文献类型：期刊文献

英文题名：A new biased estimation method based on Neumann series for solving ill-posed problems

作者：Yang, Q. W.[1]

机构：[1]Shaoxing Univ, Dept Civil Engn, Shaoxing 312000, Peoples R China

年份：2019

卷号：16

期号：4

外文期刊名：INTERNATIONAL JOURNAL OF ADVANCED ROBOTIC SYSTEMS

收录：SCI-EXPANDED(收录号：WOS:000483476600001)、、EI(收录号：20193707412412)、Scopus(收录号：2-s2.0-85071850154)、WOS

基金：The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was funded by the National Natural Science Foundation of China (11202138).

语种：英文

外文关键词：Ill-posed problem; biased estimate; Neumann series; least squares estimate; ridge estimate

外文摘要：The ill-posed least squares problems often arise in many engineering applications such as machine learning, intelligent navigation algorithms, surveying and mapping adjustment model, and linear regression model. A new biased estimation (BE) method based on Neumann series is proposed in this article to solve the ill-posed problems more effectively. Using Neumann series expansion, the unbiased estimate can be expressed as the sum of infinite items. When all the high-order items are omitted, the proposed method degenerates into the ridge estimation or generalized ridge estimation method, whereas a series of new biased estimates can be acquired by including some high-order items. Using the comparative analysis, the optimal biased estimate can be found out with less computation. The developed theory establishes the essential relationship between BE and unbiased estimation and can unify the existing unbiased and biased estimate formulas. Moreover, the proposed algorithm suits for not only ill-conditioned equations but also rank-defect equations. Numerical results show that the proposed BE method has improved accuracy over the existing robust estimation methods to a certain extent.