Boundedness of the Optimal State Estimator Rejecting Unknown Inputs

• 成果类型: Article
• 署名作者: Zhang, Qinghua; Delyon, Bernard
• 署名单位: Universite Gustave-Eiffel; Inria; Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3174447
• 发表日期: 2023
• 页码: 2430-2435
• 关键词: Covariance matrices; Kalman filters; Upper bound; Time-varying systems; Stability criteria; asymptotic stability; Symmetric matrices; disturbance rejection; Kalman filter; stability analysis; State estimation; time-varying system; unknown input observer

摘要

The Kitanidis filter is a natural extension of the Kalman filter to systems subject to arbitrary unknown inputs or disturbances. Though the optimality of the Kitanidis filter was founded for general time varying systems more than 30 years ago, its boundedness and stability analysis is still limited to time-invariant systems, up to the authors' knowledge. In the framework of general time varying systems, this article establishes upper and lower bounds of the error covariance of the Kitanidis filter, as well as upper bounds of all the auxiliary variables involved in the filter. By preventing data overflow, upper bounds are crucial for all recursive algorithms in real-time applications. The upper and lower bounds of the error covariance will also serve as the basis of the Kitanidis filter stability analysis, such as in the case of the time-varying system Kalman filter.