病态不确定性平差模型的岭估计算法

doi:10.11947/j.AGCS.2019.20180044

测绘学报 ›› 2019, Vol. 48 ›› Issue (4): 403-411.doi: 10.11947/j.AGCS.2019.20180044

• 大地测量学与导航 • 下一篇

病态不确定性平差模型的岭估计算法

鲁铁定^1,2,3, 吴光明¹, 周世健⁴

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;
4. 南昌航空大学, 江西南昌 330063

收稿日期:2018-01-25 修回日期:2019-01-29 出版日期:2019-04-20 发布日期:2019-05-15
通讯作者: 周世健 E-mail:shjzhou@nchu.edu.cn
作者简介:鲁铁定(1974-),男,博士,教授,研究方向为误差理论与测量平差。E-mail:tdlu@whu.edu.cn
基金资助:
国家自然科学基金（41464001）；测绘地理信息公益性行业科技专项（201512026）；江西省教育厅科技项目（KJLD12077）；国家重点研发计划（2016YFB0501405；2016YFB0502601-04）；江西省自然科学基金（2017BAB203032）

Ridge estimation algorithm to ill-posed uncertainty adjustment model

LU Tieding^1,2,3, WU Guangming¹, ZHOU Shijian⁴

1. Faculty of Geomatics, East China University of Technology, Nanchang 330013, China;
2. Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASMG, Nanchang 330013, China;
3. Jiangxi Province Key Lab for Digital Land, Nanchang 330013, China;
4. Nanchang Hangkong University, Nanchang 330063, China

Received:2018-01-25 Revised:2019-01-29 Online:2019-04-20 Published:2019-05-15
Supported by:
The National Natural Science Foundation of China(No.41464001); The Special S-cientific Research Fund for Public Welfare Profession of Surveying, Mapping and Geoinformation (No.201512026); The Science and Technology Project of the Education Department of Jiangxi Province (No. KJLD12077); The State's Key Project of Research and Development Plan(Nos. 2016YFB0501405; 2016YFB0502601-04); The Natural Science Foundation of Jiangxi Province of China(No. 2017BAB203032)

摘要/Abstract

摘要： 测量数据在获取的过程中，常存在不确定性，它们会影响参数估计结果，不确定性平差模型的解算方法可以有效提高参数估计的有效性和可靠性。当观测方程的系数矩阵存在接近零的奇异值，采用岭估计可有效抑制观测方程病态性对参数估值结果的影响。当不确定性平差模型出现病态，其受系数矩阵误差和观测值误差的影响更为严重，本文将岭估计法应用于病态不确定性平差模型，推导了迭代算法，以提高解的稳定性，并用算例验证，结果表明了新方法的有效性和可行性。

关键词: 病态, 不确定性, 平差模型, 岭估计

Abstract: Uncertainties usually exist in the process of acquisition of measurement data, which affects the parameter estimation results. The solution method of uncertainty adjustment model can effectively improve the validity and reliability of parameter estimation. When the coefficient matrix of the observation equation has a singular value close to zero, the ridge estimation can effectively suppress the influence of the ill-posed state of the observation equation on the parameter estimation results.When the uncertainty adjustment model is ill-posed, it is more seriously affected by the error of the coefficient matrix and the observation,this paper applies ridge estimation method to ill-posed uncertainty adjustment model, derives an iterative algorithm to improve the stability and reliability of the result, and verifies it with two examples. The results show that the new method is effective and feasible.

Key words: ill-posed, uncertainty, adjustment model, ridge estimation

中图分类号:

P227

鲁铁定, 吴光明, 周世健. 病态不确定性平差模型的岭估计算法[J]. 测绘学报, 2019, 48(4): 403-411.

LU Tieding, WU Guangming, ZHOU Shijian. Ridge estimation algorithm to ill-posed uncertainty adjustment model[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(4): 403-411.

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病态不确定性平差模型的岭估计算法

Ridge estimation algorithm to ill-posed uncertainty adjustment model

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