Stochastic Analysis of Regularized Recursive Least-Squares Algorithm

The regularized recursive least-squares (RLS) algorithm with an appropriate regularization parameter has much better robustness performance than the regular RLS algorithm in the presence of additive intensive noise, particularly in the acoustic echo cancelation applications. In this paper, the stochastic analysis of regularized RLS algorithm is conducted on the transient convergence within the context of adaptive system identification. The asymptotic convergence property in the mean sense and the steady-state behavior in the mean-square sense are also investigated respectively. Simulation results support the validity of our new theoretical findings, which complement the understanding of stochastic behaviors of regularized RLS algorithm in real-world applications.