Errors-in-variables-based modeling using augmented principal components

Abstract

The total least-squares technique has been extensively used for the identification of dynamic systems when both the inputs and outputs are corrupted with noise. However, the major limitation of this technique has been the difficulty in identifying the actual and stable model parameters when the collinearity in the causal data block leads to several "small" singular values. This paper proposes a novel multivariate tool, namely, the augmented principal components analysis (APCA), to deal with collinearity problems under the errors-in-variables formulation. On the basis of the level of noise in each measured variable, the proposed technique is divided further into simple and generalized augmented principal components. Some of the errors-in-variables- and least-squares-based methods available in the literature have been shown as special cases of this APCA-based technique. The efficacy of the new technique over other conventional methods has been illustrated through representative case studies taken from the literature.