On the Placement of Clock Reference Nodes for Time Synchronization in Sensor Networks

The limited resource of sensor nodes requires lightweight and efficient schemes to synchronize clocks on different nodes. Network-wide time synchronization is an even more challenging problem because a sensor network usually has a large number of sensor nodes. In this paper, we consider the problem of synchronizing the clocks of all nodes in large scale sensor networks. Making all sensor nodes synchronize with one root node is limited in synchronization accuracy. We assume that multiple highly accurate clock reference nodes can be placed in the network. The clock reference nodes have some external means such as GPS to make sure they have the accurate time. Sensor nodes will adjust their system time according to the time of those clock reference nodes. The network-wide synchronization accuracy depends on where to place the clock reference nodes in the network. We formulate this placement problem to a KMedian problem, which has been proven to be NP-Complete. To make this problem tractable, we introduce simplifications to the problem and solve it using integer programming. Our numerical experiment results show that properly placing multiple clock reference nodes in the network can greatly improve the networkwide synchronization accuracy, especially for those networks where sensor nodes are unevenly distributed. In reality, the clock reference nodes may not be placed in the exact points where they should be. Our simulations show that even the placement of clock reference nodes has some deviations, the global synchronization still has good accuracy.