  This work develops robust diffusion recursive least squares algorithms to
mitigate the performance degradation often experienced in networks of agents in
the presence of impulsive noise. The first algorithm minimizes an exponentially
weighted least-squares cost function subject to a time-dependent constraint on
the squared norm of the intermediate update at each node. A recursive strategy
for computing the constraint is proposed using side information from the
neighboring nodes to further improve the robustness. We also analyze the
mean-square convergence behavior of the proposed algorithm. The second proposed
algorithm is a modification of the first one based on the dichotomous
coordinate descent iterations. It has a performance similar to that of the
former, however its complexity is significantly lower especially when input
regressors of agents have a shift structure and it is well suited to practical
implementation. Simulations show the superiority of the proposed algorithms
over previously reported techniques in various impulsive noise scenarios.
