Extending the Classical Multidimensional Scaling Algorithm Given Partial Pairwise Distance Measurements

We consider the problem of node localization given partial pairwise distance measurements. Current solutions first complete the missing distances and then apply the classical multidimensional scaling (MDS) algorithm. Instead, we extend the classical MDS to a setup where the sensor network is composed of a fully connected group of nodes that communicate with each other (e.g., beacons), and a group of nodes that cannot communicate with each other, but each one of them communicates with each node in the first group. The positions of all nodes are unknown. We localize the fully connected nodes by exploiting their distance measurements to the disconnected nodes. At the same time, the positions of the disconnected nodes are obtained up to a translation relative to the positions of the connected nodes. Recovering this translation, can be obtained with an additional step. Simulation results show that the proposed algorithm outperforms current MDS-like solutions to the problem.