Comparison of RLS and LMS algorithms for tracking a chirped signal

The authors study the capabilities of the exponentially weighted recursive-least-squares (RLS) and least-mean-squares (LMS) algorithms, when configured as adaptive predictors, to track a chirped sinusoid in white background noise. The lag and fluctuation behaviors of each of the algorithms are calculated, and their influence on the misadjustment error is determined. The optimum tracking parameters for each algorithm are evaluated. The misadjustment errors for these optimum values are compared as a function of the chirp rate ψ, the SNR ρ, and the number of filter taps M. It is shown that for sufficiently small ψ, small ρ, and M such that ρM≫1, the LMS algorithm is superior to RLS because it has a smaller lag