Multiple Target Counting and Localization Using Variational Bayesian EM Algorithm in Wireless Sensor Networks

Localization technologies play an increasingly important role in pervasive applications of wireless sensor networks. Since the number of targets is usually limited, localization benefits from compressed sensing (CS): measurements number can be greatly reduced. Despite many CS-based localization schemes, existing solutions implicitly assume that all targets fall on a fixed grid exactly. When the assumption is violated, the mismatch between the assumed and actual sparsifying dictionaries can deteriorate the localization performance significantly. To address such a problem, in this paper, we propose a novel and iterative multiple target counting and localization framework. The key idea behind the framework is to dynamically adjust the grid to alleviate or even eliminate dictionary mismatch. The contribution of this paper is twofold. First, we consider the off-grid target issue in CS-based localization and formulate multiple target counting and localization as a joint sparse signal recovery and parameter estimation problem. Second, we solve the joint optimization problem using a variational Bayesian expectation-maximization algorithm where the sparse signal and parameter are iteratively updated in the variational Bayesian expectation-step and variational Bayesian maximization-step, respectively. Extensive simulation results highlight the superior performance of the proposed framework in terms of probability of correct counting and average localization error.