附参数约束的方程赋权值解法研究  

Research on a unified resolution method for the observation model applying weight to its parameter constraint equation

作　　者：卢建兵 阳仁贵 LU Jianbing;YANG Rengui(Science and Technology Division,Lanzhou Resources&Environment Voc-Tech University,Lanzhou 730021,China;Yellow River Basin Ecotope Integration of Industry and Education Research Institute,Lanzhou Resources&Environment Voc-Tech University,Lanzhou 730021,China)

机构地区：[1]兰州资源环境职业技术大学科技处,甘肃兰州730021 [2]兰州资源环境职业技术大学黄河流域生态环境产教融合研究院,甘肃兰州730021

出　　处：《辽宁工程技术大学学报（自然科学版）》2024年第3期379-384,共6页Journal of Liaoning Technical University (Natural Science)

基　　金：甘肃省省级重点人才项目(ZB20231-01);甘肃省高校产业支撑计划项目(2023CYZC);兰州资源环境职业技术大学校级重大项目(X2022ZD-04)。

摘　　要：针对附参数约束等式方程的函数模型解算问题,提出一种对约束方程赋权值再联合观测方程统一解算的约束方程赋权统一解法。为验证此方法的可靠性和效率,基于矩阵分析法推导了适用于附参数约束方程解算的正交三角分解法和广义奇异值分解法。通过算例对3种解算法进行比较分析,结果表明:当给约束方程附加合适范围内的权值时,约束方程赋权统一解法获得的参数估计值与矩阵分解算法的参数估计结果在要求的精度范围内一致;赋权统一解法与正交三角分解法的计算效率接近,广义奇异值分解法计算效率较低;约束方程赋权统一解法更符合参数模型统一表达和平差准则设定,有利于平差算法设计和误差特性分析和研究。Aiming at the problem of function model solution with parameter constraint equation,a unified solution of constraint equation weighting is suggested,which combines the weighting value of constraint equation with the unified solution of observation equation.In order to verify the reliability and efficiency of this method,the orthogonal triangular decomposition formula and the generalized singular value decomposition formula suitable for the solution of the parameter constraint equation are deduced based on the matrix analysis method,and the three solution algorithms are compared and analyzed through examples.The results show that when a suitable weight value is given to the constraint equation,the parameter estimation values obtained through the unified solution of the constraint equation are consistent with the parameter estimation results of the matrix decomposition algorithm within the required accuracy range.The computational efficiency of the weighted unified solution is close to that of the orthogonal triangular decomposition method,and the computational efficiency of the generalized singular value decomposition method is low.The weighted unified solution of the constraint equation is more in line with the unified expression of the parameter model and the adjustment criterion,which is conducive to the design of the adjustment algorithm and the analysis and research of the error characteristics.

关 键 词：参数估计 约束方程赋权 统一解法 正交三角分解法 广义奇异值分解法 

分 类 号：P228[天文地球—大地测量学与测量工程]