Strongly consistent parameter estimation by the introduction of strong instrumental variables
Brain Finigan, Ian H. Rowe · IEEE Transactions on Automatic Control · 1974
This paper introduces the concept of strong instrumental variables and strong instrumental matrix sequences for the estimation of the transfer function parameters of discrete-time, time-invariant models of linear systems. It is shown that the strong instrumental variable estimators are strongly consistent and a sufficient condition for the estimator to be asymtotically unbiased is given. Moreover, it is shown that with a persistently exciting signal of appropriate order for an input, "virtually" any discrete-time, time-invariant, linear system model of appropriate order can be used to generate strong instrumental variables.