基于非线性高斯-赫尔默特模型的混合整体最小二乘估计

针对EIV模型的系数矩阵同时包含固定量和随机量的情况,通过将系数矩阵中的随机量提取出来纳入平差的随机模型,从而将EIV模型表示为非线性高斯-赫尔默特(Gauss-Herlmert,GH)模型形式,推导了混合LS-TLS(least squares-total least squares,LS-TLS)算法及其精度估计公式。算法适用于系数矩阵包含固定列、固定元素和随机元素的一般情况。模拟实例结果表明,混合LS-TLS算法与已有能够解决系数矩阵同时含固定量和随机量的结构性或加权TLS算法的估计结果一致;混合LS-TLS的估计结果统计上要优于LS或TLS估计结果。

Mixed LS-TLS Estimation Based on Nonlinear Gauss-Helmert Model

For the case of design matrix in EIV (errors-in-variables)model containing both fixed elements and random elements,this paper proposes a mixed LS-TLS (least squares-total least squares)algorithm and deduces the precision estimator by reformulating an EIV model as a nonlinear Gauss-Helmert model,in which random elements are extracted to the random model of adjustment.This algorithm can be applied to the general design matrix including simultaneously fixed columns,fixed elements and random elements.The example illustrates that the solution of mixed LS-TLS equal the solution of structured or weighted TLS algorithms which can solve mixed LS-TLS problem.Additionally,the solution of mixed LS-TLS statistically superior to solution of LS or TLS.