Improved convergence model of the affine projection algorithm for system identification

The convergence analysis of the affine projection algorithm (APA) was intensively studied, however, it is far to be a trivial task. In this context, a set of assumptions have to be considered, in order to allow a tractable analytical approach. As a consequence, notable differences occur between the simulation results and the analytical model. In this paper, the convergence of APA is studied and a refined approximation is proposed, named “the third level of approximation.” The results show a near perfect matching between the theoretical model and simulation results, in terms of the asymptotic behavior and convergence speed of the studied algorithm.