8. The Spatial Smoothing Method of Clock Synchronization in Wireless Networks

Wireless sensor networks are networks of devices which collaborate to perform distributed sensing, processing, and possibly even actuation tasks. In this chapter we consider the problem of the synchronizing clocks in wireless sensor networks. We analyze an approach to clock synchronization, called spatial smoothing, that generally synchronizes clocks in a network more accurately than alternative tree-based methods. This approach leads to a distributed least-squares vector estimation problem whose goal is to smooth out the noisy estimates of clock differences of pairs of nodes that can directly exchange packets. We point out connections between the error variance of such a least squares-based clock synchronization and resistance in electrical networks. We determine the limiting clock synchronization accuracy for several types of networks of interest and quantify the improvement over the tree-based method. For random connected wireless sensor networks we show that the clock synchronization error can remain bounded even as the number of nodes in the network increases. This lends support for the feasibility of time-based computation in large networks. We further analyze the convergence time of a distributed iterative algorithm to compute the optimally spatial smoothed estimates. We also propose ways of exploiting the network connectivity graph structure in order to speed up computation.