A stochastic gradient adaptive filter with gradient adaptive step size

The step size of this adaptive filter is changed according to a gradient descent algorithm designed to reduce the squared estimation error during each iteration. An approximate analysis of the performance of the adaptive filter when its inputs are zero mean, white, and Gaussian noise and the set of optimal coefficients are time varying according to a random-walk model is presented. The algorithm has very good convergence speed and low steady-state misadjustment. The tracking performance of these algorithms in nonstationary environments is relatively insensitive to the choice of the parameters of the adaptive filter and is very close to the best possible performance of the least mean square (LMS) algorithm for a large range of values of the step size of the adaptation algorithm. Several simulation examples demonstrating the good properties of the adaptive filters as well as verifying the analytical results are also presented.>