The compressive sensing (CS) theory has been recognized as a promising technique to achieve the target localization in wireless sensor networks. However, most of the existing works require the prior knowledge of transmitting powers of targets, which is not conformed to the case that the information of targets is completely unknown. To address such a problem, in this paper, we propose a novel CS-based approach for multiple target localization and power estimation. It is achieved by formulating the locations and transmitting powers of targets as a sparse vector in the discrete spatial domain and the received signal strengths (RSSs) of targets are taken to recover the sparse vector. The key point of CS-based localization is the sensing matrix, which is constructed by collecting RSSs from RF emitters in our approach, avoiding the disadvantage of using the radio propagation model. Moreover, since the collection of RSSs to construct the sensing matrix is tedious and time-consuming, we propose a CS-based method for reconstructing the sensing matrix from only a small number of RSS measurements. It is achieved by exploiting the CS theory and designing an difference matrix to reveal the sparsity of the sensing matrix. Finally, simulation results demonstrate the effectiveness and robustness of our localization and power estimation approach.

Many basic tasks in Wireless Sensor Networks (WSNs) rely heavily on the availability and accuracy of target locations. Since the number of targets is usually limited, localization benefits from Compressed Sensing (CS) in the sense that measurements can be greatly reduced. Though some CS-based localization schemes have been proposed, all of these solutions make an assumption that all targets are located on a pre-sampled and fixed grid, and perform poorly when some targets are located off the grid. To address this problem, we develop an adaptive dictionary algorithm where the grid is adaptively adjusted. To achieve this, we formulate localization as a joint parameter estimation and sparse signal recovery problem. Additionally, we transform the problem into a tractable convex optimization problem by using Taylor approximation. Finally, the block coordinate descent method is leveraged to iteratively optimize over the parameters and sparse signal. After iterations, the measurements can be linearly represented by a sparse signal which indicates the number and locations of targets. Extensive simulation results show that the proposed adaptive dictionary algorithm provides better performance than state-of-the-art fixed dictionary algorithms.