Research articleRecursive parameter estimation for Hammerstein-Wiener systems using modified EKF algorithm

- A modified algorithm based on the EKF is proposed for the recursive parameter estimation of H-W systems.
- The proposed algorithm can be extended to a rarely mentioned MISO H-W system.
- The modification on the algorithm extends the parameter convergence domain greatly.
- The commonly used assumption on the invertibility of the output block is not necessary in the proposed algorithm.

This paper focuses on the recursive parameter estimation for the single input single output Hammerstein-Wiener system model, and the study is then extended to a rarely mentioned multiple input single output Hammerstein-Wiener system. Inspired by the extended Kalman filter algorithm, two basic recursive algorithms are derived from the first and the second order Taylor approximation. Based on the form of the first order approximation algorithm, a modified algorithm with larger parameter convergence domain is proposed to cope with the problem of small parameter convergence domain of the first order one and the application limit of the second order one. The validity of the modification on the expansion of convergence domain is shown from the convergence analysis and is demonstrated with two simulation cases.