Nonparametric modelling of a linear time varying system

The paper studies the frequency response estimation of a time varying system. The system is a sum of two parallel branches, one being a linear time invariant (LTI) branch and the other an LTI followed by a time-varying gain. A method is presented that shows how such a system can be modelled nonparametrically and gives estimates for the frequency response functions when excited by an arbitrary input signal. The frequency response of a linear system and the transient error that arise when using arbitrary signals to model the input-output behaviour are smooth functions of frequency. By a polynomial approximation of the functions and considering the time varying effect, a model that is linear in the parameters is obtained. The method is evaluated on a simulated system showing the level of the modelling error, along with the estimated frequency responses, their variances and the variance of any disturbing noise at the output.