Consistent identification of dynamic networks subject to white noise using Weighted Null-Space Fitting

Identification of dynamic networks has been a flourishing area in recent years. However, there are few contributions addressing the problem of simultaneously identifying all modules in a network of given structure. In principle the prediction error method can handle such problems but this methods suffers from well known issues with local minima and how to find initial parameter values. Weighted Null-Space Fitting is a multi-step least-squares method and in this contribution we extend this method to rational linear dynamic networks of arbitrary topology with modules subject to white noise disturbances. We show that WNSF reaches the performance of PEM initialized at the true parameter values for a fairly complex network, suggesting consistency and asymptotic efficiency of the proposed method.