Convex Combination of Three Affine Projections Adaptive Filters

This paper introduces an estimation scheme aimed at improving the performance of adaptive filters. The basic idea consists of a convex combination of three adaptive filters, all based on the affine projection algorithm with different numbers of normalization hyperplanes. The three filters are adjusted separately and then combined to minimize the MSE and to increase the speed of convergence of the overall structure. It is known that as the number of projections increases so does the computational complexity due to the need of inverting an L × L matrix, L being the number of projections. A simple scheme is proposed for efficiently computing the matrix inversions, taking advantage of the computation of the inverse matrix of a previous stage (lower order). Computer experiments show the effectiveness of the proposed estimation scheme.