A unified framework for EIV identification methods when the measurement noises are mutually correlated

In this paper, the previously introduced Generalized Instrumental Variable Estimator (GIVE) is extended to the case of errors-in-variables models where the additive input and output noises are mutually correlated white processes. It is shown how many estimators proposed in the literature can be described as various special cases of a generalized instrumental variable framework. It is also investigated how to analyze the common situation where some of the equations that define the estimator are to hold exactly, and others to hold approximately in a least squares sense, providing a detailed study of the accuracy analysis.