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arXiv · 1711.06369

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

Harm H. M. Weerts·Paul M. J. Van den Hof·Arne G. Dankers
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Abstract

Dynamic networks are interconnected dynamic systems with measured node signals and dynamic modules reflecting the links between the nodes. We address the problem of \red{identifying a dynamic network with known topology, on the basis of measured signals}, for the situation of additive process noise on the node signals that is spatially correlated and that is allowed to have a spectral density that is singular. A prediction error approach is followed in which all node signals in the network are jointly predicted. The resulting joint-direct identification method, generalizes the classical direct method for closed-loop identification to handle situations of mutually correlated noise on inputs and outputs. When applied to general dynamic networks with rank-reduced noise, it appears that the natural identification criterion becomes a weighted LS criterion that is subject to a constraint. This constrained criterion is shown to lead to maximum likelihood estimates of the dynamic network and therefore to minimum variance properties, reaching the Cramer-Rao lower bound in the case of Gaussian noise.

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Harm H. M. Weerts, Paul M. J. Van den Hof, Arne G. Dankers. 2017-11-17. Prediction error identification of linear dynamic networks with rank-reduced noise. https://doi.org/10.1016/j.automatica.2018.09.033

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