-tensor product CS (STP-CS) model to construct the measurement matrix, compared with the traditional CS model, our model not only remains more number of APs, but also decreases the dimensionality of measurement matrix, which can reduce the storage space and improve localization accuracy simultaneously.