Work

On ARX modeling with the ASYM method for errors-in-variables problems

Year: 2026

Type: article

Abstract: ARX models are often used in system identification. Using high-order ARX models one can well describe arbitrary output noise. Combining high-order ARX models and model reduction techniques, several two-step identification methods are formed, such as the asymptotic method (ASYM) (Zhu, 1998). To extend these methods into errors-in-variables (EIV) problems, it is crucial to get reliable ARX models with input noise effects compensated. The methods based on bias-compensation are classical solutions for such a purpose. By investigating the effects of input variance determination on the parameter estimates, this paper reveals that there is a fundamental limitation in these methods: one has to make a compromise between a full compensation and a reliable model. If the input variance estimate is not well selected, large biases can occur. This difficulty increases as the order of the ARX model increases. Three ways, including a revised bias-compensating method, a generalized instrumental variable estimator (GIVE) and a frequency-domain method are then proposed to avoid unreliable estimates. A comparative simulation study between ASYM and maximum likelihood (ML) methods is also included, showing that ASYM can provide estimates with nearly optimal performance.

Source: Automatica

DOI: 10.1016/j.automatica.2026.113320

Authors: Jinming Zhou, Torsten Söderström, Yucai Zhu

Institutions: Southeast University, Uppsala University, State Key Laboratory of Industrial Control Technology, Zhejiang University

Language: English

Topic: Control Systems and Identification

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,760

Funder: National Key Research and Development Program of China