Abstract — We consider a network of distributed sensors, where each sensor takes a linear measurement of some unknown parameters, corrupted by independent Gaussian noises. We propose a simple distributed iterative scheme, based on distributed average consensus in the network, to compute the maximum-likelihood estimate of the parameters. This scheme doesn’t involve explicit point-to-point message passing or routing; instead, it diffuses information across the network by updating each node’s data with a weighted average of its neighbors ’ data (they maintain the same data structure). At each step, every node can compute a local weighted least-squares estimate, which converges to the global maximum-likelihood solution. This scheme is robust to unreliable communication links. We show that it works in a network with dynamically changing topology, provided that the infinitely occurring communication graphs are jointly connected. I.

We consider a stochastic model for distributed average consensus, which arises in applications such as load balancing for parallel processors, distributed coordination of mobile autonomous agents, and network synchronization. In this model, each node updates its local variable with a weighted average of its neighbors ’ values, and each new value is corrupted by an additive noise with zero mean. The quality of consensus can be measured by the total mean-square deviation of the individual variables from their average, which converges to a steady-state value. We consider the problem of finding the (symmetric) edge weights that result in the least mean-square deviation in steady state. We show that this problem can be cast as a convex optimization problem, so the global solution can be found efficiently. We describe some computational methods for solving this problem, and compare the weights and the mean-square deviations obtained by this method and several other weight design methods.

Developing energy efficient strategies for the extraction, transmission, and dissemination of information is a core theme in wireless sensor network research. In this paper we present a novel system for decentralized data compression and predistribution. The system simultaneously computes random projections of the sensor data and disseminates them throughout the network using a simple gossiping algorithm. These summary statistics are stored in an efficient manner and can be extracted from a small subset of nodes anywhere in the network. From these measurements one can reconstruct an accurate approximation of the data at all nodes in the network, provided the original data is compressible in a certain sense which need not be known to the nodes ahead of time. The system provides a practical and universal approach to decentralized compression and content distribution in wireless sensor networks. Two example applications, network health monitoring and field estimation, demonstrate the utility of our method.

A wireless sensor network consists of a large number of small, resource-constrained devices and usually operates in hostile environments that are prone to link and node failures. Computing aggregates such as average, minimum, maximum and sum is fundamental to various primitive functions of a sensor network like system monitoring, data querying, and collaborative information processing. In this paper we present and analyze a suite of randomized distributed algorithms to efficiently and robustly compute aggregates. Our Distributed Random Grouping (DRG) algorithm is simple and natural and uses probabilistic grouping to progressively converge to the aggregate value. DRG is local and randomized and is naturally robust against dynamic topology changes from link/node failures. Although our algorithm is natural and simple, it is nontrivial to show that it converges to the correct aggregate value and to bound the time needed for convergence. Our analysis uses the eigen-structure of the underlying graph in a novel way to show convergence and to bound the running time of our algorithms. We also present simulation results of our algorithm and compare its performance to various other known distributed algorithms. Simulations show that DRG needs much less transmissions than other distributed localized schemes.

We propose random distributed multiresolution representations of sensor network data, so that the most significant encoding coefficients are easily accessible by querying a few sensors, anywhere in the network. Less significant encoding coefficients are available by querying a larger number of sensors, local to the region of interest. Significance can be defined in a multiresolution way, without any prior knowledge of the source data, as global summaries versus local details. Alternatively, significance can be defined in a dataadaptive way, as large differences between neighboring data values. We propose a distributed encoding algorithm that is robust to arbitrary wireless communication connectivity graphs, where links can fail or change with time. This randomized algorithm allows distributed computation that does not require strict global coordination or awareness of network connectivity at individual sensors. Because computations involve sensors in local neighborhoods of the communication graph, they are communication-efficient. Our framework uses local interaction among sensors to enable flexible information retrieval at the global level.

