2014
DOI: 10.1590/s1982-21702014000400053
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Orthogonal distance from an ellipsoid

Abstract: Finding the orthogonal (shortest) distance to an ellipsoid corresponds to the ellipsoidal height in Geodesy. Despite that the commonly used Earth reference systems, like WGS-84, are based on rotational ellipsoids, there have also been over the course of the years permanent scientific investigations undertaken into different aspects of the triaxial ellipsoid. Geodetic research has traditionally been motivated by the need to approximate closer and closer the physical reality. Several investigations have shown th… Show more

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Cited by 24 publications
(12 citation statements)
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“…The quantity (target function) to be minimized Bektas [12]. To overcome the problems with the algebraic distances, it is natural to replace them by the orthogonal distances which are invariant to transformations in Euclidean space and which do not exhibit the high curvature bias.…”
Section: Orthogonal (Geometric) Hyperboloid Fitting Methodsmentioning
confidence: 99%
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“…The quantity (target function) to be minimized Bektas [12]. To overcome the problems with the algebraic distances, it is natural to replace them by the orthogonal distances which are invariant to transformations in Euclidean space and which do not exhibit the high curvature bias.…”
Section: Orthogonal (Geometric) Hyperboloid Fitting Methodsmentioning
confidence: 99%
“…Throughout this paper, we assume that these conditions are satisfied. For the solution of the fitting problem, the linear or linearized relationship, written between the given data points and unknown parameters (one equation per data points), consists of equations, including unknown parameters Bektas [13].…”
Section: Fitting Hyperboloid To Noisy Datamentioning
confidence: 99%
See 1 more Smart Citation
“…The orthogonal distances, are therefore, calculated for every point of the model using the equations presented by Bektas (2014). Table 1 shows the results for patient one.…”
Section: Distances From the Ellipsoidmentioning
confidence: 99%
“…Our aim to find the orthogonal distances from a shifted-oriented ellipsoid see Figure 2. For detailed information on this subject refer to Bektas (2014). [-0.0006 -0.0008 -0.0010 0.0005 -0.0005 0.0003 0.0092 0.0050 0.0278] The conical coefficients in the Least Absolute Values Method is, v=[ -0.0071 -0.0084 -0.0096 0.0047 -0.0040 0.0023 0.0880 0.0061 0.0271]…”
Section: Finding Orthogonal Distances From the Ellipsoidmentioning
confidence: 99%