New insights on the convergence analysis of the affine projection algorithm for system identification

The convergence analysis of the affine projection algorithm (APA) is far to be an easy or trivial problem. In order to have a tractable analytical approach, a set of assumptions must be accepted. As a consequence, important differences appear between the analytical model and the simulations. In this paper the APA convergence is studied for two levels of approximation. A compact equation for a correction term is derived to refine the analysis. This result illustrates a better matching between the theoretical findings and simulation, in terms of the asymptotic behavior of the algorithm.