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

  • Jongchul Jung
  • Sangoh Han
  • Kunsoo Huh


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.


Proportional-integral observer Kalman filter Convex optimization Robustness 


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Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH 2008

Authors and Affiliations

  1. 1.Department of Automotive EngineeringHanyang UniversitySeoulKorea
  2. 2.School of Mechanical EngineeringHanyang UniversitySeoulKorea

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