Semiparametric Identification of Hammerstein Systems Using Input Reconstruction and a Single Harmonic Input

Abstract-We present a two-step method for identifying SISO Hammerstein systems. First, using a persistent input with retrospective cost optimization, we estimate a parametric model of the linear system. Next, we pass a single harmonic signal through the system. We use -delay input reconstruction with the parametric model of the linear system to estimate the inaccessible intermediate signal. Using the estimate of the intermediate signal we estimate a nonparametric model of the static nonlinearity, which is assumed to be only piecewise continuous. This method is demonstrated on several numerical and experimental examples of increasing complexity

Revisiting Hammerstein System Identification through the Two-Stage Algorithm for Bilinear Parameter Estimation

The Two-Stage Algorithm (TSA) has been extensively used and adapted for the identification of Hammerstein systems. It is essentially based on a particular formulation of Hammerstein systems in the form of bilinearly parameterized linear regressions. This paper has been motivated by a somewhat contradictory fact: though the optimality of the TSA has been established by Bai in 1998 only in the case of some special weighting matrices, the unweighted TSA is usually used in practice. It is shown in this paper that the unweighted TSA indeed gives the optimal solution of the weighted nonlinear least squares problem formulated with a particular weighting matrix. This provides a theoretical justification of the unweighted TSA, and also leads to a generalization of the obtained result to the case of colored noise with noise whitening. Numerical examples of identification of Hammerstein systems are presented to validate the theoretical analysis

Revisiting Hammerstein System Identification through the Two-Stage Algorithm for Bilinear Parameter Estimation

The Two-Stage Algorithm (TSA) has been extensively used and adapted for the identification of Hammerstein systems. It is essentially based on a particular formulation of Hammerstein systems in the form of bilinearly parameterized linear regressions. This paper has been motivated by a somewhat contradictory fact: though the optimality of the TSA has been established by Bai in 1998 only in the case of some special weighting matrices, the unweighted TSA is usually used in practice. It is shown in this paper that the unweighted TSA indeed gives the optimal solution of the weighted nonlinear least squares problem formulated with a particular weighting matrix. This provides a theoretical justification of the unweighted TSA, and also leads to a generalization of the obtained result to the case of colored noise with noise whitening. Numerical examples of identification of Hammerstein systems are presented to validate the theoretical analysis