Robust proportional-integral Kalman filter design using a convex optimization method

Jongchul Jung, Sangoh Han, Kunsoo Huh

Research output: Contribution to journalArticle

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This paper proposes a design approach to the robust proportional-integral Kalman filter for stochastic linear systems under convex bounded parametric uncertainty, in which the filter has a proportional loop and an integral loop of the estimation error, providing a guaranteed minimum bound on the estimation error variance for all admissible uncertainties. The integral action is believed to increase steady-state estimation accuracy, improving robustness against uncertainties such as disturbances and modeling errors. In this study, the minimization problem of the upper bound of estimation error variance is converted into a convex optimization problem subject to linear matrix inequalities, and the proportional and the integral Kalman gains are optimally chosen by solving the problem. The estimation performance of the proposed filter is demonstrated through numerical examples and shows robustness against uncertainties, addressing the guaranteed performance in the mean square error sense.

Original languageEnglish
Pages (from-to)879-886
Number of pages8
JournalJournal of Mechanical Science and Technology
Issue number5
Publication statusPublished - 2008 May 1



  • Convex optimization
  • Kalman filter
  • Proportional-integral observer
  • Robustness

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