A fake information matrix approach to the analysis of finite memory RLS identification techniques

In this paper, we study the performance of the least squares identification algorithm with exponential forgetting factor in a stochastic framework. The system parameter is modeled as a random-walk. Under a persistent excitation assumption of conditional type, an upper bound for the mean square norm of the parameter estimation error is derived. Such a bound is formed by the sum of two terms. The first one, which accounts for the parameter drift, is proportional to the memory length of the algorithm, while the second one, expressing the influence of the disturbance, is inversely proportional to the memory length. The bound is obtained by a novel approach based on the so-called fake information matrix, a “surrogate” of the true information matrix which is formed by that part of information which is independent of disturbance and drift terms