A super-linear converging two-point gradient algorithm for adaptive filters

In this paper, a novel gradient algorithm is proposed for adaptive filtering applications. The step-size is calculated by solving the secant equation for a specific approximation of the underlying Hessian matrix. During the convergence, the reciprocal of the step-size scans the range between the minimum and the maximum eigenvalues of the autocorrelation matrix, resulting in significant convergence rate improvement, compared with traditional gradient techniques. For two cases of statistical estimators, the corresponding adaptive algorithms are introduced and their performance is examined using simulations of a system identification experiment.