Parametric frequency domain identification of a time-varying system as a time-dependent weighted sum of time-invariant systems

A frequency domain, parametric identification procedure for single-input, single output time-varying systems is presented. The output of the model is built as a time-varying weighted sum of the responses of linear time-invariant systems. A judicious choice of the weighting functions is shown to provide an intuitive insight into the evolution of the instantaneous transfer function with time. Results of previous work are used to obtain non-parametric initial estimates of both the time-varying dynamics and the disturbing noise characteristics from the response of the system to a multisine excitation. The maximum likelihood estimator is set up and a minimization algorithm is developed. The estimator is applied to a simulation example and a measurement example (electronic circuit) which approximates the model assumptions.