Median robust nonlinear weighted total least squares estimator of nonlinear EIV models: three algorithms

IF 1.2 4区 地球科学 Q3 ENGINEERING, CIVIL
Chuan Hu, Chenghong Li, Chongyang Zhang, Lidu Zhao, Xiaomeng Fan, Yusen Zhou, Hongzhou Zhu, Zheng Chen
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引用次数: 1

Abstract

To improve robust estimation performance of fully correlated nonlinear error-in-variables model, three median robust estimate methods are discussed on base of Nonlinear Weighted Total Least Squares (NWTLS), namely, median parameter method, median parameter initial value method and median variance method. After the discussion of the median robust estimation theory and the derivation of the calculation formula of the three median robust estimation methods, three iterative algorithms are developed. Through two nonlinear regression examples, four schemes including no artificial outliers, different location of outliers, different degrees of correlation, and different ratios of outliers are adopted, which proves the feasibility and effectiveness of the proposed algorithm. The experimental results show that from the statistical point of view, although the three median methods have different antioutlier effects for different nonlinear models, they are more effective than RNWTLS and NWTLS; the robust estimation results of three median methods are related to the functional model.
非线性EIV模型的中值鲁棒非线性加权总最小二乘估计:三种算法
为了提高全相关非线性变量误差模型的鲁棒估计性能,在非线性加权总最小二乘(NWTLS)的基础上,讨论了三种中值鲁棒估计方法,即中值参数法、中值参数初值法和中值方差法。在讨论了中值鲁棒估计理论,推导了三种中值鲁棒估计方法的计算公式后,提出了三种迭代算法。通过两个非线性回归算例,采用无人工异常点、不同异常点位置、不同相关程度、不同异常点比例四种方案,验证了所提算法的可行性和有效性。实验结果表明,从统计学的角度来看,虽然三种中位数方法对不同的非线性模型具有不同的抗离群值效果,但它们比RNWTLS和NWTLS更有效;三种中值方法的鲁棒性估计结果与函数模型有关。
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来源期刊
Survey Review
Survey Review 地学-地球科学综合
CiteScore
3.50
自引率
6.20%
发文量
33
审稿时长
6 months
期刊介绍: Survey Review is an international journal that has been published since 1931, until recently under the auspices of the Commonwealth Association of Surveying and Land Economy (CASLE). The journal is now published for Survey Review Ltd and brings together research, theory and practice of positioning and measurement, engineering surveying, cadastre and land management, and spatial information management. All papers are peer reviewed and are drawn from an international community, including government, private industry and academia. Survey Review is invaluable to practitioners, academics, researchers and students who are anxious to maintain their currency of knowledge in a rapidly developing field.
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