Identification of dynamic networks with rank-reduced process noise

In dynamic network identification usually the assumption is made that there is a full rank process noise affecting the network. For large scale networks with many variables this assumption is not realistic as the noise could be generated by a limited number of sources. We extend prediction error identification methods by allowing rank-reduced process noise in the network. The developed method is based on a modification of the typical predictor expression and an appropriate modification of the identification criterion. It is shown that this method leads to consistent estimates, and we provide a method to reduce the variance of the estimates, which is confirmed by simulations.