{"title":"Median robust nonlinear weighted total least squares estimator of nonlinear EIV models: three algorithms","authors":"Chuan Hu, Chenghong Li, Chongyang Zhang, Lidu Zhao, Xiaomeng Fan, Yusen Zhou, Hongzhou Zhu, Zheng Chen","doi":"10.1080/00396265.2022.2127605","DOIUrl":null,"url":null,"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.","PeriodicalId":49459,"journal":{"name":"Survey Review","volume":"55 1","pages":"481 - 497"},"PeriodicalIF":1.2000,"publicationDate":"2022-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Survey Review","FirstCategoryId":"89","ListUrlMain":"https://doi.org/10.1080/00396265.2022.2127605","RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, CIVIL","Score":null,"Total":0}
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.
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.