Distributed Adaptive Filtering of $\alpha$ -Stable Signals

A cost-effective framework for distributed adaptive filtering of <inline-formula><tex-math notation="LaTeX">$\alpha$ </tex-math></inline-formula>-stable signals over sensor networks is proposed. First, the filtering paradigm of <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>-stable signals through multiple observations made over a network of sensors is revisited and an optimal solution is formulated. Then, an adaptive gradient descent based algorithm for distributed real-time filtering of <inline-formula><tex-math notation="LaTeX"> $\alpha$</tex-math></inline-formula>-stable signals via multiagent networks is derived. This not only provides an approximation of the formulated optimal solution, but also a cost-effective algorithm that scales with the size of the network. Moreover, performance of the derived algorithm is analyzed and convergence conditions are established.

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