A generalised instrumental variable estimator for multivariable errors-in-variables identification problems

A new and very general estimation method, the generalised instrumental variable estimator (GIVE) has been introduced to deal with the errors-in-variables identification. The GIVE contains several well-known estimation methods as special cases that can be obtained by various user choices in GIVE. These methods include the bias-eliminating least squares method, a number of different versions of the Frisch scheme and the extended compensated least squares method. This article shows how previous analysis for single-input single-output systems can be extended in a non-trivial way to also cope with multi-input multi-output systems. Various computational aspects of GIVE are presented, and it is shown how the parameter estimates can be computed in an efficient way. The asymptotic distribution of the parameter estimates is also derived and analysed.