Stability of Optimal Estimator With Unobservable Measurement Loss: The Unstable System Case

• 成果类型: Article
• 署名作者: Lin, Hong; Lam, James
• 署名单位: Shenzhen Polytechnic University; University of Hong Kong
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3397914
• 发表日期: 2024
• 页码: 7832-7838
• 关键词: Unified modeling language; Loss measurement; Stability criteria; observability; Noise measurement; Numerical stability; detectors; Measurement loss detector; optimal estimator (OE); STABILITY; unobservable measurement loss (UML)

摘要

We study the stability of the optimal estimator (OE) for an unstable system with unobservable measurement loss (UML). The results are twofold. 1) We obtain a necessary and sufficient stability condition: For an unstable UML system, there is a critical value such that the OE is stable with probability 1, if and only if the measurement-arrival rate is greater than this value. This value is identical to the critical value that determines the stability of the OE with observable measurement loss (OML). 2) As a byproduct, we obtain a property on estimation performance: When the system matrix is nonsingular, the performance of the OE with UML converges with the probability of 1 to that of the OE with OML. These two results suggest that the absence of measurement-loss observability does not affect the stability and performance of the OE.