Energy-Efficient Estimation of Clock Offset for Inactive Nodes in Wireless Sensor Networks

For a meaningful processing of the information sensed by a wireless sensor network (WSN), the clocks of the individual nodes need to be matched through some well-defined procedures. Extending the idea of having silent nodes in a WSN overhear the two-way timing message communication between two active (master and slave) nodes, this paper derives the maximum-likelihood estimator (MLE) for the clock offsets of the listening nodes located within the communication range of the active nodes by assuming an exponential link delay modeling, hence synchronizing with the reference node at a very low cost. A vital advantage for adopting such an approach is that the performance of sender-receiver protocols can be compared with receiver-receiver protocols on equal footings, because their main critical aspect was associated with the high-communication overhead induced by the point-to-point nature of communication links relative to broadcast communications. The MLE is also shown to be the minimum variance unbiased estimator (MVUE) of the clock offset when the mean of exponential link delays is known. Since it is attractive to know in advance the extent to which an estimator can perform through its lower bound, the Chapman-Robbins bound and the Barankin bound for the clock offset estimator are also derived. It is shown that for an exponential link delay model, the mean square error of the clock offset estimator is inversely proportional to the square of the number of observations, and hence its performance is on a similar scale, albeit slightly lesser, as compared to the usual sender-receiver clock offset estimator. In addition, a novel method referred to as the Gaussian mixture Kalman particle filter (GMKPF) is proposed herein to estimate the clock offsets of the listening nodes in a WSN. GMKPF represents a better and flexible alternative to the MLE for the clock offset estimation problem due to its improved performance and applicability in arbitrary and generalized non-Gaussian random delay models.