等式约束病态总体最小二乘的修正奇异值解及精度评定  

Modified singular value solution and accuracy evalu-ation of equality constrained morbid total least squares

作　　者：翁烨 邵德盛 WENG Ye;SHAO Desheng(School of Land Resource Engineering of KUST,Kunming 650093,China;Yunnan Provincial Seismological Bureau,Kunming 650200,China)

机构地区：[1]昆明理工大学国土资源与工程学院,昆明650093 [2]云南省地震局,昆明650200

出　　处：《测绘工程》2022年第2期31-39,共9页Engineering of Surveying and Mapping

基　　金：李建成院士工作站(2015IC015);国家重点研发计划课题(2018YFC1503604)。

摘　　要：参数间一些精确的先验等式约束信息可以显著提高解的准确性和精度。在样本信息和先验信息下进行联合平差,基于病态总体最小二乘平差准则,分析奇异值分布对未知参数估计的影响,借助修正法修正奇异值,引入等式约束条件。通过建立拉格朗日目标函数的最小化求解,导出未知参数的迭代解式和近似方差-协方差矩阵,对等式约束病态总体最小二乘的修正奇异值解进行精度评定。计算整周模糊度算例和两个病态测边网算例,得出病态矩阵的奇异值按照降序排列且均匀分布时,等式约束总体最小二乘的奇异值修正法相比较等式约束总体最小二乘有明显的改善效果。Some accurate prior equality constraint information among parameters can significantly improve the accuracy and accuracy of the solution.The joint adjustment is carried out under the sample information and prior information.Based on the morbid total least squares adjustment criterion,the influence of singular value distribution on the unknown parameter estimation is analyzed.The singular value is corrected by the correction method,and the equality constraint condition is introduced.The iterative solution and approximate variance-covariance matrix of unknown parameters are derived by minimizing the Lagrange objective function.The accuracy of the modified singular value solution of the equation-constrained ill-conditioned total least squares is evaluated.By calculating the integer ambiguity calculation example and two ill-conditioned edge detection network calculation examples,it is concluded that when the singular values of the ill-conditioned matrix are arranged in descending order and uniformly distributed,the singular value correction method of the equality constrained total least squares has obvious improvement effect compared with the equality constrained total least squares.

关 键 词：联合平差 总体最小二乘 修正奇异值 方差-协方差 精度评定 

分 类 号：P207[天文地球—测绘科学与技术]