Non-parametric estimate of the system function of a time-varying system

The task of identifying an unknown dynamic system is made easier with prior knowledge on its behaviour. Using a frequency domain approach, the non-parametric maximum likelihood estimator of the system function, associated with the time-dependent impulse response of a time-varying system, is constructed. This is accomplished by the use of a simple linear least squares fitting algorithm, applied to the spectral response of the system to a multisine excitation. The noise variance on the system function is estimated simultaneously, and modelling errors can be detected, as illustrated on a simulation example.