Effects of errors-in-variables on the internal and external reliability measures  

作　　者：Yanxiong Liu Yun Shi Peiliang Xu Wenxian Zeng Jingnan Liu 

机构地区：[1]First Institute of Oceanography,Ministry of Natural Resources,Qingdao 266061,China [2]School of Geomatics,Xi'an University of Science and Technology,Xi'an 710048,China [3]Disaster Prevention Research Institute,Kyoto University,Uji,Kyoto 611-0011,Japan [4]School of Geodesy and Geomatics,Wuhan University,Wuhan 430079,China [5]Research Center of GNSS,Wuhan University,Wuhan 430079,China

出　　处：《Geodesy and Geodynamics》2024年第6期568-581,共14页大地测量与地球动力学（英文版）

基　　金：supported by the National Natural Science Foundation of China, Project No. 42174045;under National Key Research and Development Program of China, Project No.2020YFB0505805;the National Natural Science Foundation of China, Project No. 41874012。

摘　　要：The reliability theory has been an important element of the classical geodetic adjustment theory and methods in the linear Gauss-Markov model. Although errors-in-variables(EIV) models have been intensively investigated, little has been done about reliability theory for EIV models. This paper first investigates the effect of a random coefficient matrix A on the conventional geodetic reliability measures as if the coefficient matrix were deterministic. The effects of such geodetic internal and external reliability measures due to the randomness of the coefficient matrix are worked out, which are shown to depend not only on the noise level of the random elements of A but also on the values of parameters. An alternative, linear approximate reliability theory is accordingly developed for use in EIV models. Both the EIV-affected reliability measures and the corresponding linear approximate measures fully account for the random errors of both the coefficient matrix and the observations, though formulated in a slightly different way. Numerical experiments have been carried to demonstrate the effects of errors-in-variables on reliability measures and compared with the conventional Baarda's reliability measures. The simulations have confirmed our theoretical results that the EIV-reliability measures depend on both the noise level of A and the parameter values. The larger the noise level of A, the larger the EIV-affected internal and external reliability measures;the larger the parameters,the larger the EIV-affected internal and external reliability measures.

关 键 词：Weighted least squares Errors-in-variables model Nonlinear adjustment Total least squares Reliability theory 

分 类 号：P207.1[天文地球—测绘科学与技术]