Identification of errors‐in‐variables systems: An asymptotic approach

This work studies the identification of errors‐in‐variables (EIV) systems. An asymptotic method (ASYM) is developed for the EIV system. Firstly, an auto regressive with exogeneous (ARX) model estimation method is proposed, which is consistent for EIV systems. Then the asymptotic variance expression of the estimated high‐order ARX model is derived, which forms the basis of the ASYM method. In parameter estimation, the ASYM starts with a high‐order ARX model estimation followed by a frequency domain weighted model reduction. The obtained model is consistent, and its efficiency needs to be investigated. Besides parameter estimation, a criterion for model order selection is proposed, which is based on frequency domain considerations, and the frequency domain error bound is established that can be used for model validation. Simulations and comparisons with other methods are used to illustrate the performance of the method.