A Novel Hierarchical Gradient Identification Method for Hammerstein State Space Systems Based on the Adaptive State Filter

ABSTRACT This paper presents a novel identification scheme for Hammerstein state space systems under colored noise interference. A recursive algorithm is developed to simultaneously estimate the system states and unknown parameters. For parameter estimation, a hierarchical weighted extended stochastic gradient algorithm is proposed, which leverages innovation and residual information to achieve high accuracy. Then, by employing the concept of an auxiliary model, the estimated parameters are integrated into an adaptive extended Kalman filter for state estimation. Theoretical analysis demonstrates that the proposed algorithm can consistently identify the system parameters under persistent excitation conditions. Simulation results validate the effectiveness and reliability of the proposed method.