Evolving Systems

, Volume 8, Issue 3, pp 211–219 | Cite as

Discrete-time Kalman filter for Takagi–Sugeno fuzzy models

  • L. A. Páramo-Carranza
  • J. A. Meda-Campaña
  • José de Jesús Rubio
  • R. Tapia-Herrera
  • A. V. Curtidor-López
  • A. Grande-Meza
  • I. Cázares-Ramírez
Original Paper


In this work, the Kalman Filter (KF) and Takagi–Sugeno fuzzy modeling technique are combined to extend the classical Kalman linear state estimation to the nonlinear field. The framework for such extension is given, and in this sense the discrete-time fuzzy Kalman filter (DFKF) is obtained. It will be shown that the fuzzy version gives some advantages when is compared with the Extended Kalman Filter (EKF), which is the most typical extension of the KF to the nonlinear field. The proposed approach provides a significantly smaller processing time than the processing time of the EKF while the mean square error is also reduced. Finally, some examples, such as the Lorenz chaotic attractor and under actuated mechatronic system (pendubot), are used to compare the DFKF and EKF.


Kalman filtering Fuzzy systems Chaotic systems 



Authors want to express their deepest thank to CONACyT and Instituto Politécnico Nacional for the scholarships granted and research projects.

Compliance with ethical standards

Conflict of interest

The authors declare that they do not have conflict of interests.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • L. A. Páramo-Carranza
    • 1
  • J. A. Meda-Campaña
    • 1
  • José de Jesús Rubio
    • 2
  • R. Tapia-Herrera
    • 1
  • A. V. Curtidor-López
    • 1
  • A. Grande-Meza
    • 1
  • I. Cázares-Ramírez
    • 1
  1. 1.Instituto Politécnico NacionalSEPI-ESIME ZacatencoMéxicoMexico
  2. 2.Instituto Politécnico NacionalSEPI-ESIME AzcapotzalcoMéxicoMexico

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