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

doi:10.11947/j.AGCS.2021.20200126

摘要/Abstract

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

中图分类号:

P207

王乐洋, 陈涛, 邹传义. 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[J]. 测绘学报, 2021, 50(5): 589-599.

WANG Leyang, CHEN Tao, ZOU Chuanyi. Weighted least squares regularization iteration solution and precision estimation for ill-posed multiplicative error model[J]. Acta Geodaetica et Cartographica Sinica, 2021, 50(5): 589-599.

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