通用EIV平差模型及其加权整体最小二乘估计

Weighted Total Least Squares of Universal EIV Adjustment Model

以平差基本理论为基础,提出了EIV(errors-in-variables)平差模型的通用形式,涵盖了间接平差、条件平差、附有参数的条件平差及附有限制条件的间接平差等基本EIV模型形式。基于整体最小二乘估计准则,研究了通用EIV模型的加权整体最小二乘算法,并推导了估计结果的近似精度公式。通用EIV模型及其整体最小二乘算法是对EIV模型估计理论的进一步完善,统一的整体最小二乘算法有利于软件的编程实现,有助于推动EIV模型估计理论的应用。

This paper proposes the universal errors-in-variables （EIV）adjustment model based on the fundamental adjustment theory,which covers the parametric adjustment model,conditional adjustment model,conditional adjustment model with parameters and parametric adjustment model with constrains. Applying total least squares （TLS）principle,we deduce the weighted TLS （WTLS）algorithm and the approximated precision of the EIV model.The universal EIV adjustment model and its estimator of WTLS contribute to the integrity of theory of EIV model estimation.The proposed uniform WTLS algorithm is appropriate for programming in software,which can contribute to the geodetic application of the theory of the EIV model estimation.