Estimating a Nonparametric Colored-Noise Model for Linear Slowly Time-Varying Systems

This paper proposes a methodology to easily extract some valuable nonparametric information on linear slowly time-varying systems, which have been excited by multisines. More specifically, it is first explained how time-varying systems behave when excited by multisines and how a rough nonparametric idea of the speed of variation of the instantaneous frequency response function is estimated. Second, a nonparametric model of the disturbing colored noise on the measured input and output signals is estimated. The methodology circumvents the need for repeated experiments, which are, for time-varying systems, usually difficult to perform. The estimation of the disturbing noise is mandatory when identifying dynamic systems within an errors-in-variables framework. The estimated noise model is intended for system identification performed in the frequency domain, where a nonparametric noise model is easily implemented. The noise model is estimated independently of the parameters of the time-varying system under consideration. The estimate of the speed of variation of the instantaneous frequency response function gives some insight into the measured system. It might actually provide an idea of which poles or zeros are actually moving and which are not.