Penalized total least squares method for dealing with systematic errors in partial EIV model and its precision estimation

Abstract When the total least squares (TLS) solution is used to solve the parameters in the errors-in-variables (EIV) model, the obtained parameter estimations will be unreliable in the observations containing systematic errors. To solve this problem, we propose to add the nonparametric part (systematic errors) to the partial EIV model, and build the partial EIV model to weaken the influence of systematic errors. Then, having rewritten the model as a nonlinear model, we derive the formula of parameter estimations based on the penalized total least squares criterion. Furthermore, based on the second-order approximation method of precision estimation, we derive the second-order bias and covariance of parameter estimations and calculate the mean square error (MSE). Aiming at the selection of the smoothing factor, we propose to use the U curve method. The experiments show that the proposed method can mitigate the influence of systematic errors to a certain extent compared with the traditional method and get more reliable parameter estimations and its precision information, which validates the feasibility and effectiveness of the proposed method.