Strongly consistent parameter estimation by the introduction of strong instrumental variables

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.