Identification of ARX models with noisy input and output

ARX (AutoRegressive models with eXogenous variables) are the simplest models within the equation error family but are endowed with many practical advantages concerning both their estimation and their predictive use. On the other hand the (implicit) assumption of noise-free inputs and of outputs affected by an additive colored noise whose spectrum is defined only by the model poles can be considered as non realistic when all measures are affected by additive errors. This paper considers the family of ARX + noise models that describe ARX processes whose measures are affected by additive white noise. The identification of these models is then mapped into the problem of identifying errors-in-variables models in the context of the Frisch scheme and a specific identification algorithm is described. A Monte Carlo simulation confirms the good results that can be obtained with the whole procedure.