4,371 research outputs found

    Gossip Algorithms for Distributed Signal Processing

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    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

    Geographic Gossip: Efficient Averaging for Sensor Networks

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    Gossip algorithms for distributed computation are attractive due to their simplicity, distributed nature, and robustness in noisy and uncertain environments. However, using standard gossip algorithms can lead to a significant waste in energy by repeatedly recirculating redundant information. For realistic sensor network model topologies like grids and random geometric graphs, the inefficiency of gossip schemes is related to the slow mixing times of random walks on the communication graph. We propose and analyze an alternative gossiping scheme that exploits geographic information. By utilizing geographic routing combined with a simple resampling method, we demonstrate substantial gains over previously proposed gossip protocols. For regular graphs such as the ring or grid, our algorithm improves standard gossip by factors of nn and n\sqrt{n} respectively. For the more challenging case of random geometric graphs, our algorithm computes the true average to accuracy ϵ\epsilon using O(n1.5lognlogϵ1)O(\frac{n^{1.5}}{\sqrt{\log n}} \log \epsilon^{-1}) radio transmissions, which yields a nlogn\sqrt{\frac{n}{\log n}} factor improvement over standard gossip algorithms. We illustrate these theoretical results with experimental comparisons between our algorithm and standard methods as applied to various classes of random fields.Comment: To appear, IEEE Transactions on Signal Processin

    Belief Consensus Algorithms for Fast Distributed Target Tracking in Wireless Sensor Networks

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    In distributed target tracking for wireless sensor networks, agreement on the target state can be achieved by the construction and maintenance of a communication path, in order to exchange information regarding local likelihood functions. Such an approach lacks robustness to failures and is not easily applicable to ad-hoc networks. To address this, several methods have been proposed that allow agreement on the global likelihood through fully distributed belief consensus (BC) algorithms, operating on local likelihoods in distributed particle filtering (DPF). However, a unified comparison of the convergence speed and communication cost has not been performed. In this paper, we provide such a comparison and propose a novel BC algorithm based on belief propagation (BP). According to our study, DPF based on metropolis belief consensus (MBC) is the fastest in loopy graphs, while DPF based on BP consensus is the fastest in tree graphs. Moreover, we found that BC-based DPF methods have lower communication overhead than data flooding when the network is sufficiently sparse

    Convergence Rate Analysis of Distributed Gossip (Linear Parameter) Estimation: Fundamental Limits and Tradeoffs

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    The paper considers gossip distributed estimation of a (static) distributed random field (a.k.a., large scale unknown parameter vector) observed by sparsely interconnected sensors, each of which only observes a small fraction of the field. We consider linear distributed estimators whose structure combines the information \emph{flow} among sensors (the \emph{consensus} term resulting from the local gossiping exchange among sensors when they are able to communicate) and the information \emph{gathering} measured by the sensors (the \emph{sensing} or \emph{innovations} term.) This leads to mixed time scale algorithms--one time scale associated with the consensus and the other with the innovations. The paper establishes a distributed observability condition (global observability plus mean connectedness) under which the distributed estimates are consistent and asymptotically normal. We introduce the distributed notion equivalent to the (centralized) Fisher information rate, which is a bound on the mean square error reduction rate of any distributed estimator; we show that under the appropriate modeling and structural network communication conditions (gossip protocol) the distributed gossip estimator attains this distributed Fisher information rate, asymptotically achieving the performance of the optimal centralized estimator. Finally, we study the behavior of the distributed gossip estimator when the measurements fade (noise variance grows) with time; in particular, we consider the maximum rate at which the noise variance can grow and still the distributed estimator being consistent, by showing that, as long as the centralized estimator is consistent, the distributed estimator remains consistent.Comment: Submitted for publication, 30 page

    Consensus and Products of Random Stochastic Matrices: Exact Rate for Convergence in Probability

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    Distributed consensus and other linear systems with system stochastic matrices WkW_k emerge in various settings, like opinion formation in social networks, rendezvous of robots, and distributed inference in sensor networks. The matrices WkW_k are often random, due to, e.g., random packet dropouts in wireless sensor networks. Key in analyzing the performance of such systems is studying convergence of matrix products WkWk1...W1W_kW_{k-1}... W_1. In this paper, we find the exact exponential rate II for the convergence in probability of the product of such matrices when time kk grows large, under the assumption that the WkW_k's are symmetric and independent identically distributed in time. Further, for commonly used random models like with gossip and link failure, we show that the rate II is found by solving a min-cut problem and, hence, easily computable. Finally, we apply our results to optimally allocate the sensors' transmission power in consensus+innovations distributed detection
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