Super-accurate source localization via multiple measurement vectors and compressed sensing techniques

In this paper we propose a novel Compressed Sensing (CS) approach for source localization in wireless sensor networks (WSN). While this is not the first work on applying CS to target localization, it is the first one (to our knowledge) to construct the sensing matrix based only on distance information and a discrete grid. Most of the CS approaches are based on received signal strength (RSS) fingerprinting methods. Moreover, we propose to use this new CS approach in conjunction with a multiple measurement vectors (MMV) problem, which we solve by the Simultaneous Orthogonal Matching Pursuit (SOMP) algorithm. Finally, we demonstrate the superiority of this new approach (even with a relatively small number of measurements) over the non-CS based and more complex Super Multidimensional Scaling (SMDS) algorithm, which is an improved version of the metric MDS. In order for the latter algorithm to be fairly compared against the MMV approach, based on the number of measurements, the noisy distances were fed to a maximum likelihood estimator (MLE) which first estimated the parameters of the Gamma distribution corresponding to the noisy measured distances. The mode of the estimated distribution was then fed to the SMDS.