On basic properties of localization using distance-difference measurements

We study basic properties related to the task of localizing a source using distance-difference measurements to it. These properties are related to minimalistic realizations of localization systems in terms of the number of sensors and computational complexity. We first establish conditions for unique identification of a source in Euclidean plane. We then derive the minimum number of sensors needed for uniquely identifying a source for cases where it is located anywhere in the Euclidean plane and inside a polygonal monitoring region. The localization problem may be solved by computing the intersections points of two hyperbolas. While there are four intersection points in general, we show that there are only 2 for this localization problem, which in turn bounds the potential source estimates to be considered.