Extended least-correlation estimates for errors-in-variables non-linear models

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 a capability to cope with errors-in-variables linear models, to the equivalent model with extended parameters and augmented regressors yields an extended least-correlation estimator. Analysis shows that, for non-linear systems with third or lower order polynomials, the parameters estimated by the proposed method asymptotically converge to the true values. Numerical examples also support analytical results. Applications of the approach to Volterra models, Hammerstein models and Weiner non-linear systems are included.