Bias-eliminating least-squares identification of errors-in-variables models with mutually correlated noises

This paper proposes a bias-eliminating least-squares (BELS) approach for identifying linear dynamic errors-in-variables (EIV) models whose input and output are corrupted by additive white noise. The method is based on an iterative procedure involving, at each step, the estimation of both the system parameters and the noise variances. The proposed identification algorithm differs from previous BELS algorithms in two aspects. First, the input and output noises are allowed to be mutually correlated, and second, the estimation of the noise covariances is obtained by exploiting the statistical properties of the equation error of the EIV model.