Combined state and parameter estimation for Hammerstein systems with time-delay using the Kalman filtering

Junxia Ma, Feng Ding, Weili Xiong, Erfu Yang

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17 Citations (Scopus)
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This paper discusses the state and parameter estimation problem for a class of Hammerstein state space systems with time-delay. Both the process noise and the measurement noise are considered in the system. Based on the observable canonical state space form and the key term separation, a pseudo-linear regressive identification model is obtained. For the unknown states in the information vector, the Kalman filter is used to search for the optimal state estimates. A Kalman-filter based least squares iterative and a recursive least squares algorithms are proposed. Extending the information vector to include the latest information terms which are missed for the time-delay, the Kalman-filter based recursive extended least squares algorithm is derived to obtain the estimates of the unknown time-delay, parameters and states. The numerical simulation results are given to illustrate the effectiveness of the proposed algorithms.
Original languageEnglish
Pages (from-to)1139-1151
Number of pages13
JournalInternational Journal of Adaptive Control and Signal Processing
Issue number8
Early online date25 Jan 2017
Publication statusPublished - 31 Aug 2017


  • parameter identification
  • Kalman filter
  • state estimation
  • least squares
  • Hammerstein systems
  • state space model

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