Fractional-Order Correntropy Adaptive Filters for Distributed Processing of $\alpha$-Stable Signals

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 <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>-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 <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>-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.

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