一类新函数模型及通用加权总体最小二乘平差方法

General weighted total least squares method for a type of new functional model

针对摄影测量、计算机视觉、三维激光扫描、遥感影像几何纠正等领域中观测数据的特性,将y≈Aξ的变量含误差模型(EIV)拓展为y≈A(x)ξ的函数模型,该模型首先给出了设计矩阵协方差阵的计算方法,其次推导了一种通用的加权总体最小二乘(WTLS)平差算法和近似精度评定方法,并通过直线拟合、自回归模型参数估计算例进行验证计算.结果表明:无论观测值独立还是观测值相关,该方法与已有方法的WTLS平差结果及其精度一致,从而验证了该方法的正确性,且其算法更简洁方便.对于完善WTLS平差理论和方法,拓展总体最小二乘方法在3S技术中的应用有理论与现实意义.

A functional model y≈A（x）ξwas derived from the errors-in-varibles（EIV）model of y≈Aξ,according to the characteristics of observation data from photogrammetry and computer vision,three dimensional laser scanning and geometric rectification of remote sensing imageries.Covariance matrix algorithms of design matrix was first introduced,then general weighted total least squares（WTLS）method and approximate accuracy assessment methods were presented.The validity of the proposed methodology was verified by a linear fitting example and an auto-regression example.The experimental results show that：whether the observations are correlated or not,the adjustment method proposed in this paper can achieve the same WTLS results and accuracy as existing methods.Moreover,it is more simple and convenient,and has practical significance in promoting WTLS adjustment theory and methods,as well as expanding applications of total least squares method in 3Stechnology.