On the influence of the forgetting factor of the RLS adaptive filter in system identification

The overall performance of the recursive least-squares (RLS) algorithm is governed by the forgetting factor. The value of this parameter leads to a compromise between low misadjustment and stability on the one hand, and fast convergence rate and tracking on the other hand. In this paper, we analyze another important phenomenon that has to be considered when choosing the value of the forgetting factor. Considering a system identification setup, there is a “leakage” of the system noise into the output of the adaptive filter. This process is highly influenced by the value of the forgetting factor but it also depends on the length of the adaptive filter. Simulations performed in an echo cancellation configuration prove these theoretical findings.