A non-parametric approach for linear system identification using principal component analysis

This paper considers the applications of principal component analysis (PCA) for signal-based linear system identification. Linear time-invariant (LTI) single-input-single-output (SISO) and multi-input-multi-output (MIMO) system frequency response function (FRF) estimation problems are formulated on the basis of the eigen-value decomposition (EVD) of the input–output measurement spectral correlation matrix. It is demonstrated that resulting algorithms for the SISO and MIMO cases are equivalent to that of the maximum likelihood (ML) and the total least squares (TLS) approaches respectively. Originating from the proposed FRF estimation scheme, a moving-segment EVD procedure is developed for SISO time-varying transfer function estimation. Based on the sensitivity of the time-domain PCA to delays/shifts between signals, an extended lagged-covariance-matrix approach is introduced for delay detection from time series.