A Bias-Eliminated Subspace Identification Method for Errors-in-Variables Systems

For model identification of industrial operating systems subject to noisy input-output observations, known as the error-in-variables (EIV) problem, a subspace identification method is proposed in this paper by developing an orthogonal projection approach to guarantee consistent estimation of the deterministic part of such a system. The rank condition for such orthogonal projection is analyzed in terms of the nominal state-space model structure. Using the principal component analysis (PCA), the extended observability matrix and low triangular block-Toeliptz matrix of the state-space model are analytically derived. Accordingly, the system state-space matrices can be retrieved in a transparent manner from the above matrices through linear algebra or an ordinary least-squares (LS) algorithm. A benchmark example used in the existing references is adopted to demonstrate the effectiveness and merit of the proposed subspace identification method.