测绘学报 ›› 2021, Vol. 50 ›› Issue (5): 589-599.doi: 10.11947/j.AGCS.2021.20200126

• 大地测量学与导航 • 上一篇    下一篇

病态乘性误差模型的加权最小二乘正则化迭代解法及精度评定

王乐洋1, 陈涛1, 邹传义1,2   

  1. 1. 东华理工大学测绘工程学院, 江西 南昌 330013;
    2. 武汉大学测绘学院, 湖北 武汉 430079
  • 收稿日期:2020-04-07 修回日期:2020-09-27 发布日期:2021-06-03
  • 作者简介:王乐洋(1983-),男,博士,教授,研究方向为大地测量反演及大地测量数据处理。E-mail:wleyang@163.com
  • 基金资助:
    国家自然科学基金(41874001;41664001);东华理工大学研究生创新专项(DHYC-202020)

Weighted least squares regularization iteration solution and precision estimation for ill-posed multiplicative error model

WANG Leyang1, CHEN Tao1, ZOU Chuanyi1,2   

  1. 1. Faculty of Geomatics, East China University of Technology, Nanchang 330013, China;
    2. School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China
  • Received:2020-04-07 Revised:2020-09-27 Published:2021-06-03
  • Supported by:
    The National Natural Science Foundation of China (Nos. 41874001;41664001);The Innovation Fund Designated for Graduate Students of ECUT (No. DHYC-202020)

摘要: 针对乘性误差模型的病态问题,引入Tikhonov正则化方法,导出了病态乘性误差模型的加权最小二乘正则化解。顾及加权最小二乘正则化法在求解病态乘性误差模型时,参数估值与观测值之间存在复杂的非线性关系,本文利用一种无需求导、通过加权的方式便能够计算非线性函数的均值和均方误差阵的比例对称采样的无迹变换(scaled unscented transformation,SUT)法,对病态乘性误差模型进行精度评定。模拟算例和真实算例结果表明,本文提出的加权最小二乘正则化迭代解法可以有效减弱模型的病态性,基于SUT法的精度评定方法能够得到比已有方法更为合理的精度信息,具有较强的适用性。

关键词: 病态乘性误差模型, Tikhonov正则化, L曲线法, 精度评定, SUT法

Abstract: Aiming at the ill-posed problem of multiplicative error model, this paper introduces the Tikhonov regularization method to derive the weighted least squares regularization solution. Considering the complex nonlinear relationship between parameter estimations and the observations when using weighted least squares regularization method to solve the ill-posed multiplicative error model, the scaled unscented transformation (SUT) method is used to calculate the mean value and mean square error matrix of the nonlinear function by weighted without derivation for precision estimation of ill-posed multiplicative error model. The simulated and actual examples results show that the weighted least squares regularization iterative solution proposed in this paper can effectively weaken the ill-posed model, and the precision estimation method based on SUT method can obtain more reasonable precision information than the existing methods, and has strong applicability.

Key words: ill-posed multiplicative error model, Tikhonov regularization, L-curve method, precision estimation, SUT method

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