Identification of Output-Error (OE) Models using Generalized Spectral Decomposition

This article proposes a novel approach for the identification of output-error (OE) models. Classical approaches like prediction error minimization (PEM) and Steiglitz-McBride deliver consistent estimates of model parameters for given information of delay, input-output orders of the underlying process. In the absence of such critical information, user is forced to adapt trial and error approach. In this work, we propose a novel two-step non-iterative framework to estimate the delay and order in automated manner using the generalized spectral decomposition. The first step of the proposed algorithm computes the order by analyzing generalized eigenvalues of the covariance matrix for the lagged input-output measurements. The second step involves the parameter estimation by utilizing the same approach of spectral decomposition on lagged input-output measurements with correct stacking order. Simulation studies are presented to show the efficacy of proposed method.