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

TL;DR

This paper develops a joint prediction error identification method for linear dynamic networks with spatially correlated, rank-reduced noise, achieving maximum likelihood estimates and minimum variance properties.

Contribution

It generalizes classical direct methods to handle correlated, rank-reduced noise in dynamic networks, providing a constrained weighted least squares criterion.

Findings

The method yields maximum likelihood estimates.

It reaches the Cramer-Rao lower bound with Gaussian noise.

The approach handles singular spectral densities of noise.

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.