Brief Announcement: Network Synchronization and Localization Based on Stolen Signals

We consider an anchor-free, relative localization and synchronization problem where a set of n receiver nodes and m wireless signal sources are independently, uniformly, and randomly distributed in a disk in the plane. The signals can be distinguished and their capture times can be measured. At the beginning neither the positions of the signal sources and receivers are known nor the sending moments of the signals. Now each receiver captures each signal after its constant speed journey over the unknown distance between signal source and receiver position. Given these nm capture times the task is to compute the relative distances between all synchronized receivers. In a more generalized setting the receiver nodes have no synchronized clocks and need to be synchronized from the capture times of the stolen signals.