Parameter estimation of fractional-order Hammerstein state space system based on the extended Kalman filter

This paper addresses the combined estimation issues of the parameters and states for fractional-order Hammerstein state space systems with colored noises. An extended state estimator is derived by using the parameter estimates to replace the unknown system parameters in Kalman filter. The hierarchical identification principle is introduced to solve the unknown parameters of measurement noises. By introducing the forgetting factor, an extended Kalman filtering-based hierarchical forgetting factor stochastic gradient algorithm is presented to estimate the unknown states, parameters and fractional-order. A numerical example is respectively presented to demonstrate the feasibility of the proposed identification algorithm. It can be seen that the estimation errors are relatively small, which reflects the proposed algorithms have good identification effect.