Three‐stage forgetting factor stochastic gradient parameter estimation methods for a class of nonlinear systems

Abstract This article focuses on the parameter estimation for a class of nonlinear systems, that is, multi‐input single‐output or two‐input single‐output Hammerstein finite impulse response systems with autoregressive moving average noise. The key is to investigate new estimation methods for on‐line parameter estimation of the considered system. By using the gradient search and introducing the forgetting factor, the forgetting factor stochastic gradient estimation method is developed. For the purpose of improving the parameter estimation accuracy, the system is decomposed into three subsystems with fewer variables applying the key term separation technique: the first two subsystems contain the unknown parameters related to the input and the third subsystem contains the unknown parameters related to the noise. Then a three‐stage forgetting factor stochastic gradient algorithm is proposed based on the hierarchical identification principle for interactively identifying each subsystem. The simulation results show the effectiveness of the presented algorithm.