A partially decoupled RLS algorithm for Volterra filters

In this correspondence, we consider a partially decoupled variation of the RLS algorithm. It is based on a constrained optimization of the cumulative filter error using the higher order sets of filter weights to improve on the performance of the lower order weight sets whose values are already established. From this constrained optimization, a recursive algorithm is developed whose form closely resembles the standard Volterra RLS algorithm but with structural differences that arise from eliminating the dependence of the lower order weight sets on the higher order weight sets while retaining the dependence of the higher order weights on the lower order weights. The resulting algorithm, while suboptimal, requires less computational effort than the fully coupled version, converges to steady state in the same amount of time, and is shown by example not to exhibit a substantial degradation in performance