Diffusion Hammerstein Spline Adaptive Filtering Based on Orthogonal Gradient Adaptive Algorithm

Abstract

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.

Diffusion recursive least squares algorithm based on triangular decomposition

“…The According to nonlinear cooperative adaptation, the diffusion spline adaptive filterings in [16] have shown that they can perform well in comparison with the non-cooperative network. Sitjongsataporn [17] a class of nonlinear diffusion adaptive filtering has been furnished in the framework of orthogonal gradientbased algorithm. While, the combined diffusion affine algorithm has been presented over the distributed networks [18], Merched [19], [20] has derived with the diffusion adaptation to fuse data based on least squares mechanism against the colored inputs in the single-task and multi-task scenes.…”