Distributed estimation in diffusion networks using affine least-squares combiners

We propose a diffusion scheme for adaptive networks, where each node obtains an estimate of a common unknown parameter vector by combining a local estimate with the combined estimates received from neighboring nodes. The combination weights are adapted in order to minimize the mean-square error of the network employing a local least-squares (LS) cost function. This adaptive diffusion network with LS combiners (ADN-LS) is analyzed, deriving expressions for its network mean-square deviation that characterize the convergence and steady-state performance of the algorithm. Experiments carried out in stationary and tracking scenarios show that our proposal outperforms a state-of-art scheme for adapting the weights of diffusion networks (ACW algorithm from [10]), both during convergence and in tracking situations. Despite its good convergence behavior, our proposal may present a slightly worse steady-state performance in stationary or slowly-changing scenarios with respect to ACW due to the error inherent to the least-squares adaptation with sliding window. Therefore, to take advantage of these different behaviors, we also propose a hybrid scheme based on a convex combination of the ADN-LS and ACW algorithms.