Localization involves the estimation of the precise location of an object based on various forms of relative position information available of the object. Source and sensor localization is a fundamental capability broadly useful in a number of emerging applications. For example a network of sensors deployed to combat bioterrorism, must not only detect the presence of a potential threat, but also must pinpoint the source of the threat. Similarly, in pervasive computing, locating an errant mobile user permits the computer network to identify the most appropriate server with matching capabilities for the user. Likewise, in sensor networks individual sensors must know their own positions, so as to route packets, detect faults, and sense and record events. There is also an emerging multibillion dollar wireless localization industry. This research will address issues that hold the key to fast efficient localization. The investigators will adopt a three pronged approach. First, various optimum estimates will be investigated under a variety of practical signal models. These include maximum likelihood and minimum variance estimates. Theoretical performance limits will be determined. Secondly, the investigators will generalize and analyze various algorithms that obtain these estimates efficiently with low complexity. Specifically, the investigators will study optimal localization involving minimization of non-convex cost functions that admit multiple local minima. To overcome the problem of multiple local minima, the investigators will develop a relaxation framework based on convex optimization to obtain fast near optimal solutions. Finally, the proper placement of wireless sensors and anchors impacts both the accuracy and the complexity with which localization is performed. Thus, the investigators will study optimum anchor placement to aid both these attributes. These investigations are critical to the understanding of the theoretical foundation of wireless source localization, and will fundamentally impact its broad applications.
