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

• 作者: Leyang Wang Luyun Xiong Tao Chen
• 来源期刊: 大地测量与地球动力学（英文版）
• 年，卷（期）: 2021,（4）
• 页码范围: 249-257
• 页数: 9页
• 语种: 英文

摘要

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 sys-tematic 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 estima-tions 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 effec-tiveness of the proposed method.