应用分块矩阵求逆解算约束秩亏间接平差模型  

Calculation of Rank-Defective Indirect Adjustment Model with Constraint by Inverting Block Matrix

作　　者：谢波 刘连旺 XIE Bo;LIU Lianwang(School of Civil Engineering and Architecture,Hefei Technology College,1 South-Laoshan Road,Hefei 238000,China;Bowen College of Management,Guilin University of Technology,317 Yanshan Street,Guilin 541006,China)

机构地区：[1]合肥职业技术学院建筑工程学院,合肥市238000 [2]桂林理工大学博文管理学院,桂林市541006

出　　处：《大地测量与地球动力学》2021年第2期157-161,共5页Journal of Geodesy and Geodynamics

基　　金：安徽省高校自然科学重点研究项目(KJ2019A1114);安徽省高校质量工程项目(2018jxtd037)。

摘　　要：在通常的四分块矩阵求广义逆矩阵和凯利逆矩阵公式基础上,分析左上角子矩阵为秩亏、右下角子矩阵为零的特殊四分块矩阵的凯利逆矩阵存在条件,应用广义逆矩阵法和矩阵变换法推导该类特殊四分块矩阵的凯利逆矩阵显性表达公式,并用于解算约束秩亏间接平差模型的参数估计。实验数据表明,当满足存在性条件时,应用分块矩阵求逆公式解算约束秩亏间接平差模型的结果与间接平差模型的解算结果一致,表明推导的显性表达公式具有可行性。Based on the general formula of generalized inverse matrix and Kelly inverse four block matrix,we analyze the existence conditions of a special kind of Kelly inverse four block matrix with a rank defective sub-block matrix in the upper left corner and a zero sub-block matrix in the lower right corner.The explicit expression formula of a Kelly inverse matrix of this kind is derived using the generalized inverting matrix method and the matrix transformation method,and is applied to the parameter estimation of rank-defective indirect adjustment model with constraints.The results show that when existence conditions are satisfied,the solution of rank-defective indirect adjustment model with constraints by inverting block matrix is consistent with that of the indirect adjustment model.This proves that the derived explicit expression formula is feasible.

关 键 词：测量平差 分块矩阵 广义逆矩阵 约束秩亏间接平差模型 

分 类 号：P207[天文地球—测绘科学与技术]