In this paper, identification algorithms whose convergence and rate of convergence hinge on the regressor vector being persistently exciting are discussed. It is then shown that if the regressor vector is constructed out of radial basis function approximants, it will be persistently exciting, provided a kind of “ergodic” condition is satisfied. In addition, bounds on parameters associated with the persistently exciting regressor vector are provided; these parameters are connected with both the convergence and rates of convergence of the algorithms involved.