This paper deals with identification of discrete-time errors-in-variables models where the input and output data are both perturbed by different additive noises. The goal is to study the effects of input noise on the model which is estimated based on the prediction error method. The obtained model is then improved by modifying the results and implementing the instrumental variable method. It is proved that the identification of the errors-in-variables models based on the proposed approach could result in an unbiased estimation in the presence of independent colour noises on the input and output data with adequate accuracy and mediocre complexity.