  A recursive least squares algorithm with variable rate forgetting (VRF) is
derived by minimizing a quadratic cost function.Under persistent excitation and
boundedness of the forgetting factor, the minimizer given by VRF is shown to
converge to the true parameters. In addition, under persistent excitation and
with noisy measurements, where the noise is uncorrelated with the regressor,
conditions are given under which the minimizer given by VRF is a consistent
estimator of the true parameters.The results are illustrated by a numerical
example involving abruptly changing parameters.
