Errors-in-variables identification of dynamic systems excited by arbitrary non-white input

This work deals with the identification of dynamic systems from noisy input–output observations, where the noise-free input is not parameterized. The basic assumptions made are (1) the dynamic system can be modeled by a (discrete- or continuous-time) rational transfer function model, (2) the temporal input–output disturbances are mutually independent, identically distributed noises, and (3) the input power spectrum is non-white (not necessarily rational) and is modeled nonparametrically. The system identifiability is guaranteed by exploiting the non-white spectrum property of the noise-free input. A frequency domain identification strategy is developed to estimate consistently the plant model parameters and the input–output noise variances. The uncertainty bound of the estimates is calculated and compared to the Cramér–Rao lower bound. The efficiency of the proposed algorithm is illustrated on numerical examples.