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This paper introduces a method of parameter estimation working on errors-in-variables polynomial non-linear models in which all measurements are corrupted by noise. The first step is to develop the linear regression models which are equivalent to polynomial non-linear systems. A main idea is to extend the parameter vector by even-order components of noise and to augment the regression vector by appropriate constants or measurements. Applying the method of least correlation, which has adoi:10.1080/00207170600999884 fatcat:yggao4ug65anregnzaxtsriqhe