Multi-innovation stochastic gradient identification for Hammerstein controlled autoregressive autoregressive systems based on the filtering technique

This paper presents two estimation algorithms for Hammerstein controlled autoregressive autoregressive systems. The key-term separation principle is used to solve the problem that the identification model contains the products of the parameters of the nonlinear part and the linear part, which causes large amount of computation. To improve the parameter estimation accuracy of the stochastic gradient algorithm, we derive a forgetting factor multi-innovation generalized stochastic gradient algorithm expanding the innovation length. To improve the convergence rate, we derive a filtering-based forgetting factor multi-innovation stochastic gradient algorithm using the filtering technique. The simulation results show that the proposed algorithms are effective.