The paper deals with the identification of a process modelled by a stable, linear difference equation of known order, subject to additive output measurement noise, which is equally and independently distributed. It is shown that in the idealized situation, where the noise-free process output is assumed known, there is a set of three estimators which provide consistent estimates of the process parameters. Practical approximations to these estimators lead to on-line algorithms, in which the process parameters as well as the noise-free process outputs are estimated recursively in real time. These practical estimators are tested on simulated data obtained from time-invariant and slowly time-varying models. The performance of these estimators is compared with each other and also with some of the existing ‘bootstrap type’ estimators.