Noisy data-driven identification for errors-in-variables MISO Hammerstein nonlinear models

In this paper, we consider a multiple-input single-output (MISO) Hammerstein system whose inputs and output are disturbed by unknown Gaussian white measurement noises. The parameter estimation of such a system is a typical errors-in-variables (EIV) nonlinear system identification problem. This paper proposes a bias-correction least squares (BCLS) identification methods to compute a consistent estimate of EIV MISO Hammerstein systems from noisy data. To obtain the unbiased parameter estimates of EIV MISO Hammerstein system, the analytical expression of estimated bias for the standard least squares (LS) algorithm is derived first, which is a function about the variances of noises. And then a recursive algorithm is proposed to estimate the unknown term of noises variances from noisy data. Finally, based on bias estimation scheme, the bias caused by the correlation between the input-output signals exciting the true system and the corresponding measurement noise, resulting in unbiased parameter estimates of the EIV MISO Hammerstein system. The performance of the proposed method is demonstrated through a simulation example and a chemical continuously stirred tank reactor (CSTR) system.