This work revisits the problem of distributed adaptive filtering in multi-agent sensor networks. In contrast to classical approaches, the formulation relaxes the Gaussian assumption on the signal and noise to the generalized setting of $\alpha$-stable distributions that do not possess second- and higher-order statistical moments. Most importantly, the considered scenario allows for different characteristic exponents throughout the network. Drawing upon ideas from correntropy-type local similarity measures and fractional-order calculus, a novel class of distributed fractional-order correntropy adaptive filters, that are robust against the jittery behavior of $\alpha$-stable signals, is derived and their convergence criterion is established. The effectiveness of the proposed algorithms, as compared to existing distributed adaptive filtering techniques, is demonstrated via simulation examples.

中文翻译：

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用于 $\alpha$ 稳定信号分布式处理的分数阶相关熵自适应滤波器

这项工作重新审视了多代理传感器网络中的分布式自适应滤波问题。与经典方法相比，该公式将信号和噪声的高斯假设放宽到广义设置$\alpha$- 不具有二阶和更高阶统计矩的稳定分布。最重要的是，所考虑的场景允许在整个网络中使用不同的特征指数。借鉴了相关熵类型局部相似性度量和分数阶微积分的思想，这是一类新型的分布式分数阶相关熵自适应滤波器，它对抖动行为具有鲁棒性$\alpha$- 稳定信号，导出并建立它们的收敛标准。与现有的分布式自适应滤波技术相比，所提出的算法的有效性通过仿真示例得到了证明。