Identification of fractional-order Hammerstein nonlinear ARMAX system with colored noise

For the fractional-order Hammerstein nonlinear ARMAX system with colored noise, there are many identification parameters and coupling variables, difficulty in estimating the fractional order, slow convergence of the identification algorithm and low accuracy, and this paper proposes a new multi-innovation principle based on the principle of multi-innovation information identification method. First, construct a fractional-order Hammerstein nonlinear ARMAX discrete system model with colored noise; secondly, a multi-innovative Levenberg–Marquardt algorithm with an innovation vector composed of fractional-order variables as the model input is designed, and the auxiliary model method is combined to solve the unknown noise variables to estimate the system parameters and fractional order. Finally, a fractional-order Hammerstein nonlinear ARMAX system with colored noise and a flexible manipulator system are taken as examples to prove the effectiveness of the proposed algorithm.