An algorithm for clock synchronization with the gradient property in sensor networks

We introduce a distributed algorithm for clock synchronization in sensor networks. Our algorithm assumes that nodes in the network only know their immediate neighborhoods and an upper bound on the network's diameter. Clock-synchronization messages are only sent as part of the communication, assumed reasonably frequent, that already takes place among nodes. The algorithm has the gradient property of [2], achieving an O(1) worst-case skew between the logical clocks of neighbors. As in the case of [3,8], the algorithm's actions are such that no constant lower bound exists on the rate at which logical clocks progress in time, and for this reason the lower bound of [2,5] that forbids constant skew between neighbors does not apply

Modelling Clock Synchronization in the Chess gMAC WSN Protocol

We present a detailled timed automata model of the clock synchronization algorithm that is currently being used in a wireless sensor network (WSN) that has been developed by the Dutch company Chess. Using the Uppaal model checker, we establish that in certain cases a static, fully synchronized network may eventually become unsynchronized if the current algorithm is used, even in a setting with infinitesimal clock drifts

Fast Desynchronization For Decentralized Multichannel Medium Access Control

Distributed desynchronization algorithms are key to wireless sensor networks as they allow for medium access control in a decentralized manner. In this paper, we view desynchronization primitives as iterative methods that solve optimization problems. In particular, by formalizing a well established desynchronization algorithm as a gradient descent method, we establish novel upper bounds on the number of iterations required to reach convergence. Moreover, by using Nesterov's accelerated gradient method, we propose a novel desynchronization primitive that provides for faster convergence to the steady state. Importantly, we propose a novel algorithm that leads to decentralized time-synchronous multichannel TDMA coordination by formulating this task as an optimization problem. Our simulations and experiments on a densely-connected IEEE 802.15.4-based wireless sensor network demonstrate that our scheme provides for faster convergence to the steady state, robustness to hidden nodes, higher network throughput and comparable power dissipation with respect to the recently standardized IEEE 802.15.4e-2012 time-synchronized channel hopping (TSCH) scheme.Comment: to appear in IEEE Transactions on Communication

Limited benefit of cooperation in distributed relative localization

Important applications in robotic and sensor networks require distributed algorithms to solve the so-called relative localization problem: a node-indexed vector has to be reconstructed from measurements of differences between neighbor nodes. In a recent note, we have studied the estimation error of a popular gradient descent algorithm showing that the mean square error has a minimum at a finite time, after which the performance worsens. This paper proposes a suitable modification of this algorithm incorporating more realistic "a priori" information on the position. The new algorithm presents a performance monotonically decreasing to the optimal one. Furthermore, we show that the optimal performance is approximated, up to a 1 + \eps factor, within a time which is independent of the graph and of the number of nodes. This convergence time is very much related to the minimum exhibited by the previous algorithm and both lead to the following conclusion: in the presence of noisy data, cooperation is only useful till a certain limit.Comment: 11 pages, 2 figures, submitted to conferenc

Cooperative Synchronization in Wireless Networks

Synchronization is a key functionality in wireless network, enabling a wide variety of services. We consider a Bayesian inference framework whereby network nodes can achieve phase and skew synchronization in a fully distributed way. In particular, under the assumption of Gaussian measurement noise, we derive two message passing methods (belief propagation and mean field), analyze their convergence behavior, and perform a qualitative and quantitative comparison with a number of competing algorithms. We also show that both methods can be applied in networks with and without master nodes. Our performance results are complemented by, and compared with, the relevant Bayesian Cram\'er-Rao bounds

Ergodic Randomized Algorithms and Dynamics over Networks

Algorithms and dynamics over networks often involve randomization, and randomization may result in oscillating dynamics which fail to converge in a deterministic sense. In this paper, we observe this undesired feature in three applications, in which the dynamics is the randomized asynchronous counterpart of a well-behaved synchronous one. These three applications are network localization, PageRank computation, and opinion dynamics. Motivated by their formal similarity, we show the following general fact, under the assumptions of independence across time and linearities of the updates: if the expected dynamics is stable and converges to the same limit of the original synchronous dynamics, then the oscillations are ergodic and the desired limit can be locally recovered via time-averaging.Comment: 11 pages; submitted for publication. revised version with fixed technical flaw and updated reference