Estimation of impulse response functions in two-output systems

Abstract

A single input–double output (SIDO) linear time-invariant (LTI) system is considered, whose impulse response function (IRF) is assumed to have one unknown component. The problem is to estimate this unknown component after observations of the second component. Both IRF’s components are supposed to be L₂-integrable, and the estimation is made by cross-correlating the outputs, given that the input is a standard Wiener process on R. Weak asymptotic normality of appropriately centred estimators is proved.