NDLI: On symmetrical three-dimensional datum conversion

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On symmetrical three-dimensional datum conversion

Content Provider	Springer Nature Link
Author	Felus, Yaron A. Burtch, Robert C.
Copyright Year	2008
Abstract	A 3-D similarity transformation is frequently used to convert GPS-WGS84-based coordinates to those in a local datum using a set of control points with coordinate values in both systems. In this application, the Gauss-Markov (GM) model is often employed to represent the problem, and a least-squares approach is used to compute the parameters within the mathematical model. However, the Gauss–Markov model considers the source coordinates in the data matrix (A) as fixed or error-free; this is an imprecise assumption since these coordinates are also measured quantities and include random errors. The errors-in-variables (EIV) model assumes that all the variables in the mathematical model are contaminated by random errors. This model may be solved using the relatively new total least-squares (TLS) estimation technique, introduced in 1980 by Golub and Van Loan. In this paper, the similarity transformation problem is analyzed with respect to the EIV model, and a novel algorithm is described to obtain the transformation parameters. It is proved that even with the EIV model, a closed form Procrustes approach can be employed to obtain the rotation matrix and translation parameters. The transformation scale may be calculated by solving the proper quadratic equation. A numerical example and a practical case study are presented to test this new algorithm and compare the EIV and the GM models.
Starting Page	65
Ending Page	74
Page Count	10
File Format	PDF
ISSN	10805370
Journal	GPS Solutions
Volume Number	13
Issue Number	1
e-ISSN	15211886
Language	English
Publisher	Springer-Verlag
Publisher Date	2008-08-09
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Datum conversion Total least-squares adjustment Procrustes algorithm Electronic and Computer Engineering Automotive and Aerospace Engineering, Traffic Extraterrestrial Physics, Space Sciences Meteorology/Climatology Geophysics/Geodesy
Content Type	Text
Resource Type	Article
Subject	Earth and Planetary Sciences

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

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