Generalized gradient adaptive step sizes for stochastic gradient adaptive filters

We derive new adaptive step size algorithms for two general classes of modified stochastic gradient adaptive filters that include the sign-error, sign-data, sign-sign, and normalized gradient adaptive filters as specific cases. These computationally-simple parameter adjustment algorithms are based on stochastic gradient approximations of steepest descent procedures for the unknown parameters. Analyses of the algorithms show that the stationary points of the steepest descent procedures yield the optimum step size values at each time instant as obtained from statistical analyses of the adaptive filter updates. Simulations verify the theoretical results and indicate that near-optimal tracking performance can be obtained from each of the adaptive step size algorithms without any knowledge of the rate of change of the unknown system