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Dynamic networks are interconnected dynamic systems with measured nodesignals and dynamic modules reflecting the links between the nodes. We addressthe problem of \red{identifying a dynamic network with known topology, on thebasis of measured signals}, for the situation of additive process noise on thenode signals that is spatially correlated and that is allowed to have aspectral density that is singular. A prediction error approach is followed inwhich all node signals in the network are jointly predicted. The resultingjoint-direct identification method, generalizes the classical direct method forclosed-loop identification to handle situations of mutually correlated noise oninputs and outputs. When applied to general dynamic networks with rank-reducednoise, it appears that the natural identification criterion becomes a weightedLS criterion that is subject to a constraint. This constrained criterion isshown to lead to maximum likelihood estimates of the dynamic network andtherefore to minimum variance properties, reaching the Cramer-Rao lower boundin the case of Gaussian noise.

Prediction error identification of linear dynamic networks with rank-reduced noise