Noise reduction in the swept sine identification procedure of nonlinear systems

The Hammerstein model identification technique based on swept sine excitation signals proved in numerous applications to be particularly effective for the definition of a model for non-linear systems. In this paper we address the problem of the robustness of this model parameter estimation procedure in the presence of noise in the measurement step. The relationship between the different functions that enter the identification procedure is analyzed to assess how the presence of additive noise affects model parameters estimation. This analysis allows us to propose an original technique to mitigate the effects of additive noise in order to improve the accuracy of model parameters estimation. The different aspects addressed in the paper and the technique for mitigating the effects of noise on the accuracy of parameter estimation are verified on both synthetic and experimental data acquired with an ultrasonic system. The results of both simulations and experiments on laboratory data confirm the correctness of the assumptions made and the effectiveness of the proposed mitigation methodology.