Maximum Total Fractional-Order Correntropy Adaptive Filtering Algorithm for Parameter Estimation Under Impulsive Noises

As an adaptive finite impulse response filtering algorithm, the maximum total correntropy (MTC) algorithm plays an important role in parameter estimation of the errors-in-variables model where both input and output signals are contaminated with impulsive noises. However, the MTC algorithm is difficult to obtain a sufficiently high estimation accuracy under impulsive noises because the MTC cost function contains second-order moments of the error signal and its first-order gradient is susceptible to large outliers in the input noise. In this paper, a maximum total fractional-order correntropy (MTFOC) cost function is proposed and then a fractional-order gradient based MTFOC adaptive filtering algorithm is developed to improve the estimation accuracy of MTC. Moreover, the local stability and computational complexity of the proposed algorithm are analyzed. Simulation results indicate that the estimation accuracy and robustness of the MTFOC algorithm are superior to previous algorithms in both Gaussian mixture noise environments and \(\alpha \)-stable distribution noise environments.