State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors

Xiao Zhang, Feng Ding, Erfu Yang

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115 Citations (Scopus)
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This paper considers the state estimation problem of bilinear systems in the presence of disturbances. The standard Kalman filter is recognized as the best state estimator for linear systems, but it is not applicable for bilinear systems. It is well known that the extended Kalman filter (EKF) is proposed based on the Taylor expansion to linearize the nonlinear model. In this paper, we show that the EKF method is not suitable for bilinear systems because the linearization method for bilinear systems cannot describe the behavior of the considered system. Therefore, this paper proposes a state filtering method for the single-input–single-output bilinear systems by minimizing the covariance matrix of the state estimation errors. Moreover, the state estimation algorithm is extended to multiple-input–multiple-output bilinear systems. The performance analysis indicates that the state estimates can track the true states. Finally, the numerical examples illustrate the specific performance of the proposed method.
Original languageEnglish
Pages (from-to)1157-1173
Number of pages17
JournalInternational Journal of Adaptive Control and Signal Processing
Issue number7
Early online date9 Jun 2019
Publication statusPublished - 31 Jul 2019


  • bilinear state estimator
  • Kalman filter
  • signal processing
  • state estimation

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