Diffusion Hammerstein Spline Adaptive Filtering Based on Orthogonal Gradient Adaptive Algorithm

In this paper, we propose a class of nonlinear diffusion filtering based on Hammerstein function with the spline adaptive filter (HSAF) implemented by normalised version of orthogonal gradient adaptive (NOGA) algorithm over the distributed network. Diffusion adaptation algorithm approximates a variable vector with the help of a network of agents using a joint optimisation on the sum of cost function. A HSAF comprises of memoryless function during learning by interpolating polynomials with respect to the linear filter. We derive a diffusion adaptation framework on HSAF motivated from NOGA algorithm; called DHSAF-NOGA. There are two types of adaptive diffusion strategies with the combine-then-adapt (CTA) algorithm and the adapt-then-combine (ATC) algorithm that are considered and implemented by DHSAF-NOGA algorithm. The network stability and performance over mean square error networks is derived. Experiment results depict that proposed CTA-DHSAF-NOGA and ATC-DHSAF-NOGA algorithms can learn robustly underlying the nonlinear Hammerstein model compared with a non-cooperative solution and existing techniques.