The general Cauchy loss (GCL) criterion has been successfully proposed to improve the performance of the Cauchy loss (CL) criterion for linear adaptive filtering in the presence of complex non-Gaussian noise. However, the commonly used adaptive filtering algorithms based on the GCL criterion utilize the stochastic gradient descent (SGD) method to update their weights with slow convergence rate and poor steady-state performance. To overcome these issues, a general Cauchy-loss conjugate gradient (GCCG) method is first developed by solving the proposed half-quadratic general Cauchy loss (HQGCL) with the conjugate gradient method. To further tackle complex nonlinear issues, novel multiple random Fourier features (MRFF) spaces are then constructed in finite-dimensional features spaces, which is proven effective for approximation of multi-kernel adaptive filter (MKAF), theoretically. The GCCG method is thus applied into the constructed MRFF spaces to generate novel multiple random Fourier features GCCG (MRFGCG) algorithms, curbing the linear growth structures of kernel adaptive filters (KAFs) and MKAFs. The proposed MRFGCG algorithms in fixed networks have lower computational complexity and higher filtering accuracy than sparsification KAFs in non-Gaussian environments. Monte Carlo simulations on the prediction of synthetic and real-world time-series and the identification of nonlinear system confirm the superiorities of the proposed MRFGCG algorithms.

中文翻译：

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基于多重随机傅里叶特征的通用柯西共轭梯度算法

已经成功提出了一般柯西损耗（GCL）准则，以在复杂非高斯噪声存在的情况下提高线性自适应滤波的柯西损耗（CL）准则的性能。然而，常用的基于GCL准则的自适应滤波算法利用随机梯度下降（SGD）方法以较慢的收敛速度和较差的稳态性能来更新其权重。为了克服这些问题，首先通过使用共轭梯度法解决了提出的半二次一般柯西损耗（HQGCL），从而开发了一种一般的柯西损耗共轭梯度法（GCCG）。为了进一步解决复杂的非线性问题，然后在有限维特征空间中构造了新颖的多个随机傅立叶特征（MRFF）空间，从理论上讲，它被证明对逼近多核自适应滤波器（MKAF）有效。因此，将GCCG方法应用于构造的MRFF空间中，以生成新颖的多重随机傅里叶特征GCCG（MRFGCG）算法，从而抑制了内核自适应滤波器（KAF）和MKAF的线性增长结构。与非高斯环境中的稀疏化KAF相比，固定网络中提出的MRFGCG算法具有更低的计算复杂度和更高的过滤精度。蒙特卡洛模拟对合成和现实世界时间序列的预测以及对非线性系统的识别，证实了所提出的MRFGCG算法的优越性。抑制内核自适应滤波器（KAF）和MKAF的线性增长结构。与非高斯环境中的稀疏化KAF相比，固定网络中提出的MRFGCG算法具有更低的计算复杂度和更高的过滤精度。蒙特卡洛模拟对合成和现实世界时间序列的预测以及对非线性系统的识别，证实了所提出的MRFGCG算法的优越性。抑制内核自适应滤波器（KAF）和MKAF的线性增长结构。与非高斯环境中的稀疏化KAF相比，固定网络中提出的MRFGCG算法具有更低的计算复杂度和更高的过滤精度。蒙特卡洛模拟对合成和现实世界时间序列的预测以及对非线性系统的识别，证实了所提出的MRFGCG算法的优越性。