Recursive parameter identification of Hammerstein–Wiener systems with measurement noise

• A recursive method is proposed to identify Hammerstein–Wiener systems with measurement noise.
• The commonly used invertibility assumption on the output block is not needed.
• The measurement noise is heteroscedastic.
• The parameter convergence property is analyzed and the conditions of uniform convergence are obtained.

A recursive algorithm is proposed in this paper to identify Hammerstein–Wiener systems with heteroscedastic measurement noise. Based on the parameterization model of Hammerstein–Wiener systems, the algorithm is derived by minimizing the expectation of the sum of squared parameter estimation errors. By replacing the immeasurable internal variables with their estimations, the need for the commonly used invertibility assumption on the output block can be eliminated. The convergence of the proposed algorithm is also studied and conditions for achieving the uniform convergence of the parameter estimation are determined. The validity of this algorithm is demonstrated with three simulation examples, including a practical electric arc furnace system case.