Nonparametric estimation of the instantaneous transfer function of linear periodically time-varying systems excited by arbitrary signals

Recently, a nonparametric identification scheme was developed to achieve high quality estimates of the evolution of the time-varying dynamics of continuous-time periodically time-varying systems (PTV). The method was founded upon a local polynomial approximation of the harmonic transfer functions using a single experiment, and this within an output-error framework. The proposed method imposes restrictions on the type of input (i.e. a broad band periodic signal), which could be a limitation in certain applications, especially where the user is not able to impose the type of excitation signal. In this work, this assumption is relaxed, such that the methodology presented here allows for arbitrary inputs as long as its power spectrum is band-limited. On top of that, we assume that an integer number of periods of the time-variation are observed. Due to the non-periodicity of the input-output a transient term will pop up in the expression of the frequency domain model which can also locally be very well described by a polynomial. The price being paid to relax the assumption to arbitrary inputs is that we can no longer distinguish the nonlinear distortions from the noise disturbances if the system behaves to some extent nonlinearly. Therefore, in this paper we restrict ourselves to linear PTV systems. The identification scheme is supported by simulations and real measurements to show the robustness of the proposed method.