Errors-in-variables identification in dynamic networks - consistency results for an instrumental variable approach

In this paper we consider the identification of a linear module that is embedded in a dynamic network using noisy measurements of the internal variables of the network. This is an extension of the errors-in-variables (EIV) identification framework to the case of dynamic networks. The consequence of measuring the variables with sensor noise is that some prediction error identification methods no longer result in consistent estimates. The method developed in this paper is based on a combination of the instrumental variable philosophy and closed-loop prediction error identification methods, and leads to consistent estimates of modules in a dynamic network. We consider a flexible choice of which internal variables need to be measured in order to identify the module of interest. This allows for a flexible sensor placement scheme. We also present a method that can be used to validate the identified model.