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 a s our performance measure, we show that the algorithm exhibits a varia ble performance that depends on the particular combination of the init ialization and noise level. Specifically when the observation noise le vel is low (high SNR) RLS, when initialized with a matrix of small nor m, it has an exceptionally fast convergence, Convergence speed decreas es as we increase the norm of the initialization matrix, In a medium S NR environment, the optimum convergence speed of the algorithm is redu ced as compared with the previous case; however, RLS becomes more inse nsitive to initialization, Finally, in a low SNR environment, we show that it is preferable to initialize the algorithm with a matrix of lar ge norm.