  Identification methods for dynamic networks typically require prior knowledge
of the network and disturbance topology, and often rely on solving poorly
scalable non-convex optimization problems. While methods for estimating network
topology are available in the literature, less attention has been paid to
estimating the disturbance topology, i.e., the (spatial) noise correlation
structure and the noise rank in a filtered white noise representation of the
disturbance signal. In this work we present an identification method for
dynamic networks, in which an estimation of the disturbance topology precedes
the identification of the full dynamic network with known network topology. To
this end we extend the multi-step Sequential Linear Regression and Weighted
Null Space Fitting methods to deal with reduced rank noise, and use these
methods to estimate the disturbance topology and the network dynamics in the
full measurement situation. As a result, we provide a multi-step least squares
algorithm with parallel computation capabilities and that rely only on explicit
analytical solutions, thereby avoiding the usual non-convex optimizations
involved. Consequently we consistently estimate dynamic networks of Box Jenkins
model structure, while keeping the computational burden low. We provide a
consistency proof that includes path-based data informativity conditions for
allocation of excitation signals in the experimental design. Numerical
simulations performed on a dynamic network with reduced rank noise clearly
illustrate the potential of this method.
