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We consider a multi-task wireless sensor network (WSN) where some of the nodes aim at applying a multi-channel Wiener filter to denoise their local sensor signals, whereas others aim at implementing a linearly constrained minimum variance beamformer to extract node-specific desired signals and cancel interfering signals, and again others aim at estimating the node-specific direction-of-arrival of a set of desired sources. For this multi-task WSN, by relying on distributed signal estimation techniques that incorporate a low-rank approximation of the desired signals correlation matrix, we design a distributed algorithm under which the nodes cooperate with reduced communication resources even though they are solving different signal processing tasks and do not know the tasks of the other nodes. Convergence and optimality results show that the proposed algorithm lets all the nodes achieve the network-wide centralized solution of their node-specific estimation problem. Finally, the algorithm is applied in a wireless acoustic sensor network scenario with multiple speech sources to show the effectiveness of the algorithm and support the theoretical results. [ABSTRACT FROM PUBLISHER]

In this paper, we address the problem of distributed adaptive estimation of node-specific signals for signal enhancement or noise reduction in wireless sensor networks with multi-sensor nodes. The estimation is performed by a multi-channel Wiener filter (MWF) in which a low-rank approximation based on a generalized eigenvalue decomposition (GEVD) is incorporated. In non-stationary or low-SNR conditions, this GEVD-based MWF has been demonstrated to be more robust than the original MWF. In a centralized realization where a fusion center has access to all the nodes’ sensor signal observations, the network-wide sensor signal correlation matrices and the low-rank approximation can be directly estimated and used to compute the network-wide GEVD-based MWF. However, in this paper, we aim to avoid centralizing the sensor signal observations, in which case the network-wide sensor signal correlation matrices cannot be estimated. To this end, we start from the so-called distributed adaptive node-specific signal estimation (DANSE) algorithm, and include GEVD-based low-rank approximations in the per-node local computations. Remarkably, the new algorithm is able to significantly compress the signal observations transmitted between the nodes, while still converging to the network-wide GEVD-based MWF as if each node would have access to all sensor signal observations, even though the low-rank approximations are applied locally at each node. We provide a theoretical convergence analysis, which shows that the algorithm converges to the network-wide GEVD-based MWF under conditions that are less strict than in the original DANSE algorithm. The convergence and performance of the algorithm are further investigated via numerical simulations. [ABSTRACT FROM AUTHOR]

Canonical correlation analysis (CCA) is a widely used data analysis tool that allows to assess the correlation between two distinct sets of signals. It computes optimal linear combinations of the signals in both sets such that the resulting signals are maximally correlated. The weight vectors defining these optimal linear combinations are referred to as “principal CCA directions”. In addition to this particular type of data analysis, CCA is also often used as a blind source separation (BSS) technique, i.e., under certain assumptions, the principal CCA directions have certain demixing properties. In this paper, we propose a distributed CCA (DCCA) algorithm that can operate in wireless sensor networks (WSNs) with a fully connected or a tree topology. The algorithm estimates the Q principal CCA directions from the sensor signal observations collected by the different nodes in the WSN and extracts the corresponding sources. These network-wide principal CCA directions are estimated in a time-recursive fashion without explicitly constructing the corresponding network-wide correlation matrices, i.e., without the need for data centralization. Instead, each node locally computes smaller CCA problems and only transmits compressed sensor signal observations (of dimension Q), which significantly reduces the bit rate over the wireless links of the WSN. We prove convergence and optimality of the DCCA algorithm, and we demonstrate its performance by means of numerical simulations in a blind source separation scenario. [ABSTRACT FROM AUTHOR]

The generalized eigenvalue decomposition (GEVD) of a pair of matrices generalizes the concept of the eigenvalue decomposition (EVD) of a single matrix. It is a widely used tool in signal processing applications, in particular in a context of spatial filtering and subspace estimation. In this paper, we describe a distributed adaptive algorithm to estimate generalized eigenvectors (GEVCs) of a pair of sensor signal covariance matrices in a fully connected wireless sensor network. The algorithm computes these GEVCs in an iterative fashion without explicitly constructing the full network-wide covariance matrices. Instead, the nodes only exchange compressed sensor signal observations, providing a significant reduction in per-node communication and computational cost compared to the scenario where all the raw sensor signal observations are collected and processed in a fusion center. [ABSTRACT FROM AUTHOR]

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]

Total least squares (TLS) estimation is a popular solution technique for overdetermined systems of linear equations with a noisy data matrix. In this paper, we revisit the distributed total least squares (D-TLS) algorithm, which operates in an ad hoc network, where each node has access to a subset of the linear equations. The D-TLS algorithm computes the TLS solution of the full system of equations in a fully distributed fashion (without fusion center). To reduce the large computational complexity due to an eigenvalue decomposition (EVD) at every node and in each iteration, we modify the D-TLS algorithm based on inverse power iterations (IPIs). In each step of the modified algorithm, a single IPI is performed, which significantly reduces the computational complexity. We show that this IPI-based D-TLS algorithm still converges to the network-wide TLS solution under certain assumptions, which are often satisfied in practice. We provide simulation results to demonstrate the convergence of the algorithm, even when some of these assumptions are not satisfied. [ABSTRACT FROM PUBLISHER]

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]

We study the problem of distributed least-squares estimation over ad hoc adaptive networks, where the nodes have a common objective to estimate and track a parameter vector. We consider the case where there is stationary additive colored noise on both the regressors and the output response, which results in biased local least-squares estimators. Assuming that the noise covariance can be estimated (or is known a priori), we first propose a bias-compensated recursive least-squares algorithm (BC-RLS). However, this bias compensation increases the variance or the mean-square deviation (MSD) of the local estimators, and errors in the noise covariance estimates may still result in residual bias. We demonstrate that the MSD and residual bias can then be significantly reduced by applying diffusion adaptation, i.e., by letting nodes combine their local estimates with those of their neighbors. We derive a necessary and sufficient condition for mean-square stability of the algorithm, under some mild assumptions. Furthermore, we derive closed-form expressions for its steady-state mean and mean-square performance. Simulation results are provided, which agree well with the theoretical results. We also consider some special cases where the mean-square stability improvement of diffusion BC-RLS over BC-RLS can be mathematically verified. [ABSTRACT FROM AUTHOR]

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]

We present a distributed adaptive node-specific signal estimation (DANSE) algorithm that operates in a wireless sensor network with a tree topology. The algorithm extends the DANSE algorithm for fully connected sensor networks, as described in previous work. It is argued why a tree topology is the natural choice if the network is not fully connected. If the node-specific desired signals share a common latent signal subspace, it is shown that the distributed algorithm converges to the same linear MMSE solutions as obtained with the centralized version of the algorithm. The computational load is then shared between the different nodes in the network, and nodes exchange only linear combinations of their sensor signal observations and data received from their neighbors. Despite the low connectivity of the network and the multi-hop signal paths, the algorithm is fully scalable in terms of communication bandwidth and computational power. Two different cases are considered concerning the communication protocol between the nodes: point-to-point transmission and local broadcasting. The former assumes that there is a reserved communication link between node-pairs, whereas with the latter, nodes communicate the same data to all of their neighbors simultaneously. The convergence properties of the algorithm are demonstrated by means of numerical examples. [ABSTRACT FROM AUTHOR]