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Abstract: We describe a distributed adaptive algorithm to estimate the eigenvectors corresponding to the Q largest or smallest eigenvalues of the network-wide sensor signal covariance matrix in a wireless sensor network. The proposed algorithm recursively updates the eigenvector estimates without explicitly constructing the full covariance matrix that defines them, i.e., without centralizing all the raw sensor signal observations. By only sharing fused Q-dimensional observations, each node obtains estimates of (a) the node-specific entries of the Q covariance matrix eigenvectors, and (b) Q-dimensional projections of the full set of sensor signal observations onto the Q eigenvectors. We also explain how the latter can be used for, e.g., compression and reconstruction of the sensor signal observations based on principal component analysis (PCA), in which each node acts as a data sink. We describe a version of the algorithm for fully-connected networks, as well as for partially-connected networks. In the latter case, we assume that the network has been pruned to a tree topology to avoid cycles in the network. We provide convergence proofs, as well as numerical simulations to demonstrate the convergence and optimality of the algorithm. [Copyright &y& Elsevier]

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]

Abstract: In this paper, we consider distributed signal estimation in sensor networks where the nodes exchange compressed sensor signal observations to estimate different node-specific signals. In particular, we revisit the so-called distributed adaptive node-specific signal estimation (DANSE) algorithm, which applies to the case where the nodes share a so-called ‘common interest’, and cast it in the more general setting where the nodes have ‘different interests’. We prove existence of an equilibrium state for such a setting by using a result from fixed point theory. By establishing a link between the DANSE algorithm and game theory, we point out that any equilibrium of the DANSE algorithm is a Nash equilibrium of the corresponding game. This provides an intuitive interpretation to the resulting signal estimators. The equilibrium state existence proof also reveals a problem with discontinuities in the DANSE update function, which may result in non-convergence of the algorithm. However, since these discontinuities are identifiable, they can easily be avoided by applying a minor heuristic modification to the algorithm. We demonstrate the effectiveness of this modification by means of numerical examples. [Copyright &y& Elsevier]

Abstract: A wireless sensor network is envisaged that performs signal estimation by means of the distributed adaptive node-specific signal estimation (DANSE) algorithm. This wireless sensor network has constraints such that only a subset of the nodes are used for the estimation of a signal. While an optimal node selection strategy is NP-hard due to its combinatorial nature, we propose a greedy procedure that can add or remove nodes in an iterative fashion until the constraints are satisfied based on their utility. With the proposed definition of utility, a centralized algorithm can efficiently compute each nodes's utility at hardly any additional computational cost. Unfortunately, in a distributed scenario this approach becomes intractable. However, by using the convergence and optimality properties of the DANSE algorithm, it is shown that for node removal, each node can efficiently compute a utility upper bound such that the MMSE increase after removal will never exceed this value. In the case of node addition, each node can determine a utility lower bound such that the MMSE decrease will always exceed this value once added. The greedy node selection procedure can then use these upper and lower bounds to facilitate distributed node selection. [Copyright &y& Elsevier]

Abstract: In this paper, we present an iterative method for estimation of pitches from signals containing multiple sources using subspace techniques. The resulting estimator is termed Iterative Harmonic MUltiple SIgnal Classification (I-HMUSIC). Different modifications of I-HMUSIC are proposed that improve upon the classical MUSIC algorithm, including a computationally efficient method for noise subspace updating I-HMUSIC and its modifications are evaluated and compared with both the Cramér–Rao lower bound (CRLB) and non-iterative HMUSIC; good statistical performances have been obtained. [Copyright &y& Elsevier]