测绘学报 ›› 2016, Vol. 45 ›› Issue (1): 22-29.doi: 10.11947/j.AGCS.2016.20140560

• 大地测量学与导航 • 上一篇    下一篇

Partial EIV模型的解法

王乐洋1,2,3, 余航1, 陈晓勇1,2,3   

  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:2014-10-30 修回日期:2015-04-15 出版日期:2016-01-20 发布日期:2016-01-28
  • 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。
  • 基金资助:
    国家自然科学基金 (41204003; 41161069; 41304020);测绘地理信息公益性行业科研专项(201512026);江西省自然科学基金 (20132BAB216004;20151BAB203042);江西省教育厅科技项目(GJJ13456; KJLD12077; KJLD14049);地理空间信息工程国家测绘地理信息局重点实验室项目(201308);东华理工大学博士科研启动金(DHBK201113)

An Algorithm for Partial EIV Model

WANG Leyang1,2,3, YU Hang1, CHEN Xiaoyong1,2,3   

  1. 1. Faculty of Geomatics, East China Institute of Technology, Nanchang 330013, China;
    2. Key Laboratory of Watershed Ecology and Geographical Environment Monitoring of NASG, Nanchang 330013, China ;
    3. Jiangxi Province Key Lab for Digital Land, Nanchang 330013, China
  • Received:2014-10-30 Revised:2015-04-15 Online:2016-01-20 Published:2016-01-28
  • Supported by:
    The National Natural Science Foundation of China (Nos.41204003;41161069;41304020);National Department Public Benefit Research Foundation (Surveying,Mapping and Geoinformation) (No. 201512026);Natural Science Foundation of Jiangxi Province (Nos.20132BAB216004;20151BAB203042);Science and Technology Project of the Education Department of Jiangxi Province (Nos.GJJ13456;KJLD12077;KJLD14049);Key Laboratory of Geo-informatics of State Bureau of Surveying and Mapping (No.201308);Scientific Research Foundation of ECIT (No.DHBK201113).

摘要: 提出了一种求解partial errors-in-variables(partial EIV)模型的思路。通过对partial EIV模型的部分元素进行移项,重组成新形式下的平差函数模型,两次运用间接平差原理分别求解平差参数与系数矩阵中的随机元素,把总体最小二乘平差问题转化为最小二乘平差问题,并通过适当变换提高了新解法的收敛速度。最后分别采用实测数据和模拟数据进行验证,求解了本文算法与已有算法的估值结果。算例结果表明,本文算法能取得与已有算法相同的结果,是切实可行的。

关键词: 总体最小二乘, 部分变量含误差模型, 间接平差, 平面坐标转换, 直线拟合

Abstract: A new thinking for solving partial errors-in-variables (partial EIV) model was proposed. Through the transposition processing in partial EIV model, a new functional model was reconstructed. Adjustment of indirect observations has been used two times to calculate the model parameters and the stochastic elements in coefficient matrix, translating total least squares problem to least squares problem. It also achieves high convergence rate through some simple variables transformation. Finally, real and simulation data were implemented to compare with the existing algorithms and to analysis the applicability of the proposed algorithms. The results show that the new algorithms are feasible and it can achieve the same values with the existing algorithms.

Key words: total least squares, partial errors-in-variables model, indirect observations adjustment, coordinate transformation, straight line fit

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