3D compressive sensing for nodes localization in WNs based on RSS

Compressive sensing (CS) intends to recover signals at a sampling rate significantly (much) lower than that classically used according to the Nyquist theorem. This allows avoiding unnecessary sampling and complexity. In this paper, a Three-Dimensional Compressive Sensing (3D-CS) approach is proposed for nodes localization in wireless networks. In 3D-CS-R2S2 approach, which is based on the ratio of received signal strength (RSS), a 3D sparsity basis and a 3D measurement matrix are used as radio map and noisy measurements respectively in order to recover the target position. A specific multi-linear algebra procedure was developed using N-way array products, together with an adequate decomposition. Both allow formulating the localization problem in a way that is solvable by an ℓ₁-minimization algorithm based on CS theory. 3D-CS-R2S2 improves localization accuracy even if propagation conditions change significantly and/or the effective isotropic radiated power (EIRP) is unknown. Additionally, it enables practical Real Time Localization Systems (RTLS) development since 3D-CS-R2S2 can be functional with a reduced number of base stations without compromising position recovery accuracy. The simulation results show the efficiency of the method that not only succeeds to recover a target position but also improves localization accuracy in presence of noise.