On robust Kalman filter for two-dimensional uncertain linear discrete time-varying systems: A least squares method

• Published in: Automatica (Oxford) Vol. 99; pp. 203 - 212
• Main Authors: Zhao, Dong, Ding, Steven X., Karimi, Hamid Reza, Li, Yueyang, Wang, Youqing
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2019
• Subjects: Kalman filter; Least squares method; Time-varying systems; Two-dimensional systems; Uncertain systems; Two-dimensional systems; Uncertain systems; Least squares method; Kalman filter; Time-varying systems
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2018.10.029

The robust Kalman filter design problem for two-dimensional uncertain linear discrete time-varying systems with stochastic noises is investigated in this study. First, we prove that the solution to a certain deterministic regularized least squares problem constrained by the nominal two-dimensional system model is equivalent to the generalized two-dimensional Kalman filter. Then, based on this relationship, the robust state estimation problem for two-dimensional uncertain systems with stochastic noises is interpreted as a deterministic robust regularized least squares problem subject to two-dimensional dynamic constraint. Finally, by solving the robust regularized least squares problem and using a simple approximation, a recursive robust two-dimensional Kalman filter is determined. A heat transfer process serves as an example to show the properties and efficacy of the proposed filter.