Optimality analysis of the Two-Stage Algorithm for Hammerstein system identification , Report no. LiTH-ISY-R-2909

The Two-Stage Algorithm (TSA) has been extensively used and adapted for the identi cation of Hammerstein systems. It essentially deals with the parameter estimation problem for a linear regression parameterized in a bilinear form. This paper is motivated by a somewhat contradictory fact: though the optimality of the TSA has been established only in the case of some special weighting matrices, this algorithm usually uses the unweighted case, i.e., no weighting matrix or an identity one is used. We nd out that the unweighted TSA indeed gives the optimal solution of the weighted nonlinear least-squares optimization problem for a particular weighting matrix. This provides a theoretical justi cation of the unweighted TSA, and leads to a generalization of the obtained result to the case of colored noise with noise whitening. Numerical examples of identi cation of Hammerstein systems are presented to validate the theoretical analysis.