Source localization in complex networks using a frequency-domain approach

In this paper, we provide a novel frequency-domain approach to locate an arbitrary number of sources in a large number of zones. In typical source localization methods, the sources are assumed to be acoustic or RF; sensors are placed in different zones to listen to these sources where each zone-to-sensor has a unique path loss and delay. Since each zone has a path loss and delay to each sensor, the sensing matrix is full and the problem of source localization effectively reduces to a sparse signal recovery problem. On the contrary, we are interested in scenarios where the sources may not have an acoustic or RF signature, e.g., locating a vehicle with cameras or a rumor in a social network; and a very few sensors may be able to sense the sources due to obstacles/occlusions. In other words, instead of having a full sensing matrix (as in sparse recovery), the sensing matrix is now highly sparse. To this aim, we provide a protocol for the sensors to collaborate among each other and devise a frequency-domain approach to assist an interrogator to locate the source. In particular, an interrogator (e.g., a UAV) analyzes the Frequency-Response (FR) of the collaborated statistic at an arbitrary sensor, and moves to a neighboring sensor whose FR magnitude is the largest among all the neighbors. With carefully designed collaboration, we show that the FR magnitude at any sensor increases in the direction of the source. In order to locate multiple sources, we characterize the diversity in the sources to arrive at their successful identification.