Improved Fast Recursive Least Squares transversal filters for adaptive tracking of time-variant systems

Adaptive filtering is used in a wide range of applications including echo cancellation, noise cancellation and equalization. In these applications, the environment in which the adaptive filter operates is often non-stationary. For satisfactory performance under non-stationary conditions, an adaptive filtering is required to follow the statistical variations of the environment. Tracking analysis provides insight into the ability of an adaptive filtering algorithm to track the changes in surrounding environment. The tracking behavior of an algorithm is quite different from its convergences behavior. While convergence is a transient phenomenon, tracking is a steady-state phenomenon. Over the last decade a class of equivalent algorithms such as the normalized least mean squares algorithm (NLMS) and the fast recursive least squares algorithm (FRLS) has been developed to accelerate the convergence speed. In this paper, we introduce an improved version for the stabilized Fast Recursive Least Squares (FRLS) algorithm. A comparative study between the Normalized Least Mean Squares algorithm and the fast recursive least squares algorithm is also presented in context of tracking systems identification.