An exposition of strongly consistent parameter estimation by strong istrumental variables

This paper discusses 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 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.