System identification for the errors-in-variables problem

In this paper we give an overview of errors-in-variables methods in system identification. Background and motivation are given. Simple examples illustrate why the identification problem can be difficult. Under general weak assumptions, the systems are not uniquely identifiable, but can be parameterized using one degree of freedom. Examples where identifiability is achieved under additional assumptions are also provided. A number of approaches for parameter estimation of errors-in-variables models are presented. The underlying assumptions and principles for each approach are highlighted.