An adaptive filter based on multigrid linear equation solvers

A recent and novel approach to the development of adaptive filtering algorithms is based on the theory of stationary iterative linear equation solvers: A classical Richardson iteration, possibly preconditioned, is applied to the Wiener-Hopf equation. Substituting estimates for various statistical quantities in the resulting recursion, a large number of classical and modern adaptive filters are developed with ease within a unified framework. Taking further inspiration from the field of numerical linear algebra, in this paper we make use of the multigrid paradigm, mostly used in the numerical solution of partial differential equations and their corresponding discretized linear equation sets, to devise a simple, yet robust adaptive filter with better performance than the NLMS algorithm.