This paper discusses a systematic technique for tuning a parameter estimator. The estimator used in this work is a discrete version of a projection algorithm estimator. Although the development is explained for linear models, the method is equally applicable to any type of linear or non-linear model that is linear with respect to the estimated parameters. The estimation scheme includes a first-order filter in the error dynamics equation and individual parameter adaptation equations. A simple analytical formula was derived for on-line tuning of the filter gain based on the maximisation of the decay of the norm of the output and parameter errors. The tuning of the parameter adaptation gains is also done based on the maximisation of the decay of this norm. The measurement noise problem was addressed using a specific dead zone approach. The algorithm performance is compared to the conventional RLS algorithm. (C) 2003 Elsevier Ltd. All rights reserved.