State-space least mean square

In this paper, we present a generalized form of the well-known least mean square (LMS) filter. The proposed filter incorporates linear time-varying state-space model of the underlying environment and hence is termed as state-space LMS (SSLMS). This attribute results in marked improvement in its tracking performance over the standard LMS. Furthermore, the use of SSLMS in state estimation in control systems is straightforward. Overall performance of SSLMS, however, depends on factors like model uncertainty and time-varying nature of the problem. SSLMS with adaptive memory, having time-varying step-size parameter, provides solutions to such cases. The step-size parameter is iteratively tuned by stochastic gradient method so as to minimize the mean square value of the prediction error. Different computer simulations demonstrate the ability of the algorithms suggested in this paper. A detailed study of computational complexities of the proposed algorithms is carried out at the end.