Introduction to multiple regression equations in datum transformations and their reversibility

Ruffhead, A. C.

doi:10.1080/00396265.2016.1244143

Cited by 7 publications

(10 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…MREs are usually polynomial functions of intermediate coordinates U (based on latitude) and V (based on longitude). The range of possible ways of defining these intermediate coordinates is summarised in Ruffhead (2018). The form used by DMA is that given by ( 3) and (4) except that a single scale factor K is used.…”

Section: Construction Of Mresmentioning

confidence: 99%

“…The inverse (or reverse transformation) of an MRE can be computed by applying the model with a change of sign for each coefficient. This was recommended by Appelbaum (1892) and is described by Ruffhead and Whiting (2020) as a simple same-formula inverse (SSFI). It is not exact relative to the original model, because U and V are calculated from ϕ and λ in the other datum.…”

Section: Construction Of Mresmentioning

confidence: 99%

See 1 more Smart Citation

Partitions of normalised multiple regression equations for datum transformations

Ruffhead

2022

Bol. Ciênc. Geod.

View full text Add to dashboard Cite

Multiple regression equations (MREs) provide an empirical direct method of transforming coordinates between geodetic datums. Since they offer a means of modelling distortions, they are capable of a more accurate fit to datumshift datasets than more basic direct methods. MRE models of datum shifts traditionally consist of polynomials based on relative latitude and longitude. However, the limited availability of low-power terms often leads to high-power terms being included, and these are a potential cause of instability. This paper introduces three variations based on simple partitions and 2 or 4 smoothly conjoined polynomials. The new types are North/South, East/West and Four-Quadrant. They increase the availability of low-order terms, enabling distortions to be modelled with fewer side effects. Case studies in Great Britain, Slovenia and Western Australia provide examples of partitioned MREs that are more accurate than conventional MREs with the same number of terms.

show abstract

Section: Construction Of Mresmentioning

confidence: 99%

Section: Construction Of Mresmentioning

confidence: 99%

Partitions of normalised multiple regression equations for datum transformations

Ruffhead

2022

Bol. Ciênc. Geod.

View full text Add to dashboard Cite

show abstract

“…In the forward transformation, R Z is applied to the longitude after the translations; therefore, in the reverse transformation, -R Z must be applied to the longitude before application of the reverse translations. If the user wishes a corrected inverse (CI) which is more exact, the misclosure can be applied in much the same way as in Sections 2.4, 2.5 and 2.13 of Ruffhead and Whiting (2020).…”

Section: Computing the Inverse Transformationmentioning

confidence: 99%

Partially-conformal variations of the Standard Molodensky datum transformation

Ruffhead

2022

Bol. Ciênc. Geod.

View full text Add to dashboard Cite

Standard Molodensky is a recognised method of transforming coordinates between geodetic datums. Although less accurate than some other methods, it has the merit of being direct. That is to say it can be applied to geodetic coordinates, without involving Cartesian coordinates that give rise to difficulties in computing latitude. This paper considers the use of Standard Molodensky when at least one of the datums is 2D+1D in nature, meaning that that horizontal and vertical positions are obtained by different methods. This was generally the case before 3D positioning by satellites and is a widespread characteristic of local datums that are still used. The 2D+1D property weakens the argument for 3D conformality, and invites the possibility that different translation parameters might be used for horizontal and vertical shifts. The possibility of including a Z-rotation as a 7th parameter is also considered. Besides being ideal for those who favour the simplicity of Standard Molodensky, the variations introduced in this paper offer significant improvements in accuracy such as error reductions of 75%, 69% and 99% in the three selected case studies.

show abstract

“…To be useful practically, a single transformation method and parameter set between two CRSs must either be reversible, or be reported with separate sets of forward and reverse parameters and equations (cf. Ruffhead, 2018). Here, reversible is considered to have two forms: (i) a rigorous mathematical form where the algorithm of the forward method is inverted and the defined transformation parameters are applied to the reverse calculation;…”

Section: Reversibilitymentioning

confidence: 99%

Comparative Review of Molodensky–Badekas and Burša–Wolf Methods for Coordinate Transformation

Abbey

Featherstone

2020

J. Surv. Eng.

View full text Add to dashboard Cite

J. Badekas reinterpreted M.S. Molodensky's three-dimensional similarity transformation as a vector solution using a centroid. The solution has since been [mis]interpreted by some others with inconsistent reference to the methods of both Molodensky and Badekas, principally relating to the translation vector and the stochastic model. This appears to have led to incorrect claims that the Molodensky-Badekas method is superior to the Helmert similarity and Burša-Wolf methods. This paper reviews the development and description of the original Badekas method, reconfirming its equivalence to the Burša-Wolf method in the forward direction, and provides an alternative solution that suits the same-formula reversal common in commercial surveying software. It is also demonstrated that the Molodensky-Badekas method has no inherent superiority over the Burša-Wolf method, has an ambiguous functional model, and nominally underestimates its parameter statistics when these are compared directly to those from the Burša-Wolf method.

show abstract

Introduction to multiple regression equations in datum transformations and their reversibility

Cited by 7 publications

References 10 publications

Partitions of normalised multiple regression equations for datum transformations

Partitions of normalised multiple regression equations for datum transformations

Partially-conformal variations of the Standard Molodensky datum transformation

Comparative Review of Molodensky–Badekas and Burša–Wolf Methods for Coordinate Transformation

Contact Info

Product

Resources

About