## 1 Introduction
Processing this output signal allows to identify the parameters of the model, as will be detailed in the following sections. An aspect of this technique, which is of great importance in practical applications, but which has been only partially addressed in the technical literature, is the analysis of the effects of noise that inevitably adds to the useful signal in the acquisition step of the identification procedure. The problem has been addressed in some particular cases such as in [17], where an iterative procedure for the identification of the Hammerstein model is defined in the particular case in which the noise, added to the useful signal at the output of the system to be identified, can be modeled as a correlated noise, assumed to be the output of a digital filter with a zero mean random sequence as input. In [18], a protocol is proposed to determine the location of the process noise in a Wiener-Hammersstein system with respect to the static nonlinearity by using a periodic, nonstationary input test signal. Hypothesizing the location of the process noise is addressed as a preliminary step in order to improve the successive model identification. In [19], the hypothesis that damage causes the structure to exhibit a nonlinear response is tested, and thus the use of Nonlinear Model Based Features is shown to increase classification performance: although the study does not directly analyze the effects of measurement noise in the model identification phase, it evaluates the performance degradation of the classification procedure in the presence of noise added to the measured signals at the output of the system under study. In [20], the identification of the nonlinear model is considered in the presence of uncertainties: Under the assumption of stationarity of the system to be modeled, the effect of uncertainties is reduced by using repetitions of the input swept sine signal, which is repeated several times in order to excite the system with a pseudo periodic signal; a period synchronized with the duration of the swept sine signal is adopted to simplify the implementation. [PERSON] and [PERSON] in [21] compare two methodologies of identification of the Hammerstein model by evaluating, for both, specific performance indexes on systems defined as bench test, and in the presence of noise. In the present paper we deal with the problem of the accuracy in the identification of the Hammerstein model using the identification technique based on exponential swept sine test signals. We consider the presence of noise that is added to the useful signal when measuring the response of the nonlinear system. In the paper we propose an original analysis of the link that exists between the environmental noise superimposed on the measurement result and the uncertainty in the estimation of the kernels that identify the Hammerstein model in the case that the identification technique is based on exponential swept sine signals. This original analysis, besides clarifying the connection between the presence of measurement noise and the uncertainties in the estimation of the different parameters characterizing the identification procedure, represents the basis to define a novel technique, that we propose in the paper, to mitigate the effects of the superimposed noise on the quality of the estimation of the parameters that identify the model. The technique we propose is based on the use of lowpass filters, each designed to operate on one of the kernels, characterizing the different branches of the Hammerstein model. The different aspects of the uncertainty reduction procedure are verified both on synthetic data and in an experimental case. The latter is an ultrasonic measurement setup with transducers operating in air, chosen because the possible effects due to measurement noise are particularly relevant: The limited impedance matching and the attenuation due to air propagation make this an experimental setup where the signal-to-noise ratio can degrade significantly.