  In this article, we present a method to learn the interaction topology of a
network of agents undergoing linear consensus updates in a non invasive manner.
Our approach is based on multivariate Wiener filtering, which is known to
recover spurious edges apart from the true edges in the topology. The main
contribution of this work is to show that in the case of undirected consensus
networks, all spurious links obtained using Wiener filtering can be identified
using frequency response of the Wiener filters. Thus, the exact interaction
topology of the agents is unveiled. The method presented requires time series
measurements of the state of the agents and does not require any knowledge of
link weights. To the best of our knowledge this is the first approach that
provably reconstructs the structure of undirected consensus networks with
correlated noise. We illustrate the effectiveness of the method developed
through numerical simulations as well as experiments on a five node network of
Raspberry Pis.
