Filtering-based gradient joint identification algorithms for nonlinear fractional-order models with colored noises.

The main focus is to realize the on-line parameter estimation of the nonlinear fractional-order model with colored noises in this paper. Firstly, an auxiliary model gradient descent algorithm is derived to synchronously produce the estimates of the parameters, including the fractional-order. In order to decrease the noise interference, the filtering-based gradient descent estimation framework by constructing a linear filter provides a feasible method. Furthermore, the forgetting factor is introduced to the proposed filtering-based algorithm for the sake of improving the convergence rate. Comparative simulation results demonstrate the proposed effectiveness and high approximation accuracy of the proposed algorithms. • An auxiliary model is built to obtain the estimates of these unmeasurable variables. • The proposed auxiliary model gradient algorithm can realize on-line identification. • A filtering-based gradient algorithm is proposed to reduce the colored noise impact. [ABSTRACT FROM AUTHOR]