A closed-loop subspace identification method is proposed for industrial systems subject to noisy input-output observations

known as the error-in-variables (EIV) problem.Using the orthogonal projection approach to eliminate the noise influence

consistent estimation is guaranteed for the deterministic part of such a system.A strict proof is given for analyzing the rank condition for such orthogonal projection

in order to use the principal component analysis (PCA) based singular value decomposition (SVD) to derive the extended observability matrix and lower triangular Toeliptz matrix of the plant state-space model.In the result

the plant state matrices can be retrieved in a transparent manner from the above matrices.An illustrative example is shown to demonstrate the effectiveness and merits of the proposed subspace identification method.