Analytic center approach to parameter estimation: convergence analysis

The so-called analytic center approach to parameter estimation has been proposed recently as an alternative to the well-known least squares approach. This new approach offers a parameter estimate that is consistent with the past data observations, has a simple geometric interpretation, and is computable sequentially. In this paper, we study the asymptotic performance of the analytic center approach and show that the resulting estimate converges to the true parameter asymptotically, provided some mild conditions are satisfied. These conditions involve some weak persistent excitation and independence between noise and regressor, similar to the least squares case. This result is used to derive a new parameter estimation approach which offers both good transient and asymptotic performances.