Model recovery for Hammerstein systems using the hierarchical orthogonal matching pursuit method

Most papers concentrate on the parameter identification of Hammerstein systems with known orders. This paper, motivated by the recent developments in sparse approximations, investigates the combined parameter and order determination of Hammerstein systems. The methodology used relies on greedy schemes-the orthogonal matching pursuit (OMP) algorithm in the compressive sensor (CS) theory. In particular, the first step recasts a bilinear Hammerstein system into two fictitious pseudo-regressive sub-systems which respectively contain the parameters of the nonlinear part or the parameters of the linear part by the hierarchical identification principle. The second step adopts a hierarchical orthogonal matching pursuit (H-OMP) selection procedure to interactively select the parameters and orders of the two sub-systems under the frame of the compressive sensor. Finally, the proposed algorithm is tested on a simulation example.