Convergence Performance of the Cascaded RLS-LMS Prediction

In this paper, we use a stochastic fixed-point theorem to analyze the stochastic convergence properties of the cascaded RLS-LMS prediction filter in terms of conditions of convergence and the misadjustment. It is shown that the cascaded RLS-LMS prediction filter converges to almost the same optimal solution of the conventional RLS filter. The misadjustment is shown to be exponentially dependent on the number of stages in the cascade structure and is higher than the misadjustment of the conventional RLS filter. However, the cascaded RLS-LMS prediction filter allows us to build up a low complexity RLS-like predictor with time-varying learning rate, which may be useful in uncertain and non-stationary environments.