Tracking of linear time-varying systems using state-space least mean square

Abstract

In this paper, we present a generalized least mean square (LMS) algorithm. This new filter, which has been termed as state-space least mean square (SSLMS), incorporates linear time-varying state-space model of the underlying environment. The tracking ability of the LMS is limited due to linear regression model assumption. By overcoming this restriction, SSLMS exhibits a marked improvement in tracking performance over standard LMS and its known variants. The derivation of SSLMS is based on the minimum norm solution of an underdetermined linear least squares problem. An example of tracking a linear time-varying system demonstrates the ability and flexibility of SSLMS.