利用均方误差相对变化规律确定正则化参数及其在PolInSAR测量反演中的应用

doi:10.11947/j.AGCS.2023.20220453

测绘学报 ›› 2023, Vol. 52 ›› Issue (9): 1480-1491.doi: 10.11947/j.AGCS.2023.20220453

利用均方误差相对变化规律确定正则化参数及其在PolInSAR测量反演中的应用

林东方^1,2,3, 姚宜斌¹, 郑敦勇^2,3, 廖孟光^2,3, 谢建^2,3

1. 武汉大学测绘学院, 湖北武汉 430079;
2. 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;
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

收稿日期:2022-07-22 修回日期:2023-08-09 发布日期:2023-10-12
通讯作者: 姚宜斌 E-mail:ybyao@whu.edu.cn
作者简介:林东方(1986-),男,博士,副教授,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);中国博士后科学基金(2021M702509);湖南省自然资源科技计划(2022-07);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;2022JJ30254)

Regularization parameter determination method based on MSE relative variation rule and its application in PolInSAR surveying inversion

LIN Dongfang^1,2,3, YAO Yibin¹, ZHENG Dunyong^2,3, LIAO Mengguang^2,3, XIE Jian^2,3

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

Received:2022-07-22 Revised:2023-08-09 Published:2023-10-12
Supported by:
The National Natural Science Foundation of China (No. 42104025);China Postdoctoral Science Foundation (No. 2021M702509);The Natural Resources Sciences and Technology Project of Hunan Province (No. 2022-07);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 (Nos. 2021JJ30244;2022JJ30254)

摘要/Abstract

摘要： 正则化方法是大地测量解算病态问题的常用方法,而正则化参数是影响正则化方法解算结果的关键参数。以均方误差最小为准则选取正则化参数,具有较充分的理论依据,可有效实现模型参数估值精度的提升。但是,均方误差计算过程中需要未知参数的真值,在实际情形中只能通过参数估值替代真值估算均方误差,难以获得可靠准确的均方误差值,限制了正则化参数的有效性。鉴于此,本文分析了正则化参数变化引起的方差与偏差变化规律,提出了一种均方误差相对变化值确定方法。依据不同正则化参数下模型参数真值不变原则,计算不同正则化参数下的方差与偏差相对变化量,从而消除参数真值对均方误差估计的影响。本文首先利用不同正则化参数计算两相邻正则化参数间的方差与标准差相对变化量;然后计算两正则化参数间模型参数估值变化量,通过差分运算分析得到两相邻正则化参数下的偏差相对变化量;最后综合标准差变化与偏差变化关系,得到均方误差最大降幅的正则化参数。通过PolInSAR植被高测量试验对本文方法的可行性进行了验证。试验表明,本文方法可有效改善正则化法模型参数估计精度。两个PolInSAR测量试验模型参数反演精度均得到了提高,合理验证了本文方法的可行性与有效性。

关键词: 均方误差, 正则化方法, 正则化参数, 相对变化, PolInSAR测量

Abstract: The regularization method is currently the most widely used method for solving ill-posed problems in geodesy, and the regularization parameter is the key parameter that affects the solution result of the regularization method. With sufficient theoretical basis, the regularization parameter determination method based on the minimum mean square error (MSE) criterion can increase the estimation accuracy of model parameters efficiently. However, the calculation of the mean square error requires the true value of model parameters which is replaced by the estimated value in practice. As a result, the accurate mean square error is difficult to obtain, which greatly limits the effectiveness of the regularization parameters. In view of this, this paper analyzes the variation law of variance and bias caused by the changes of regularization parameter, and proposes a determination method for relative variation of mean square error. According to the principle that the true value of model parameters does not change under different regularization parameters, the calculation of the relative changes of variance and bias under different regularization parameters can effectively remove the influence of unknown true values of model parameters on mean square error estimation. This paper firstly uses different regularization parameters to calculate the relative changes of variance and standard deviation between the two regularization parameters; then calculates the model parameter estimate change between the two regularization parameters. The relative variation of bias under the two regularization parameters is obtained by difference operation analysis of variance change and model parameter estimate change. Finally, the regularization parameter with the maximum reduction of the mean square error is obtained by integrating the changes of standard deviation and bias. The feasibility of the new method is verified by the polarimetric interferometric synthetic aperture radar (PolInSAR) vegetation height inversion experiment. All Experiments show that the new method can effectively enhance the parameter estimation accuracy of the regularization method. Both of the parameter inversion accuracy of the two PolInSAR surveying experiments are improved. Those reasonably verify the feasibility and effectiveness of the new method.

Key words: mean square error, regularization method, regularization parameter, relative change, PolInSAR surveying

中图分类号:

P227

林东方, 姚宜斌, 郑敦勇, 廖孟光, 谢建. 利用均方误差相对变化规律确定正则化参数及其在PolInSAR测量反演中的应用[J]. 测绘学报, 2023, 52(9): 1480-1491.

LIN Dongfang, YAO Yibin, ZHENG Dunyong, LIAO Mengguang, XIE Jian. Regularization parameter determination method based on MSE relative variation rule and its application in PolInSAR surveying inversion[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(9): 1480-1491.

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利用均方误差相对变化规律确定正则化参数及其在PolInSAR测量反演中的应用

Regularization parameter determination method based on MSE relative variation rule and its application in PolInSAR surveying inversion

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