(1. 中南大学 有色金属成矿预测教育部重点实验室 长沙 410083；
2. 中南大学 地球科学与信息物理学院，长沙 410083)
摘 要: 推导了将线性GM模型转换为变量含误差(EIV)模型并采用总体最小二乘(TLS)平差的方法，介绍了加权总体最小二乘、混合总体最小二乘和附限制条件的总体最小二乘问题及其解算方法。以经典大地测量控制网平差和数据拟合算例比较各种TLS估计的精度和计算效益。理论分析和算例表明：对于EIV模型，WTLS为最优估计，实际应用时需根据具体函数模型和随机假设选择合理的TLS平差方法。
关键字: 线性EIV模型；GM模型；测量平差；总体最小二乘
linear errors-in-variables model and its typical applications
（1. Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education, Changsha 410083, China;
2. School of Geosciences and Info-Physics, Central South University, Changsha 410083, China）
Abstract:The method of converting linear Gauss-Markov (GM) model to linear errors-in-variables (EIV) model was given, an ordinary total least squares (TLS) adjustment algorithm were introduced as an alternative method for converted EIV model. Extended TLS methods of weight TLS, mixed ordinary LS and TLS, constrained TLS estimators with computational schemes were introduced as well. A typical geodetic control network adjustment and a curve fitting data experiments are given to compare the adjustment results in accuracy and computation efficiency by TLS and traditional LS methods. The data experiments and theoretic analysis indicate that WTLS method is an optimal estimator for EIV model, reasonable TLS algorithms should be selected according to the function model and associated stochastic model in practical application.
Key words: linear error in variables (EIV) model; Gauss-Markov (GM) model; least squares adjustment; total least squares
