Performance Analysis of Fractional-Order Adaptive Filtering Algorithm and Its Improvement

Considering the
$ \alpha$
-stable input signals and noises, several robust fractional-order adaptive filtering algorithms have been proposed in recent years. However, the mean-square performance analysis of the FoAF algorithm has not been well studied in the literature. Toward that end, this letter provide a theoretical mean-square performance analysis of the FoAF algorithm, involving transient and steady-state behavior. Furthermore, an improved fractional-order adaptive filtering algorithm is derived by utilizing the M-estimate technique. Simulation experiments verify the results of the theoretical analysis and demonstrate the advantages of the proposed algorithm in heavy-tailed non-Gaussian environments.