测绘学报 ›› 2019, Vol. 48 ›› Issue (4): 412-421.doi: 10.11947/j.AGCS.2019.20170693

• 大地测量学与导航 • 上一篇    下一篇

偏差改正的Partial EIV模型方差分量估计

王乐洋1,2,3, 温贵森1,2   

  1. 1. 东华理工大学测绘工程学院, 江西 南昌 330013;
    2. 流域生态与地理环境监测国家测绘地理信息局重点实验室, 江西 南昌 330013;
    3. 江西省数字国土重点实验室, 江西 南昌 330013
  • 收稿日期:2017-12-14 修回日期:2018-12-28 出版日期:2019-04-20 发布日期:2019-05-15
  • 作者简介:王乐洋(1983-),男,博士,副教授,主要研究方向为大地测量反演及大地测量数据处理。E-mail:wleyang@163.com
  • 基金资助:
    国家自然科学基金(41664001;41874001);江西省杰出青年人才资助计划(20162BCB23050);国家重点研发计划(2016YFB0501405)

Bias-corrected variance components estimation of Partial EIV model

WANG Leyang1,2,3, WEN Guisen1,2   

  1. 1. Faculty of Geomatics, East China University of Technology, Nanchang 330013, China;
    2. Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG, Nanchang 330013, China;
    3. Key Laboratory for Digital Land and Resources of Jiangxi Province, Nanchang 330013, China
  • Received:2017-12-14 Revised:2018-12-28 Online:2019-04-20 Published:2019-05-15
  • Supported by:
    The National Natural Science Foundation of China (Nos. 41664001; 41874001); The Outstanding Youth Talents in Jiangxi Province (No. 20162BCB23050); The National Key Research and Development Program (No. 2016YFB0501405)

摘要: 针对Partial EIV模型的方差分量估计中未考虑参数估值偏差所带来的影响,将Partial EIV模型视为非线性函数得到参数估值的偏差及二阶近似协方差表达式,计算得到偏差改正后的参数估值,结合方差分量估计方法,更新由参数估值影响的矩阵变量,给出了基于偏差改正的方差分量估计迭代方法。试验结果表明,参数估值及其协方差主要受参数估值偏差大小的影响,加入偏差改正能够得到更加合理的参数估值及方差分量估值,偏差改正后的方差分量估值可更加合理地评估参数估值的精度信息。

关键词: Partial EIV模型, 非线性, 偏差改正, 方差分量估计

Abstract: Considering the methods of variance components estimation (VCE) in Partial errors-in-variables (Partial EIV) model have not considered the effect of the bias of parameter estimates, the formulas of bias and second-order covariance matrix of parameter estimates are presented with the Partial EIV model regarded as a non-linear function and the parameter estimates after bias-correct are calculated. Combining the VCE method, the matrix variable influenced by the parameter estimates is updated, and an iterative method of variance components estimation based on bias-correct is given. The experiments show that the reasonable parameter estimates and its second-order approximate covariance results are affected by the bias of parameter estimates. The reasonable parameter estimates and variance components estimates can be obtained through the bias-correct and the second-order information obtained can reasonably evaluate precision of parameter estimates.

Key words: Partial EIV model, non-linear, bias correction, variance components estimation

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