Localization from Imperfect and Incomplete Ranging

Source localization from imperfect and incomplete range information is considered. The problem is formulated as a combination of the well-known Euclidean distance matrix (EDM) approximation/completion problem and multidimensional scaling (MDS). A powerful technique that solves the EDM approximation/completion problem by exploiting the semi-definiteness property of a corresponding Euclidean kernel has been recently proposed (A.Y. Alfakih et al., 1999). That technique requires, however, that the entries of the input EDM be weighted in accordance to their reliability. In this paper, a formula for such a weight function, based on confidence-bound statistics of the distance estimates and on graph spectral properties is studied. Computer simulations show that significant improvement in localization accuracy can be achieved by utilizing the weight function derived