Least-correlation estimates for errors-in-variables nonlinear models

In this paper, we introduce a method of parameter estimation working on errors-in-variables nonlinear models whose all variables are corrupted by noise. Main idea is to augment the parameters and the regressors of the linear regressor models by even-order components of noises and by appropriate constants, respectively, and to employ the method of least correlation, which has a capability to cope with errors-in-variables models, for the extended models. Analysis shows that for the polynomial nonlinearity of up to third order, the estimate converge to the true parameters as the number of samples increases toward infinity. We discuss the expected performance of the estimates applied to fourth or higher-order polynomial nonlinear models. Monte Carlo simulations of simple numerical examples support the analytical results.