Time synchronization is an important aspect of sensor network operation. However, it is well known that synchro- nization error accumulates over multiple hops. This presents a challenge for large-scale, multi-hop sensor networks with a large number of nodes distributed over wide areas. In this work, we present a protocol that uses spatial averaging to reduce error accumulation in large-scale networks. We provide an analysis to quantify the synchronization improvement achieved using spatial averaging and find that in a basic cooperative network, the skew and offset variance decrease approximately as 1 ¯ N where ¯ N is the number of cooperating nodes. For general networks, simulation results and a comparison to basic cooperative network results are used to illustrate the improvement in synchronization performance.
The problem with these emergent synchronization results is that the fundamental theory assumes all nodes have nearly the same firing period. Results from @cite_0 and @cite_18 show that the convergence results may hold when nodes have approximately the same firing period, but the authors of @cite_18 explain that clock skew will degrade synchronization performance. Since we are not aware of any results that provide an extension to deal with networks of nodes with arbitrary firing periods, our work focuses on synchronization algorithms that explicitly estimate clock skew.
@cite_0 @cite_18
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We introduce the distributed gradient clock synchronization problem. As in traditional distributed clock synchronization, we consider a network of nodes equipped with hardware clocks with bounded drift. Nodes compute logical clock values based on their hardware clocks and message exchanges, and the goal is to synchronize the nodes' logical clocks as closely as possible, while satisfying certain validity conditions. The new feature of gradient clock synchronization (GCS for short) is to require that the skew between any two nodes' logical clocks be bounded by a nondecreasing function of the uncertainty in message delay (call this the distance) between the two nodes. That is, we require nearby nodes to be closely synchronized, and allow faraway nodes to be more loosely synchronized. We contrast GCS with traditional clock synchronization, and discuss several practical motivations for GCS, mostly arising in sensor and ad hoc networks. Our main result is that the worst case clock skew between two nodes at distance d from each other is Ω(d + log D log log D), where D is the diameter1 of the network. This means that clock synchronization is not a local property, in the sense that the clock skew between two nodes depends not only on the distance between the nodes, but also on the size of the network. Our lower bound implies, for example, that the TDMA protocol with a fixed slot granularity will fail as the network grows, even if the maximum degree of each node stays constant. We present a distributed clock synchronization algorithm that guarantees an exponentially improved bound of O(log D) on the clock skew between neighboring nodes in any graph G of diameter D. In light of the lower bound of Omega(log D log log D), this result is almost tight. Moreover, the global clock skew between any two nodes, particularly nodes that are not directly connected, is bounded by O(D), which is optimal up to a constant factor. Our algorithm further ensures that the clock values are always within a linear envelope of real time. A better bound on the accuracy with respect to real time cannot be achieved in the absence of an external timer. These results all hold in a general model where both the clock drifts and the message delays may vary arbitrarily within pre-specified bounds. Time-based localization approaches attract a lot of interest due to their high accuracy and potentially low cost for wireless sensor networks (WSNs). However, time-based localization is tightly coupled with clock synchronization. Thus, the reliability of timestamps in time-based localization becomes an important yet challenging task to deal with. In this paper, we propose robust time-based localization strategies to locate a target node with the help of anchors (nodes with known positions) in asynchronous networks. Two kinds of asynchronous networks are considered: one only with clock offsets, labeled quasi-synchronous networks, whereas the other with not only clock offsets but also clock skews, labeled fully asynchronous networks. A novel ranging protocol is developed for both networks, namely asymmetric trip ranging (ATR), to reduce the communication load and explore the broadcast property of WSNs. Regardless of the reliability of the timestamp report from the target node, closed-form least-squares (LS) estimators are derived to accurately estimate the target node position. As a result, we counter the uncertainties caused by the target node by ignoring the timestamps from this node. Furthermore, in order to simplify the estimator in fully asynchronous networks, localization and synchronization are decoupled. A simple yet efficient method is proposed to first Calibrate the Clock Skews of the anchors, and then Estimate the Node Position (CCS-ENP). Finally, Cramer-Rao bounds (CRBs) and simulation results corroborate the efficiency of our localization schemes. Recently, a few efficient timing synchronization protocols for wireless sensor networks (WSNs) have been proposed with the goal of maximizing the accuracy and minimizing the power utilization. This paper proposes novel clock skew estimators assuming different delay environments to achieve energy-efficient network-wide synchronization for WSNs. The proposed clock skew correction mechanism significantly increases the re-synchronization period, which is a critical factor in reducing the overall power consumption. The proposed synchronization scheme can be applied to the conventional protocols without additional overheads. Moreover, this paper derives the Cramer-Rao lower bounds and the maximum likelihood estimators under different delay models and assumptions. These analytical metrics serves as good benchmarks for the thus far reported experimental results