Rapidly converging adaptive IIR algorithms

Several new adaptive infinite-impulse (IIR) filtering algorithms based upon the algorithm developed by Fan and Jenkins are proposed in this paper. The Fan-Jenkins algorithm was shown to experimentally possess the ability to converge to the global minimum of the mean square error (MSE) even in cases where the mean square error (MSE) surface is ill-conditioned. By incorporating estimates of the Hessian matrix in the adaptive filter coefficient update expressions, the new versions of the algorithm appear to improve convergence performance in comparison to traditional Least Mean Square (LMS) type algorithms and to preserve the ability of the algorithm to converge to the global minimum of the mean square error (MSE). Least Mean Square (LMS), Recursive Least Square (RLS), Gauss-Newton (GN), and Fast Quasi-Newton forms of the algorithm are formulated and compared via simulation.