  In this paper, single input--double output linear time-invariant systems are
studied. Both components of system's impulse response function (IRF) are
supposed to be real-valued and square-integrable. One component is unknown
while the second one is controlled. The problem is to estimate the unknown
component after observations of the other component. We apply cross-correlating
of the outputs given that the input is a standard Wiener process. Weak
asymptotic normality of appropriately centred estimators in spaces of
continuous functions is proved. This enables us to construct confidence
intervals in these spaces. Our results employ techniques related to Gaussian
processes and bilinear forms of Gaussian processes.
