利用TSVD参数估值变化特性确定算法截断参数

doi:10.11947/j.AGCS.2022.20210377

测绘学报 ›› 2022, Vol. 51 ›› Issue (8): 1787-1796.doi: 10.11947/j.AGCS.2022.20210377

利用TSVD参数估值变化特性确定算法截断参数

林东方^1,2,3, 姚宜斌^2,4, 郑敦勇^1,3, 李朝奎^1,3

1. 湖南科技大学测绘遥感信息工程湖南省重点实验室, 湖南湘潭 411201;
2. 武汉大学测绘学院, 湖北武汉 430079;
3. 湖南科技大学地理空间信息技术国家地方联合工程实验室, 湖南湘潭 411201;
4. 武汉大学地球空间环境与大地测量教育部重点实验室, 湖北武汉 430079

收稿日期:2021-07-22 修回日期:2022-05-11 发布日期:2022-09-03
通讯作者: 姚宜斌 E-mail:ybyao@whu.edu.cn
作者简介:林东方(1986-),男,博士,讲师,研究方向为测量平差与PolInSAR数据处理。E-mail:lindongfang223@163.com
基金资助:
国家自然科学基金(42104025);湖南省自然科学基金创新研究群体项目(2020JJ1003);湖南省重点研发计划(2018GK2015);中国博士后科学基金(2021M702509);地球空间环境与大地测量教育部重点实验室测绘基础研究基金(20-01-04);湖南省自然科学基金(2021JJ30244);湖南省自然资源科技计划(2022-07;2022-29)

Determination of truncation parameter based on the differences of TSVD parameter estimates for ill-posed problems in geodesy

LIN Dongfang^1,2,3, YAO Yibin^2,4, ZHENG Dunyong^1,3, LI Chaokui^1,3

1. Hunan Provincial Key Laboratory of Geo-Information Engineering in Surveying, Mapping and Remote Sensing, Hunan University of Science and Technology, Xiangtan 411201, China;
2. School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China;
3. National-Local Joint Engineering Laboratory of Geo-Spatial Information Technology, Hunan University of Science and Technology, Xiangtan 411201, China;
4. Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University, Wuhan 430079, China

Received:2021-07-22 Revised:2022-05-11 Published:2022-09-03
Supported by:
The National Natural Science Foundation of China (No.42104025);Innovative Research Groups of the Natural Science Foundation of Hunan Province (No.2020JJ1003);Provincial Key Research and Development Program of Hunan (No.2018GK2015);China Postdoctoral Science Foundation (No.2021M702509);Surveying and Mapping Basic Research Foundation of Key Laboratory of Geospace Environment and Geodesy,Ministry of Education (No.20-01-04);The Natural Science Foundation of Hunan Province (No.2021JJ30244);The Natural Resources Science and Technology Project of Hunan Province (Nos.2022-07;2022-29)

摘要/Abstract

摘要： TSVD是大地测量病态问题解算的常用有效方法。影响TSVD解算效果的关键因素是截断参数,现有截断参数确定方法可提供有效的截断参数,但仍难以给出最优截断参数。以均方误差最小为准则确定截断参数是一种理论依据较充分的截断参数确定方法,但均方误差计算所需的模型参数真值在实际应用中无法获得,导致该方法难以给出理论最优截断参数。鉴于此,本文研究了基于均方误差影响下(方差与偏差联合影响)参数估值变化特性的TSVD截断参数确定方法。通过TSVD依次截掉小奇异值,获得奇异值截掉前后的方差与参数估值变化,利用两者变化分析确定偏差影响,避免依赖参数真值计算偏差,从而确定出均方误差最小理论下的截断参数。数值与应用试验结果表明,本文方法确定的截断参数可有效改善TSVD解算效果,是一种行之有效的截断参数确定方法。

关键词: 病态问题, 截断奇异值法, 截断参数, 均方误差, 偏差

Abstract: TSVD is an effective method commonly used in solving ill-posed geodetic problems.In this method,truncation parameter is a critical factor.However,the existing methods can only work out effective truncation parameters rather than identify the optimal truncation parameter.Determining truncation parameters based on the minimum mean square error is a relatively complete theoretical way to determine truncation parameters.But the true values of the model parameters required for the calculation of the mean square error cannot be obtained in practical applications,which makes it difficult to calculate the optimal truncation parameter theoretically.To solve these,this paper develops a method to identify the TSVD truncation parameter on the basis of the variation characteristics of the parameter estimation in the influence of the mean square error (including variance and bias).To achieve this,this paper truncates small singular values in turn based on TSVD to acquire the changes of the variance and parameter estimation and analyzes the changes to determine the effects of the biases,which can avoid the calculation biases in the use of the true value of the parameters.Thereby,based on the theory of the minimum mean square error,the truncation parameter can be determined.The results in numerical experiments and practical applications show that the truncation parameters in the new method can effectively improve the quality of TSVD solution.Therefore,the proposed method is an effective method to determine the truncation parameters.

Key words: ill-posed problem, TSVD, truncation parameter, mean square error, bias

中图分类号:

P207

林东方, 姚宜斌, 郑敦勇, 李朝奎. 利用TSVD参数估值变化特性确定算法截断参数[J]. 测绘学报, 2022, 51(8): 1787-1796.

LIN Dongfang, YAO Yibin, ZHENG Dunyong, LI Chaokui. Determination of truncation parameter based on the differences of TSVD parameter estimates for ill-posed problems in geodesy[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(8): 1787-1796.

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利用TSVD参数估值变化特性确定算法截断参数

Determination of truncation parameter based on the differences of TSVD parameter estimates for ill-posed problems in geodesy

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