加权秩亏自由网平差的奇异值分解方法研究  

Study on the Singular Value Decomposition Method of Weighted Rank-deficient Free Network Adjustment

作　　者：汪俊帆 何虹儒 李凡 游为 WANG Junfan;HE Hongru;LI Fan;YOU Wei(School of Earth Sciences and Environmental Engineering,Southwest Jiaotong University,Chengdu 610031,China)

机构地区：[1]西南交通大学地球科学与环境工程学院,四川成都610031

出　　处：《测绘与空间地理信息》2024年第8期52-57,共6页Geomatics & Spatial Information Technology

基　　金：国家自然科学面上基金——融合MASCON和病态加权总体最小二乘的高精度高分辨率时变地球重力场计算(41974013)资助。

摘　　要：针对传统的加权秩亏自由网平差方法需要对法方程系数阵求广义逆或者需要提前获取约束条件或伪观测方程的问题,本文提出了一种基于奇异值分解系统的加权秩亏自由网平差方法。该方法不仅避免了传统方法的上述步骤,而且适用于观测值权矩阵以及参数先验权矩阵为任意形式的情况,实现了计算流程的简化和适用范围的扩展。加权秩亏自由网平差较多应用于水准网和GPS网,本文分别对相应算例进行验证。结果表明:本文所提出的方法与广义逆法、附加条件法和伪观测法这3种传统方法的计算结果和平差精度完全一致,同时计算效率大致相当,从而为加权秩亏自由网平差提供了一种可供选择的方法,可在控制网内部数据质量检核和变形分析等领域发挥作用。To solve the problem that the traditional weighted rank-deficient free network adjustment methods need to obtain the generalized inverse of the coefficient matrix of the normal equation or to obtain the constraint conditions or pseudo-observation equations in advance,this paper proposes a weighted rank-deficient free network adjustment method based on singular value decomposition system.This method not only avoids the above steps of the traditional methods,but also could be applied to the case where the observation value weight matrix and the parameter priori weight matrix are of arbitrary forms,which realizes the simplification of the calculation process and the expansion of the application range.The weighted rank-deficient free network adjustment is widely used in leveling network and GPS network,and the corresponding examples are verified in this paper.The results show that the adjustment accuracy and calculation efficiency of the proposed method are completely consistent with the traditional approaches.Thus,it provides an alternative method for the weighted rank-deficient free network adjustment and can play a role in the fields of data quality inspection and deformation analysis within the control network.

关 键 词：加权秩亏自由网平差 奇异值分解 加权最小范数最小二乘解 

分 类 号：P208[天文地球—地图制图学与地理信息工程]