不确定性平差模型的平差准则与解算方法

doi:10.11947/j.AGCS.2015.20130213

测绘学报 ›› 2015, Vol. 44 ›› Issue (2): 135-141.doi: 10.11947/j.AGCS.2015.20130213

不确定性平差模型的平差准则与解算方法

宋迎春, 谢雪梅, 陈晓林

中南大学地球科学与信息物理学院, 湖南长沙 410083

收稿日期:2014-03-21 修回日期:2014-10-27 出版日期:2015-02-20 发布日期:2015-02-14
作者简介:宋迎春(1963—),男,教授,博士,研究方向为测量平差与数据处理。E-mail:csusyc@csu.edu.cn
基金资助:
地理信息工程国家重点实验室开放基金(SKLGIE2013-M-2-5);中国博士后科学基金(2013M540641)

Adjustment Criterion and Algorithm in Adjustment Model with Uncertain

SONG Yingchun, XIE Xuemei, CHEN Xiaoling

School of Geosciences and Info-Physics, Central South University, Changsha 410083, China

Received:2014-03-21 Revised:2014-10-27 Online:2015-02-20 Published:2015-02-14
Supported by:
Open Research Fund of State Key Laboratory of Geography Information Engineering(No.SKLGIE 2013-M-2-5);China Postdoctoral Science Foundation(No.2013M540641)

摘要/Abstract

摘要： 在测量数据的获取过程中, 经常存在着不确定性, 它们影响着参数估计的可靠性。本文通过把不确定度作为参数融入函数模型, 建立了不确定性平差模型。依据残差中不确定性传播规律, 确定了残差最大不确定度达到最小的平差准则, 利用迭代算法得到了不确定性平差模型的解算方法。通过实例分析了最小二乘平差、整体最小二乘平差和不确定性平差准则下最优解的不同特点, 从一个新的角度探讨了不确定性观测数据处理方法, 推广了现有的误差理论。

关键词: 不确定度, 平差准则, 残差, 整体最小二乘平差, 平差模型

Abstract: Uncertainty often exists in the process of obtaining measurement data, which affects the reliability of parameter estimation. This paper establishes a new adjustment model in which uncertainty is incorporated into the function model as a parameter. A new adjustment criterion and its iterative algorithm are given based on uncertainty propagation law in the residual error, in which the maximum possible uncertainty is minimized. This paper also analyzes, with examples, the different adjustment criteria and features of optimal solutions about the least-squares adjustment, the uncertainty adjustment and total least-squares adjustment. Existing error theory is extended with new observational data processing method about uncertainty.

Key words: uncertain, adjustment criterion, residual error, total least-squares adjustment, adjustment model

中图分类号:

P207

宋迎春, 谢雪梅, 陈晓林. 不确定性平差模型的平差准则与解算方法[J]. 测绘学报, 2015, 44(2): 135-141.

SONG Yingchun, XIE Xuemei, CHEN Xiaoling. Adjustment Criterion and Algorithm in Adjustment Model with Uncertain[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(2): 135-141.

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不确定性平差模型的平差准则与解算方法

Adjustment Criterion and Algorithm in Adjustment Model with Uncertain

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