An Enhanced Fractional Least Mean Square Filter Encountering the Specific Unknown System Vector

This brief proposes an enhanced fractional derivative that can prevent the tap weight coefficients from destroying the gradient information, solve the problem caused by the fractional extreme point, and improve the convergence speed with the help of error estimation information and Sign function. Based on this fractional derivative, an enhanced fractional least mean square (EFLMS) filter algorithm is proposed. We analyze the influence of unknown system vector on the convergence performance of the EFLMS algorithm. The computational complexity of the proposed algorithm is also analyzed. Simulation experiments show that the EFLMS algorithm achieves better performance in system identification than the classic least mean square (LMS) algorithm and the existing algorithms based on fractional calculus.