Boundedness of the Optimal State Estimator Rejecting Unknown Inputs

• Published in: IEEE transactions on automatic control Vol. 68; no. 4; pp. 2430 - 2435
• Main Authors: Zhang, Qinghua, Delyon, Bernard
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Algorithms; Asymptotic stability; Automatic Control Engineering; Computer Science; Covariance; Covariance matrices; Disturbance rejection; Kalman filter; Kalman filters; Lower bounds; Optimization; Stability analysis; Stability criteria; State estimation; Symmetric matrices; Time invariant systems; time-varying system; Time-varying systems; unknown input observer; Upper bound; Upper bounds; unknown input observer; disturbance rejection; State estimation; time varying system; Kalman filter; stability analysis
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2022.3174447

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.