Distributed adaptive eigenvector estimation of the sensor signal covariance matrix in a fully connected sensor network

In this paper, we describe a distributed adaptive (time-recursive) algorithm to estimate and track the eigenvectors corresponding to the Q largest or smallest eigenvalues of the global sensor signal covariance matrix in a wireless sensor network (WSN). We only address the case of fully connected (broadcast) networks, in which the nodes broadcast compressed Q-dimensional sensor observations. It can be shown that the algorithm converges to the desired eigenvectors without explicitely constructing the global covariance matrix that actually defines them, i.e., without the need to centralize all the raw sensor observations. The algorithm allows each node to estimate (a) the node-specific entries of the global covariance matrix eigenvectors, and (b) Q-dimensional observations of the full set of sensor observations projected onto the Q estimated eigenvectors. The theoretical results are validated by means of numerical simulations.