Hierarchical parameter estimation for a class of MIMO Hammerstein systems based on the reframed models

Block-oriented Hammerstein systems consist of a nonlinear static block followed by a linear dynamic block. For the identification of a complex class of multi-input multi-output (MIMO) Hammerstein systems with different types of coefficients: a matrix coefficient and scalar coefficients, it is difficult to express this class of complex Hammerstein systems as a regression identification model in all parameters of the nonlinear part and the linear part in which the standard least squares method can be easily applied to implement parameter estimation. By the matrix transformation, this paper reframes an MIMO Hammerstein system with different types of coefficients into two models, each of which is expressed as a regression form in the parameters of the nonlinear part or in the parameters of the linear part. Then a hierarchical extended least squares algorithm is applied to these two models to alternatively estimate the parameters of the nonlinear part and the linear part.