Outlier-Aware Recursive Instantaneous Minimum Error Entropy Algorithm

The minimum error entropy (MEE) criterion closely relies on the quadratic information potential (QIP) estimates of Renyi’s entropy. Nevertheless, the conventional obtained QIP estimates are numerically unstable, especially when the error samples contain outliers, resulting in the optimal solution of the MEE criterion deviating from the target vector to a certain extent. To address this problem, we introduce the M-estimate method from robust statistics into the QIP estimation process; thus, a robust estimation method called instantaneous M-estimate QIP (IM-QIP) is proposed, and several important properties of IM-QIP are presented. The proposed IM-QIP estimates could be implemented simply while ensuring great robustness. Naturally, we further propose the corresponding instantaneous M-estimate MEE (IM-MEE) criterion and apply it to adaptive filtering. A robust recursive adaptive filtering algorithm, called the recursive IM-MEE (RIM-MEE) algorithm, is proposed and analyzed in this article, along with its stability and theoretical steady-state performance. Additionally, we demonstrate that the RIM-MEE algorithm achieves a smaller theoretical bound compared to the traditional MEE algorithm under heavy-tailed and skewed noise conditions. The simulation results revealed the robustness of the IM-QIP estimates and verified the theoretical expectations and superior performance of the RIM-MEE algorithm.