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 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 steady-state 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.

中文翻译：

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基于改进基准点最小误差熵准则的计算高效鲁棒自适应滤波算法

最近，人们对从信息论学习中导出的最小误差熵（MEE）准则产生了浓厚的兴趣，它可以有效地处理多模态非高斯噪声情况。然而，核函数是平移不变的，导致 MEE 准则对错误位置不敏感。现有的解决方案是将最大熵（MC）与MEE准则相结合，产生带有基准点的MEE准则（MEEF）。然而，基于MEEF准则的算法通常需要较高的计算复杂度。针对这一问题，设计了一种改进的MEEF（IMEEF）准则，旨在避免误差的重复计算，并提出了一种基于梯度下降（GD）方法的自适应滤波算法，即基于GD的IMEEF（IMEEF-GD） ） 算法。此外，我们还提供了均值意义上的收敛条件，并分析了 IMEEF-GD 在均方意义上的稳态和瞬态行为。还分析了其计算复杂度。仿真结果表明，我们算法的计算要求不会随着误差样本数量的变化而发生显着变化，并且推导的理论模型与学习曲线高度一致。最终，我们在系统识别、风信号幅度预测、温度预测和声学回声消除（AEC）等任务中采用了 IMEEF-GD 算法，以验证 IMEEF-GD 算法的有效性。