Total least squares algorithm for errors-in-variables systems: Iterative algorithm or two-step algorithm

Chen, Jing; Na, Jing; Li, Junhong; Zhu, Quanmin

Abstract

The total least squares (TLS) algorithm is a superior identification tool for low-order errors-in-variables (EIV) systems, where the estimate can be obtained by solving an eigenvector of the minimum eigenvalue of an augmented matrix. However, the TLS algorithm demonstrates inefficiency when applied to high-order EIV systems. This study introduces two innovative TLS algorithms: an iterative TLS algorithm, offering superior performance for low-order EIV models, and a two-step TLS algorithm, designed to effectively handle high-order EIV models. In comparison to the conventional TLS algorithm, these proposed methodologies present noteworthy advantages, including: (1) reduced computational costs, (2) the utilization of an iterative technique to calculate the inverse, and (3) the diversification of EIV identification methods. Simulation bench test examples are selected to show the efficacy of the proposed algorithms and transparent procedure for applications.

• Journal Article Type: Article
• Acceptance Date: Jan 1, 2025
• Online Publication Date: Jan 13, 2025
• Publication Date: 2025
• Deposit Date: Jan 29, 2025
• Publicly Available Date: Jan 29, 2025
• Journal: IEEE Transactions on Automation Science and Engineering
• Print ISSN: 1545-5955
• Publisher: Institute of Electrical and Electronics Engineers
• Peer Reviewed: Peer Reviewed
• Volume: 22
• Pages: 10753-10763
• DOI: https://doi.org/10.1109/tase.2025.3528532
• Public URL: https://uwe-repository.worktribe.com/output/13648648