Silvana Silva Pereira

Mean Square Convergence of Consensus Algorithms in Random WSNs

Distributed consensus algorithms for estimation of parameters or detection of events in wireless sensor networks have attracted considerable attention in recent years. A necessary condition to achieve a consensus on the average of the initial values is that the topology of the underlying graph is balanced or symmetric at every time instant. However, communication impairments can make the topology vary randomly in time, and instantaneous link symmetry between pairs of nodes is not guaranteed unless an acknowledgment protocol or an equivalent approach is implemented. In this paper, we evaluate the convergence of the consensus algorithm in the mean square sense in wireless sensor networks with random asymmetric topologies. For the case of links with equal probability of connection, a closed form expression for the mean square error of the state along with the dynamical range and the optimum value of the link weights that guarantee convergence are derived. For the case of links with different probabilities of connection, an upper bound for the mean square error of the state is derived. This upper bound can be computed for any time instant and can be employed to compute a link weight that reduces the convergence time of the algorithm.

A Diffusion-Based EM Algorithm for Distributed Estimation in Unreliable Sensor Networks

We address the problem of distributed estimation of a parameter from a set of noisy observations collected by a sensor network, assuming that some sensors may be subject to data failures and report only noise. In such scenario, simple schemes such as the Best Linear Unbiased Estimator result in an error floor in moderate and high signal-to-noise ratio (SNR), whereas previously proposed methods based on hard decisions on data failure events degrade as the SNR decreases. Aiming at optimal performance within the whole range of SNRs, we adopt a Maximum Likelihood framework based on the Expectation-Maximization (EM) algorithm. The statistical model and the iterative nature of the EM method allow for a diffusion-based distributed implementation, whereby the information propagation is embedded in the iterative update of the parameters. Numerical examples show that the proposed algorithm practically attains the Cramer-Rao Lower Bound at all SNR values and compares favorably with other approaches.

Consensus in Correlated Random Wireless Sensor Networks

This contribution studies the convergence of consensus algorithms in random wireless sensor networks with spatially correlated links. Aiming at reducing the convergence time, we adopt an optimization criterion based on the minimization of the spectral radius of a matrix for which we derive closed-form expressions for both directed and undirected topologies. We show that the minimization of the spectral radius assuming constant link weights is a convex optimization problem. The expressions derived subsume known protocols found in literature.

A diffusion-based distributed em algorithm for density estimation in wireless sensor networks

Distributed implementations of the Expectation-Maximization (EM) algorithm reported in literature have been proposed for applications to solve specific problems. In general, a primary requirement to derive a distributed solution is that the structure of the centralized version enables the computation involving global information in a distributed fashion. This paper treats the problem of distributed estimation of Gaussian densities by means of the EM algorithm in wireless sensor networks using diffusion strategies, where the information is gradually diffused across the network for the computation of the global functions. The low-complexity implementation presented here is based on a two time scale operation for information averaging and diffusion. The convergence to a fixed point of the centralized solution has been studied and the appealing results motivates our choice for this model. Numerical examples provided show that the performance of the distributed EM is, in practice, equal to that of the centralized scheme.

Distributed consensus in wireless sensor networks with quantized information exchange

In this paper we analyze the impact of quantization on the performance of a discrete-time distributed algorithm aimed at computing the average of an initial set of values in a wireless sensor network. We modify a well-known consensus model and propose a simple scheme where the transmitted data is quantized due to bandwith and/or power constraints. Conversely to existing models that include quantization noise, a closed-form expression for the residual mean square error of the state can be derived for the proposed model. This expression depends on general network parameters and provides therefore an a priori quantitative measure of the effects of quantization on the consensus.

Distributed Total Least Squares estimation over networks

We consider Total Least Squares (TLS) estimation in a network in which each node has access to a subset of equations of an overdetermined linear system. Previous distributed approaches require that the number of equations at each node be larger than the dimension L of the unknown parameter. We present novel distributed TLS estimators which can handle as few as a single equation per node. In the first scheme, the network computes an extended correlation matrix via standard iterative average consensus techniques, and the TLS estimate is extracted afterwards by means of an eigenvalue decomposition (EVD). The second scheme is EVD-free, but requires that a linear system of size L be solved at each iteration by each node. Replacing this step by a single Gauss-Seidel subiteration is shown to be an effective means to reduce computational cost without sacrificing performance.

Fast mean square convergence of consensus algorithms in WSNs with random topologies

The average consensus in wireless sensor networks is achieved under assumptions of symmetric or balanced topology at every time instant. However, communication and/or node failures, as well as node mobility or changes in the environment make the topology vary in time, and instantaneous symmetry of the links is not guaranteed unless an acknowledgment protocol or an equivalent approach is implemented. In this paper, we evaluate the convergence in the mean square sense of a well-known consensus algorithm assuming a random topology and asymmetric communication links. A closed form expression for the mean square error of the state is derived as well as the optimum choice of parameters to guarantee fastest convergence of the mean square error.

Consensus for distributed EM-based clustering in WSNs

A distributed EM algorithm with consensus is proposed for density estimation and clustering using WSNs in the presence of mixtures of Gaussians. The EM algorithm is a general framework for maximum likelihood estimation in hidden variable models, usually implemented in a central node with global information of the network. The average consensus algorithm is a simple robust scheme for computing averages in a distributed manner. In this contribution, we run a distributed EM algorithm where the nodes obtain global knowledge of the statistics through consensus with local information exchange only in a WSN with instantaneous random links. Starting from a set of initial values, the nodes are able to compute the complete statistics of a mixture of Gaussians and classify into clusters according to the sensed density using a simple decision rule. A trade off between power consumption and final accuracy of the estimates is established through simulations.

Distributed AOA-based source positioning in NLOS with sensor networks

This paper focuses on the problem of positioning a source using angle-of-arrival measurements taken by a wireless sensor network in which some of the nodes experience non line-of-sight (LOS) propagation conditions. In order to mitigate the errors induced by the nodes in NLOS, we derive an algorithm that combines the expectation-maximization algorithm with a weighted least-squares estimation of the source position so that the nodes in NLOS are eventually identified and discarded. Moreover, a distributed version of this algorithm based on a diffusion strategy that iteratively refines the position estimate while driving the network to a consensus is presented.

How to implement doubly-stochastic matrices for consensus-based distributed algorithms

Doubly-stochastic matrices are usually required by consensus-based distributed algorithms. We propose a simple and efficient protocol and present some guidelines for implementing doubly-stochastic combination matrices even in noisy, asynchronous and changing topology scenarios. The proposed ideas are validated with the deployment of a wireless sensor network, in which nodes run a distributed algorithm for robust estimation in the presence of nodes with faulty sensors.