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Principal component analysis for errors-in-variables subspace identification

This paper develops a new subspace identification algorithm using the principal component analysis (PCA) that gives consistent model estimates under the errors-in-variables (EIV) situation. PCA naturally falls into the category of EIV formulation, which resembles total least squares and allows for errors in both process input and output. We propose to use PCA to determine the A, B, C, and D matrices and the system order for an EIV formulation. Standard PCA is modified with instrumental variables in order to achieve consistent estimates of the system matrices. The proposed subspace identification method is demonstrated using one simulated processes and a real industrial process for model identification and order determination.