We analyze a distributed algorithm for estimation of scalar parameters belonging to nodes in a mobile network from noisy relative measurements. The motivation comes from the problem of clock skew and offset estimation for the purpose of time synchronization. The time variation of the network was modeled as a Markov chain. The estimates are shown to be mean square convergent under fairly weak assumptions on the Markov chain, as long as the union of the graphs is connected. Expressions for the asymptotic mean and correlation are also provided. The Markovian switching topology model of mobile networks is justified for certain node mobility models through empirically estimated conditional entropy measures.
Recently, a number of fully distributed global synchronization algorithms have been proposed that do not need spanning tree computation. Distributed protocols are therefore more readily applicable to mobile networks than tree-based protocols. Among the distributed synchronization protocols proposed, some are based on estimation of the skew and or offset of each clock with respect to a reference clock (called ). The algorithms proposed in @cite_2 @cite_27 @cite_29 @cite_26 @cite_32 belong to this category. Another class of protocols estimate a common global time that may not be related to the time of any clock in the network. The algorithms proposed in @cite_33 @cite_15 @cite_14 belong to this category, which we call .
@cite_26 @cite_14 @cite_33 @cite_29 @cite_32 @cite_27 @cite_2 @cite_15
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In a network of clocks, we consider a given reference node to determine the time evolution t. We introduce and analyze a stochastic model for clocks, in which the relative speedup of a clock, called the skew, is characterized by some given stochastic process. We study the problem of synchronizing clocks in a network, which amounts to estimating the instantaneous relative skews and relative offsets by exchange of time-stamped packets across the links of the network. We present a scheme for obtaining measurements in a communication link. We develop an algorithm for optimal filtering of measurements across a link (i; j) in order to estimate the logarithm of the relative speedup of node j with respect to node i, and we further study some implementation issues. We also present a scheme for pairwise offset estimation based on skew estimates. We study the properties of our algorithms and provide theoretical guarantees on their performance. We also develop an online centralized model-based asynchronous algorithm for optimal filtering of the time-stamps in the entire network, and an efficient distributed suboptimal scheme. In this paper a distributed algorithm for clock synchronization is proposed. This algorithm is based on an extension of the consensus algorithm able to synchronize a family of double integrators. Since the various clocks may have different drifts, the algorithm needs to be designed so that it can work also in case of heterogeneous double integrators. Through a robust control analysis it is possible to determine the maximum admissible level of heterogeneity yielding synchronization. The first part of the paper is devoted to the analysis of an unrealistic synchronous implementation of the algorithm. However, in the last part of the paper we propose a realistic pseudo-synchronous implementation which is proved to be a perturbation of the synchronous one. From arguments related the center manifold theorem, the stability of the pseudo-synchronous is finally proved. A distributed algorithm to achieve accurate time synchronization in large multihop wireless networks is presented. The central idea is to exploit the large number of global constraints that have to be satisfied by a common notion of time in a multihop network. If, at a certain instant, Oij is the clock offset between two neighboring nodes i and j, then for any loop i1, i2, i3 , ..., in, in + 1 - i1 in the multihop network, these offsets must satisfy the global constraint Sigma k = 1 nOik, ik + 1 = 0. Noisy estimates Ocirc ij of Oij are usually arrived at by bilateral exchanges of timestamped messages or local broadcasts. By imposing the large number of global constraints for all the loops in the multihop network, these estimates can be smoothed and made more accurate. A fully distributed and asynchronous algorithm which functions by simple local broadcasts is designed. Changing the time reference node for synchronization is also easy, consisting simply of one node switching on adaptation, and another switching it off. Implementation results on a forty node network, and comparative evaluation against a leading algorithm, are presented In this paper, we study the global clock synchronization problem for wireless sensor networks. Based on belief propagation, we propose a fully distributed algorithm which has low overhead and can achieve scalable synchronization. It is also shown analytically that the proposed algorithm always converges for strongly connected networks. Simulation results show that the proposed algorithm achieves better accuracy than consensus algorithms. Furthermore, the belief obtained at each sensor provides an accurate prediction on the algorithm's performance in terms of MSE. We consider the problem of estimating vector-valued variables from noisy relative measurements. The measurement model can be expressed in terms of a graph, whose nodes correspond to the variables being estimated and the edges to noisy measurements of the difference between the two variables. This type of measurement model appears in several sensor network problems, such as sensor localization and time synchronization. We consider the optimal estimate for the unknown variables obtained by applying the classical Best Linear Unbiased Estimator, which achieves the minimum variance among all linear unbiased estimators. We propose a new algorithm to compute the optimal estimate in an iterative manner, the Overlapping Subgraph Estimator algorithm. The algorithm is distributed, asynchronous, robust to temporary communication failures, and is guaranteed to converges to the optimal estimate even with temporary communication failures. Simulations for a realistic example show that the algorithm can reduce energy consumption by a factor of two compared to previous algorithms, while achieving the same accuracy. We consider the problem of estimating vector-valued variables from noisy "relative" measurements. The measurement model can be expressed in terms of a graph, whose nodes correspond to the variables being estimated and the edges to noisy measurements of the difference between the two variables. We take the value of one particular variable as a reference and consider the optimal estimator for the differences between the remaining variables and the reference. This type of measurement model appears in several sensor network problems, such as sensor localization and time synchronization. Two algorithms are proposed to compute the optimal estimate in a distributed, iterative manner. The first algorithm implements the Jacobi method to iteratively compute the optimal estimate, assuming all communication is perfect. The second algorithm is robust to temporary communication failures, and converges to the optimal estimate when certain mild conditions on the failure rate are satisfied. It also employs an initialization scheme to improve accuracy in spite of the slow convergence of the Jacobi method In this paper a distributed clock synchronization algorithm is proposed. The algorithm requires asymmetric gossip communications between the nodes of the network, and is based on an PI-like consensus protocol where the proportional part compensates the different clock speeds while the integral part eliminates the different clock offsets. Convergence of the algorithm is proved and analyzed with respect to the controller parameter, when the underlying graph is the complete graph. Simulations results show the effectiveness of the proposed strategy also for more general communication topologies.