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For identification of systems embedded in dynamic networks, applying theprediction error method (PEM) to a correct tailor-made parametrization of thecomplete network provided asymptotically efficient estimates. However, thenetwork complexity often hinders a successful application of PEM, whichrequires minimizing a non-convex cost function that in general becomes moredifficult for more complex networks. For this reason, identification in dynamicnetworks often focuses in obtaining consistent estimates of particular networkmodules of interest. A downside of such approaches is that splitting thenetwork in several modules for identification often costs asymptoticefficiency. In this paper, we consider the particular case of a dynamic networkwith the individual systems connected in a serial cascaded manner, withmeasurements affected by sensor noise. We propose an algorithm that estimatesall the modules in the network simultaneously without requiring theminimization of a non-convex cost function. This algorithm is an extension ofWeighted Null-Space Fitting (WNSF), a weighted least-squares method thatprovides asymptotically efficient estimates for single-input single-outputsystems. We illustrate the performance of the algorithm with simulationstudies, which suggest that a network WNSF may also be asymptotically efficientestimates when applied to cascade networks, and discuss the possibility ofextension to more general networks affected by sensor noise.

Weighted Null-Space Fitting for Identification of Cascade Networks