Study of the transient phase of the forgetting factor RLS

We investigate the convergence properties of the forgetting factor RLS algorithm in a stationary data environment. Using the settling time as our performance measure, we show that the algorithm exhibits a variable performance that depends on the particular combination of the initialization and noise level. Specifically when the observation noise level is low (high SNR) RLS, when initialized with a matrix of small norm, it has an exceptionally fast convergence. Convergence speed decreases as we increase the norm of the initialization matrix. In a medium SNR environment, the optimum convergence speed of the algorithm is reduced as compared with the previous case; however, RLS becomes more insensitive to initialization. Finally, in a low SNR environment, we show that it is preferable to initialize the algorithm with a matrix of large norm.