Stochastic LMS with self adaptive forgetting factor

A least-mean-square algorithm, the stochastic gradient search least-mean-square (SGSLMS) algorithm, is proposed. It is robust to noise in the gradient estimate and has fast convergence without having to use an optimal step size. The SGSLMS algorithm is realized by estimating the correlation between the adaptive error and the input signals using as proposed new adaptive one-pole correlator. The correlator is used for fast, efficient gradient estimation rather than to control the step size, as in some other LMS variants. In the convergence process, the adaptive error, being initially large and highly nonstationary, results in a large gradient estimate. After convergence, the adaptive error is small, almost random, and almost stationary, yielding a small gradient estimate. The correlator is designed to optimize the rate of convergence under these two conditions. The performance of this algorithm is compared to those of the conventional and normalized LMS algorithms.<>