System identification using augmented principal component analysis

The total least squares (TLS) technique has been extensively used for the identification of dynamic systems when both the inputs and outputs are corrupted with noise. But the major limitation of this technique has been the difficulty in identifying the actual parameters when the collinearity in the input data leads to several "small" eigenvalues. This paper proposes a novel technique namely augmented principal component analysis (APCA) to deal with collinearity problems in the error-in-variable formulation. The APCA formulation can also be used to determine the least squares prediction error when an appropriate operator is chosen. This property has been used for the nonlinear structure selection through forward selection methodology. The efficacy of the new technique has been illustrated through representative case studies taken form the literature.