An Efficient Counting and Localization Framework for Off-Grid Targets in WSNs

In this letter, we study the counting and localization problem for off-grid targets in wireless sensor networks. Existing compressed sensing-based schemes implicitly assume that all targets fall on a pre-defined grid exactly. However, when the assumption is violated, their performance deteriorates dramatically. To address this, we propose a novel counting and localization framework for off-grid targets. We first approximate the true and unknown sparsifying dictionary with its first order Taylor expansion around a known dictionary, and then formulate the counting and localization problem as a sparse recovery problem that recovers two sparse vectors with the same support. At last, we solve the problem using a variational Bayesian expectation-maximization algorithm. Simulation results highlight the superior performance of the proposed framework in terms of probability of correct counting and average localization error.