On distance reconstruction for sensor network localization

Sensor localization typically exploits distance measurements to infer sensor positions with respect to known anchor nodes. Missing or unreliable measurements for specific nodes can impede such procedures, raising the problem of distance measurement reconstruction using distance information from other nodes. Here we develop further structural features of matrices of pairwise distances, as inherited from the classical multidimensional scaling problem. We show in particular an inertial property which can be successfully exploited to overcome inconsistencies that result in certain cases from an earlier approach of. We likewise develop linear algebraic solutions to the missing distance problem.