Iterative parameter and order identification for fractional-order nonlinear finite impulse response systems using the key term separation

This article considers the parameter estimation for a fractional-order nonlinear finite impulse response system with colored noise. For the fractional-order systems, the challenge and difficulty are to identify the order and parameters of the systems simultaneously under colored noise disturbances. In order to reduce the problem of redundant parameter estimation, the output form of the system can be expressed by a linear combination of unknown parameters through the separation of the key term separation. A key term separation auxiliary model gradient-based iterative algorithm is derived by using the negative gradient search. Meanwhile, to achieve the higher estimation accuracy, we propose a key term separation auxiliary model multiinnovation gradient-based iterative algorithm by utilizing the multiinnovation theory. Finally, the simulation results test the effectiveness of the proposed algorithms.