State-Space Least Mean Square with Adaptive Memory

In this paper, we present state-space least mean square (SSLMS) algorithm with adaptive memory. SSLMS incorporates linear time-varying state-space model of the underlying environment. Therefore, it exhibits a marked improvement in tracking performance over the standard LMS and its known variants. Overall performance of SSLMS, however, depends on model uncertainty, presence of external disturbances, time- varying nature of the observed signal and nonstationary behavior of the observation noise. The step size parameter plays an important role in this context. However, because of lack of prior information of the uncertainties, it is difficult to suggest an optimum value of the step size parameter beforehand. As a logical approach to such problems, the step size parameter is iteratively tuned by stochastic gradient method so as to minimize the mean square value of the prediction error.