Identification of Errors-in-Variables Models Using Dynamic Iterative Principal Component Analysis

Identification of linear dynamic systems from input-output data has been a subject of study for several decades. A broad class of problems in this field pertain to what is widely known as the errors-in-variables (EIV) class, where both input and output are known with errors, in contrast to the traditional scenario where only outputs are assumed to be corrupted with errors. In this work, we present a novel and systematic approach to the identification of dynamic models for the EIV case in the principal component analysis (PCA) framework. The key contribution of this work is a dynamic iterative PCA (DIPCA) algorithm that has the ability to determine the correct order of the process, handle unequal measurement noise variances (the heteroskedastic case), and provide accurate estimates of the model together with the noise covariance matrix under large sample conditions. The work is presented within the scope of single-input, single-output (SISO) deterministic systems corrupted by white-noise errors. Simulation results are presented to demonstrate the effectiveness of the proposed method.