Set-valued consensus for distributed clock synchronization

This paper addresses the clock synchronization problem in a wireless sensor network (WSN) and proposes a distributed solution that consists of a form of consensus, where agents are able to exchange data representing intervals or sets. The solution is based on a centralized algorithm for clock synchronization, proposed by Marzullo, that determines the smallest interval that is in common with the maximum number of measured intervals. We first show how to convert such an algorithm into a problem involving only operations on sets, and then we convert it into a set-valued consensus. The solution is valid for more general scenarios where agents have uncertain measures of e.g. the position of an object detected by a vision system, a temperature in a room, but it will be applied to the case where a set of uncertain time values are propagated through a WSN. Under suitable joint conditions on the communication connectivity and bounded agent failure, we prove the correctness of the algorithm that indeed allows the network agents to consent on the value of a unique global time.