Stabilized least squares estimators: convergence and error propagation properties

The basic convergence and error propagation properties of the recursive least-squares estimator stabilized algorithm with invariant factors (RLS-SI) are discussed. Under the assumption that the data are generated by a deterministic LTI system, the RLS-SI algorithm is exponentially convergent for persistently exciting signals. For a nonpersistent excitation the normalized prediction errors and the estimation changes are square summable and the estimates are bounded. If the excitation is strictly limited to a hyperspace, the estimation error on the excitation hyperspace tends to zero. If the measurements are corrupted by an additive white noise the parameter error converges to a random variable having zero mean and a limited variance. Numerical properties of the algorithms are favorable. A single error introduced into an arbitrary point of the RLS-SI algorithm decays exponentially