On the sensitivity of transversal RLS algorithms to random perturbations in the filter coefficients

The author investigates the sensitivity of the RLS algorithm to random perturbations about the optimum filter coefficients. Expressions are derived for the mean and variance of the deviation from the optimum error power for the prewindowed growing memory and the experimentally windowed (λ<1) RLS algorithm. The results show that the variance of the deviation for correlated signals increases compared to uncorrelated white signals by a term related to the sum of the square of the off-diagonal elements of the sample autocorrelation matrix. For λ<1, the deviations are bounded and inversely proportional to 1-λ. For λ=1, the deviations are unbounded and increase linearly with the number of iterations