顾及系数矩阵结构性的加权总体最小二乘解算  

A weighted total least squares algorithm considering the coefficient matrix structure

作　　者：汪奇生 叶险峰[2] 

机构地区：[1]湖南软件职业学院,湖南湘潭411100 [2]湘潭大学能源工程学院,湖南湘潭411100

出　　处：《测绘科学》2017年第4期133-136,共4页Science of Surveying and Mapping

基　　金：湖南省教育厅科研项目(15C0741;13C903)

摘　　要：针对加权总体最小二乘平差模型中系数矩阵具有结构性的问题,该文设计了一种顾及系数矩阵结构性的加权总体最小二乘迭代解法:首先,利用非线性最小二乘平差方法将总体最小二乘模型线性化;然后,采用结构矩阵的方法顾及系数矩阵的重复元素和常数项,通过间接平差的原理推导了顾及系数矩阵结构性的加权总体最小二乘迭代公式,可适用于加权总体最小二乘的参数估计;最后,通过算例分析并与其他算法进行比较,验证了该算法的有效性和可行性。Considering the structural problem of coefficient matrix ior total least squares aajustmem, a new algorithm for weighted total least squares was proposed. Firstly, the adjustment model was linear- ized by the nonlinear least squares adjustment theory. Therefore, the iteration algorithm and accuracy e- valuation formulas were deuced by the method that uses the structure matrix to consider the repetitive ele- ments and constant term. This algorithm could he applied for WTLS parameter estimation. The analysis and comparison results verified the effectiveness and feasibility of the algorithm.

关 键 词：加权总体最小二乘WLTS 总体最小二乘平差EIV模型 参数估计 迭代算法 结构矩阵 

分 类 号：P207[天文地球—测绘科学与技术]