A novel filtering-based recursive identification method for a fractional-order Hammerstein state space system with piecewise nonlinearity

This paper investigates parameters and states estimation for a class of fractional-order state space systems with colored noises. To provide accurate parameter estimation, we suggest a novel gradient descent algorithm based on the extended Kalman filtering. The new approach features lower estimation error variances and a faster convergence rate than the conventional gradient descent algorithm. A data filtering is introduced to filter the input and output data, thereby reducing the impact of colored noises on the accuracy of the parameter estimates.