Adaptive multi-task compressive sensing for localisation in wireless local area networks

The spatially distributed sparsity of the mobile devices (MDs) in indoor wireless local area networks (WLANs) makes compressive sensing (CS) based localisation algorithms feasible and desirable. In this Letter, the authors exploit the most recent developments in CS to efficiently perform localisation in WLANs and design an accurate indoor localisation scheme by taking advantage of the theory of multi-task Bayesian CS (MBCS). The proposed scheme assembles the strength measurements of signals from the MDs to distinct access points (APs) and jointly utilises them at a central unit or a specific AP to achieve localisation, thus being able to alleviate the burden of MDs while simultaneously giving a precise estimation of the locations. Afterwards, they give a deeper insight into the localisation problem in more practical scenarios with varying number of MDs and investigate two different adaptive algorithms to meet the satisfactory localisation error requirement. Compared with the conventional MBCS algorithms, simulation results validate that both adaptive algorithms could provide superior localisation accuracy and exhibit stronger resilience to the changes in the number of MDs.