Instrumental Variable-Based OMP Identification Algorithm for Hammerstein Systems

Hammerstein systems are formed by a static nonlinear block followed by a dynamic linear block. To solve the parameterizing difficulty caused by parameter coupling between the nonlinear part and the linear part in a Hammerstein system, an instrumental variable method is studied to parameterize the Hammerstein system. To achieve in simultaneously identifying parameters and orders of the Hammerstein system and to promote the computational efficiency of the identification algorithm, a sparsity-seeking orthogonal matching pursuit (OMP) optimization method of compressive sensing is extended to identify parameters and orders of the Hammerstein system. The idea is, by the filtering technique and the instrumental variable method, to transform the Hammerstein system into a simple form with a separated nonlinear expression and to parameterize the system into an autoregressive model, then to perform an instrumental variable-based orthogonal matching pursuit (IV-OMP) identification method for the Hammerstein system. Simulation results illustrate that the investigated method is effective and has advantages of simplicity and efficiency.