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

Abstract

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. KEYWORDSARX model, asymptotic method, Box-Jenkins model, errors-in-variables models, input noise variance 1 1126

Identification of dual‐rate sampled errors‐in‐variables systems with time delays

“…[14][15][16][17] Therefore, it is necessary to develop new identification methods for EIV systems. An overview of EIV system identification methods can be found in Reference 18, including the instrumental variable method, 19 the bias-eliminating LS method, 20,21 the covariance matching method, 22,23 the maximum likelihood (ML) method, 24 the total least squares (TLS) method, 25 the asymptotic method, 26 and so on. Recently, Zhang et al developed a novel version of the extended ML estimator, which can deal with EIV systems containing arbitrary but persistent excitations and colored disturbing noises.…”