(1. 中南大學(xué) 有色金屬成礦預(yù)測(cè)教育部重點(diǎn)實(shí)驗(yàn)室 長(zhǎng)沙 410083；
2. 中南大學(xué) 地球科學(xué)與信息物理學(xué)院，長(zhǎng)沙 410083)
摘 要: 推導(dǎo)了將線性GM模型轉(zhuǎn)換為變量含誤差(EIV)模型并采用總體最小二乘(TLS)平差的方法，介紹了加權(quán)總體最小二乘、混合總體最小二乘和附限制條件的總體最小二乘問題及其解算方法。以經(jīng)典大地測(cè)量控制網(wǎng)平差和數(shù)據(jù)擬合算例比較各種TLS估計(jì)的精度和計(jì)算效益。理論分析和算例表明：對(duì)于EIV模型，WTLS為最優(yōu)估計(jì)，實(shí)際應(yīng)用時(shí)需根據(jù)具體函數(shù)模型和隨機(jī)假設(shè)選擇合理的TLS平差方法。
關(guān)鍵字: 線性EIV模型；GM模型；測(cè)量平差；總體最小二乘
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
