Computationally efficient robust adaptive filtering algorithm based on improved minimum error entropy criterion with fiducial points

Recently, there has been a strong interest in the minimum error entropy (MEE) criterion derived from information theoretic learning, which is effective in dealing with the multimodal non -Gaussian noise case. However, the kernel function is shift invariant resulting in the MEE criterion being insensitive to the error location. An existing solution is to combine the maximum correntropy (MC) with MEE criteria, leading to the MEE criterion with fiducial points (MEEF). Nevertheless, the algorithms based on the MEEF criterion usually require higher computational complexity. To remedy this problem, an improved MEEF (IMEEF) criterion is devised, aiming to avoid repetitive calculations of the a posteriori error, and an adaptive filtering algorithm based on gradient descent (GD) method is proposed, namely, GD-based IMEEF (IMEEF-GD) algorithm. In addition, we provide the convergence condition in terms of mean sense, along with an analysis of the steadystate and transient behaviors of IMEEF-GD in the mean -square sense. Its computational complexity is also analyzed. Simulation results demonstrate that the computational requirement of our algorithm does not vary significantly with the error sample number and the derived theoretical model is highly consistent with the learning curve. Ultimately, we employ the IMEEF-GD algorithm in tasks such as system identification, wind signal magnitude prediction, temperature prediction, and acoustic echo cancellation (AEC) to validate the effectiveness of the IMEEF-GD algorithm.