Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This article presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmitted messages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page

The paper studies average consensus with random topologies (intermittent links) and noisy channels.Consensus with noise in the network links leads to the bias-variance dilemma-running consensus for long reduces the bias of the final average estimate but increases its variance. We present two different compromises to this tradeoff: the A − N D algorithm modifies conventional consensus by forcing the weights to satisfy a persistence condition (slowly decaying to zero;) and the A − N C algorithm where the weights are constant but consensus is run for a fixed number of iterations ı, then it is restarted and rerun for a total of p runs, and at the end averages the final states of the p runs (Monte Carlo averaging). We use controlled Markov processes and stochastic approximation arguments to prove almost sure convergence of A − N D to the desired average (asymptotic unbiasedness) and compute explicitly the m.s.e. (variance) of the consensus limit. We show that A − N D represents the best of both worlds-low bias and low variance-at the cost of a slow convergence rate; rescaling the weights balances the variance versus the rate of bias reduction (convergence rate). In contrast, A − N C, because of its constant weights, converges fast but presents a different bias-variance tradeoff. For the same number of iterations ı p, shorter runs (smaller ı) lead to high bias but smaller variance (larger number p of runs to average over.) For a static non-random network with Gaussian noise, we compute the optimal gain for A − N C to reach in the shortest run length ı, with high probability (1 − δ), (ǫ, δ)-consensus (ǫ residual bias). Our results hold under fairly general assumptions on the random link failures and communication noise.

The paper studies distributed static parameter (vector) estimation in sensor networks with nonlinear observation models and noisy inter-sensor communication. It introduces separably estimable observation models that generalize the observability condition in linear centralized estimation to nonlinear distributed estimation. It studies two distributed estimation algorithms in separably estimable models, the N U (with its linear counterpart LU) and the N LU. Their update rule combines a consensus step (where each sensor updates the state by weight averaging it with its neighbors' states) and an innovation step (where each sensor processes its local current observation.) This makes the three algorithms of the consensus + innovations type, very different from traditional consensus. The paper proves consistency (all sensors reach consensus almost surely and converge to the true parameter value,) efficiency, and asymptotic unbiasedness. For LU and N U, it proves asymptotic normality and provides convergence rate guarantees. The three algorithms are characterized by appropriately chosen decaying weight sequences. Algorithms LU and N U are analyzed in the framework of stochastic approximation theory; algorithm N LU exhibits mixed time-scale behavior and biased perturbations, and its analysis requires a different approach that is developed in the paper. 2 the field, not to an estimate of the M -dimensional temperature distribution. The distributed consensus+innovations algorithms that we introduce achieve both; each sensor converges to an estimate of the entire M -dimensional field by combining consensus and processing of the sensors measurements. Subsequent to this paper, analysis of detection consensus+innovations type algorithms is, e.g., in [20], [21].Important questions that arise with consensus+innovations algorithms include: i) convergence: do the algorithms converge and if so in what sense; ii) consensus: do the agents reach a consensus on their field estimates; iii) distributed versus centralized: how good is the distributed field estimate at each sensor when compared with the centralized estimate obtained by a fusion center, in other words are the distributed estimate sequences consistent, and asymptotically unbiased, efficient, or normal; and iv) rate of convergence: what is the rate at which the distributed estimators converge. These questions are very distinct from the convergence issues considered in the "consensus only" literature.We present three distributed consensus+innovations inference algorithms: LU for linear observation models (as when each sensor makes a noisy reading of the temperature at its location, see Section II-E;) and two algorithms, N U and N LU, for nonlinear observation models (like in power grids when each sensor measures a phase differential through a sinusoidal modulation, see Section IV-D.) The paper introduces the conditions on the sensor observations model (separable estimability that we define) and on the communication network (connectedness on average) for the distributed estimate...

This paper addresses problems on the structural design of large-scale control systems. An efficient and unified framework is proposed to select the minimum number of manipulated/measured variables to achieve structural controllability/ observability of the system, and to select the minimum number of feedback interconnections between measured and manipulated variables such that the closed-loop system has no structural fixed modes. Global solutions are computed using polynomial complexity algorithms in the number of the state variables of the system. Finally, graph-theoretic characterizations are proposed, which allow a characterization of all possible solutions.