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contributor authorTomás Soler
contributor authorJen-Yu Han
date accessioned2024-04-27T22:31:41Z
date available2024-04-27T22:31:41Z
date issued2024/02/01
identifier other10.1061-JSUED2.SUENG-1460.pdf
identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4296861
description abstractThe least-squares (LS) method is universally embraced to obtain approximate unique solutions and their statistics from overdetermined scientific experiments where the number of observations amply exceeds the number of unknowns. The so-called mathematical model is the functional relationship marquee controlling the quality of the solution. A correct math model that faithfully recreates the physical properties of nature is essential for obtaining meaningful results. In this investigation, the LS outcomes using two totally different and accurate math models are compared and, amazingly, the values of the parameters (aka unknowns) computed are exactly the same as the original published values. This new exercise corroborates that, as intuitively anticipated, both solutions agree—although, remarkably, much closer than expected. In the process of this revamped research, novel innovative notation and ideas related to taking partial derivatives required to generate the design matrices are explained and, step-by-step, implemented. The derivations are presented introducing a user-friendly didactic path aimed to help readers (primarily students) working on the physical sciences and engineering to comprehend and master the entire methodology. A Matlab simple function to fit a triaxial ellipsoid to a cluster of points was coded based on the formulation developed for this study.
publisherASCE
titleLeast Squares Comparison of Two Rigorous Math Models Used to Fit a Triaxial Ellipsoid to a Cluster of Points
typeJournal Article
journal volume150
journal issue1
journal titleJournal of Surveying Engineering
identifier doi10.1061/JSUED2.SUENG-1460
journal fristpage04023019-1
journal lastpage04023019-13
page13
treeJournal of Surveying Engineering:;2024:;Volume ( 150 ):;issue: 001
contenttypeFulltext


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