  Distributed adaptive signal processing has attracted much attention in the
recent decade owing to its effectiveness in many decentralized real-time
applications in networked systems. Because many natural signals are highly
sparse with most entries equal to zero, several decentralized sparse adaptive
algorithms have been proposed recently. Most of them is focused on the single
task estimation problems, in which all nodes receive data associated with the
same unknown vector and collaborate to estimate it. However, many applications
are inherently multitask oriented and each node has its own unknown vector
different from others'. The related multitask estimation problem benefits from
collaborations among the nodes as neighbor nodes usually share analogous
properties and thus similar unknown vectors. In this work, we study the
distributed sparse multitask recursive least squares (RLS) problem over
networks. We first propose a decentralized online alternating direction method
of multipliers (ADMM) algorithm for the formulated RLS problem. The algorithm
is simplified for easy implementation with closed-form computations in each
iteration and low storage requirements. Moreover, to further reduce the
complexity, we present a decentralized online subgradient method with low
computational overhead. We theoretically analyze the convergence behavior of
the proposed subgradient method and derive an error bound related to the
network topology and algorithm parameters. The effectiveness of the proposed
algorithms is corroborated by numerical simulations and an accuracy-complexity
tradeoff between the proposed two algorithms is highlighted.
