Superiority of LMS over RLS for tracking a chirped signal

When an adaptive filter, receiving coloured inputs, has to track a nonstationary environment, it is often said that the RLS algorithm will outperform the LMS one because it is known to converge faster. However, convergence speed is a transient property, independent of the amount of noise, while tracking is a steady-state performance and is therefore also influenced by the noise level. The answer is not obvious. There is in fact no single answer, and it depends very much on the problem under consideration. It has already been proved that LMS can be superior in a context where the optimal filter W₀(k) to be tracked is a zero-mean random function of time. The case where W₀(k) has deterministic time variation is considered