NDLI: Adjustment of non-typical errors-in-variables models

Content Provider	Springer Nature Link
Author	Ebrahimzadeh, S. Ardalan, A. A. Mahboub, V.
Copyright Year	2015
Abstract	In this contribution, non-typical errors-in-variables (EIV) model is introduced as a more general form of the so-called EIV model which is highly relevant for geodetic data processing. Total least-squares (TLS) algorithms within a typical EIV model cannot deal with the non-typical EIV models since the first order moment/mean of the random design matrix in a non-typical EIV model is not linear. In this paper, we propose a new algorithm besides a standard solution to deal with this model. To achieve this goal, first we review a classic algorithm in order to solve this problem using traditional non-linear least-squares method within a non-linear mixed model. Then by comparison, weighted TLS algorithm within the typical EIV model can be replaced by the proposed approach after some slight modifications which results in an excellent approximate solution. This foundation is important because there is no need for linearization in the TLS algorithms. The proposed way is not sensitive to the approximate initial values of the unknown parameters and it is applicable to curve fitting, surface reconstruction or other non-typical EIV models. Here we employ it to the curve fitting. Also two examples convincingly demonstrate that the standard TLS solution of the non-typical EIV model is not admissible when it is incorrectly considered as a typical EIV model; i.e., the non-linear relationships of the elements of the random design matrix are neglected.
Starting Page	207
Ending Page	218
Page Count	12
File Format	PDF
ISSN	22135812
Journal	Acta Geodaetica et Geophysica Hungarica
Volume Number	50
Issue Number	2
e-ISSN	22135820
Language	English
Publisher	Springer Netherlands
Publisher Date	2015-03-25
Publisher Institution	Quarterly of the Hungarian Academy of Sciences
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Weighted total least-squares algorithm Typical EIV model Geophysics/Geodesy Curve fitting Non-typical EIV model
Content Type	Text
Resource Type	Article
Subject	Building and Construction Geology Geophysics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Variance component estimation in errors-in-variables models and a rigorous total least-squares approach

Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis

Alternative formulae for parameter estimation in partial errors-in-variables models

A total least squares solution for geodetic datum transformations

A Newton algorithm for weighted total least-squares solution to a specific errors-in-variables model with correlated measurements

Total least-squares adjustment of condition equations

L $_{1}$ norm minimization in partial errors-in-variables model

An iterative solution of weighted total least-squares adjustment

Effects of errors-in-variables on weighted least squares estimation

Adjustment of non-typical errors-in-variables models

Similar Documents

Variance component estimation in errors-in-variables models and a rigorous total least-squares approach

Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis

Alternative formulae for parameter estimation in partial errors-in-variables models

A total least squares solution for geodetic datum transformations

A Newton algorithm for weighted total least-squares solution to a specific errors-in-variables model with correlated measurements

Total least-squares adjustment of condition equations

L $_{1}$ norm minimization in partial errors-in-variables model

An iterative solution of weighted total least-squares adjustment

Effects of errors-in-variables on weighted least squares estimation

Adjustment of non-typical errors-in-variables models