On asymptotic convergence of the stochastic least squares algorithm

The asymptotic convergence of the least-squares (LSs) algorithm is investigated for stochastic inputs. It is shown that, when a forgetting factor is applied to the past data, the convergence is bounded exponentially, and prediction coefficients fluctuate around the LS coefficients in the steady state. A small forgetting factor increases the convergence rate, but results in a larger fluctuation. It is also shown that if there is no data forgetting, the convergence is O(1/T) and the coefficient fluctuation vanishes as T to infinity .<>