This paper studies the consensus problem of multi-agent systems in an asynchronous framework. Under certain assumptions, the consensus protocol leads to stable behaviors even if the updating instants and sets of the agents are asynchronously determined. The model of asynchronous multi-agent systems encompasses those synchronous ones with various communication patterns, i.e., issues of directional, delayed, or failed communication can be addressed in the same framework. The asynchronous results in this paper thus shed new light on the synchronous results reported in the literature. In particular, synchronous protocols under dynamically changing interaction topologies can be seen as a special case of the asynchronous protocol where all communication delays are zero.

In this paper, we develop algorithms for distributed computation of averages of the node data over networks with bandwidth/power constraints or large volumes of data. Distributed averaging algorithms fail to achieve consensus when deterministic uniform quantization is adopted. We propose a distributed algorithm in which the nodes utilize probabilistically quantized information, i.e., dithered quantization, to communicate with each other. The algorithm we develop is a dynamical system that generates sequences achieving a consensus at one of the quantization values almost surely. In addition, we show that the expected value of the consensus is equal to the average of the original sensor data. We derive an upper bound on the mean square error performance of the probabilistically quantized distributed averaging (PQDA). Moreover, we show that the convergence of the PQDA is monotonic by studying the evolution of the minimum-length interval containing the node values. We reveal that the length of this interval is a monotonically non–increasing function with limit zero. We also demonstrate that all the node values, in the worst case, converge to the final two quantization bins at the same rate as standard unquantized consensus. Finally, we report the results of simulations conducted to evaluate the behavior and the effectiveness of the proposed algorithm in various scenarios.

Abstract—In this paper, we propose a decentralized sensor network scheme capable to reach a globally optimum maximum-likelihood (ML) estimate through self-synchronization of nonlinearly coupled dynamical systems. Each node of the network is composed of a sensor and a first-order dynamical system initialized with the local measurements. Nearby nodes interact with each other exchanging their state value, and the final estimate is associated to the state derivative of each dynamical system. We derive the conditions on the coupling mechanism guaranteeing that, if the network observes one common phenomenon, each node converges to the globally optimal ML estimate. We prove that the synchronized state is globally asymptotically stable if the coupling strength exceeds a given threshold. Acting on a single parameter, the coupling strength, we show how, in the case of nonlinear coupling, the network behavior can switch from a global consensus system to a spatial clustering system. Finally, we show the effect of the network topology on the scalability properties of the network, and we validate our theoretical findings with simulation results. Index Terms—Distributed consensus, distributed estimation, dynamical systems, sensor networks. I.

Given a network of processes where each node has an initial scalar value, we consider the problem of computing their average asymptotically using a distributed, linear iterative algorithm. At each iteration, each node replaces its own value with a weighted average of its previous value and the values of its neighbors. We introduce the Metropolis weights, a simple choice for the averaging weights used in each step. We show that with these weights, the values at every node converge to the average, provided the infinitely occurring communication graphs are jointly connected.

The problem of distributed consensus has recently received a lot of attention, particularly in the framework of ad hoc sensor networks. The average consensus problem in the distributed signal processing context is addressed by linear iterative algorithms, with asymptotic convergence to the consensus. The convergence of the average consensus for an arbitrary weight matrix satisfying the convergence conditions is unfortunately slow refraining the use of the developed algorithms in applications. In this paper, we propose the use of extrapolation methods in order to accelerate distributed linear iterations. We utilize a linear operator to predict the future node state values and then combine the prediction with the current node state value in a convex fashion driving overall system state closer to the true consensus value faster than the standard consensus algorithms. A faster convergence is, hence, achieved by the bypassing of redundant states. The proposed method is linear and computationally effective. We focus on a special case of the proposed framework and derive the optimal mixing parameter. Noting that the optimal mixing parameter requires knowledge about the eigenvalues of the arbitrary weight matrix, we present a bound on the optimal parameter requiring only local information, and prove the validity of the suboptimal solution in the practical cases by showing that its performance is close–to–optimal and it is feasible in practical scenarios. Finally, we provide simulation results that demonstrate the validity and effectiveness of the proposed scheme. These results also indicate that in general situation the consensus based on the proposed approach significantly outperforms the optimum algorithm based on weight matrix optimization relying on semidefinite programming paradigm. Index Terms distributed signal processing, average consensus, linear prediction. 2 I.