谢波,刘连旺

• 1:合肥职业技术学院建筑工程学院
• 2:桂林理工大学博文管理学院

摘要(Abstract)：

针对等式约束和病态平差模型之间没有定量关系结论的问题，该文利用加权虚拟观测法和谱分解法推导出等式约束消除平差模型病态性的条件。首先将等式约束方程看作加权虚拟观测值，应用求条件极值的拉格朗日乘数法求得其一种正则化最小二乘解，然后利用矩阵的谱分解法推导出当等式约束的个数等于或大于病态平差模型的较小特征根个数时，等式约束能够消除平差模型的病态性。数据实验验证了理论的正确性和有效性。

关键词(KeyWords)： 加权虚拟观测;谱分解;等式约束;病态;正则化

Abstract:

Keywords:

基金项目(Foundation): 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);; 合肥职业技术学院科研项目(2021DTR04)

作者(Author): 谢波,刘连旺

DOI: 10.16251/j.cnki.1009-2307.2022.04.007

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