Two-stage ARMAX parameter identification based on bias-eliminated least squares estimation and Durban's method

This paper proposes a two-stage identification approach for the parameter identification of autoregressive moving average with exogenous variable (ARMAX) model. First, a bias-eliminated least squares method is employed to identify the autoregressive part with exogenous variable (ARX). Then, the Durbin's method is employed to transform the parameter identification of the moving average (MA) part into that of a long autoregressive (AR) model. The MA parameters are derived directly from the parameter relationship between the MA part and its equivalent long AR model. Finally, the noise variance can be computed by using the identified MA parameters. The performance comparison against the extended least-squares method in numerical simulations validates the effectiveness of the two-stage identification approach.