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Diffusion adaptation techniques have shown great promise in addressing the problem of node-specific distributed estimation where the nodes in the network are interested in different, possibly overlapping, sets of parameters. In this work, node-specific distributed detection, which has remained largely unexamined, is considered. In particular, the problem is formulated as one of binary hypothesis testing at each node for each of its parameters of interest. A distributed, online solution for this problem is sought based on diffusion adaptation techniques. In this setting, a signal to be detected by one node constitutes interference that may compromise the ability of the other nodes to detect their signals of interest reliably. Under mild assumptions on the data and network, it is shown that, for sufficiently small adaptation step-sizes, interference can be kept in check. Local detectors are developed where the test-statistics and thresholds adapt to changing conditions in real time. The distributed algorithm is analyzed; and its detection performance characterized and illustrated through numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract: The Fiedler vector of a graph is the eigenvector corresponding to the smallest non-trivial eigenvalue of the graph''s Laplacian matrix. The entries of the Fiedler vector are known to provide a powerful heuristic for topology inference, e.g., to identify densely connected node clusters, to search for bottleneck links in the information dissemination, or to increase the overall connectivity of the network. In this paper, we consider ad hoc networks where the nodes can process and exchange data in a synchronous fashion, and we propose a distributed algorithm for in-network estimation of the Fiedler vector and the algebraic connectivity of the corresponding network graph. The algorithm is fully scalable with respect to the network size in terms of per-node computational complexity and data transmission. Simulation results demonstrate the performance of the algorithm. [Copyright &y& Elsevier]

In this paper, we consider the linearly constrained distributed adaptive node-specific signal estimation (LC-DANSE) algorithm, which generates a node-specific linearly constrained minimum variance (LCMV) beamformer, i.e., with node-specific linear constraints, at each node of a wireless sensor network. The algorithm significantly reduces the number of signals that are exchanged between nodes, and yet obtains the optimal LCMV beamformers as if each node has access to all the signals in the network. We consider the case where all the steering vectors are known, as well as the blind beamforming case where the steering vectors are not known. We formally prove convergence and optimality for both versions of the LC-DANSE algorithm. We also consider the case where nodes update their local beamformers simultaneously instead of sequentially, and we demonstrate by means of simulations that applying a relaxation is often required to obtain a converging algorithm in this case. We also provide simulation results that demonstrate the effectiveness of the algorithm in a realistic speech enhancement scenario. [ABSTRACT FROM PUBLISHER]

Total least squares (TLS) is a popular solution technique for overdetermined systems of linear equations, where both the right-hand side and the input data matrix are assumed to be noisy. We consider a TLS problem in an ad hoc wireless sensor network, where each node collects observations that yield a node-specific subset of linear equations. The goal is to compute the TLS solution of the full set of equations in a distributed fashion, without gathering all these equations in a fusion center. To facilitate the use of the dual-based subgradient algorithm (DBSA), we transform the TLS problem to an equivalent convex semidefinite program (SDP), based on semidefinite relaxation (SDR). This allows us to derive a distributed TLS (D-TLS) algorithm, that satisfies the conditions for convergence of the DBSA, and obtains the same solution as the original (unrelaxed) TLS problem. Even though we make a detour through SDR and SDP theory, the resulting D-TLS algorithm relies on solving local TLS-like problems at each node, rather than computationally expensive SDP optimization techniques. The algorithm is flexible and fully distributed, i.e., it does not make any assumptions on the network topology and nodes only share data with their neighbors through local broadcasts. Due to the flexibility and the uniformity of the network, there is no single point of failure, which makes the algorithm robust to sensor failures. Monte Carlo simulation results are provided to demonstrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]