Diffusion Spline Adaptive Filtering

Diffusion adaptation (DA) algorithms allow a network of agents to collectively estimate a parameter vector, by jointly minimizing the sum of their local cost functions. This is achieved by interleaving local update steps with 'diffusion' steps, where information is combined with their own neighbors. In this paper, we propose a novel class of nonlinear diffusion filters, based on the recently proposed spline adaptive filter (SAF). A SAF learns nonlinear models by local interpolating polynomials, with a small overhead with respect to linear filters. This arises from the fact that only a small subset of parameters of the nonlinear component are adapted at every time-instant. By applying ideas from the DA framework, in this paper we derive a diffused version of the SAF, denoted as D-SAF. Experimental evaluations show that the D-SAF is able to robustly learn the underlying nonlinear model, with a significant gain compared to a non-cooperative solution.