Introduction to multiple regression equations in datum transformations and their reversibility

Abstract

This paper provides an introduction to multiple regression equations as a method of performing geodetic datum transformations. The formulae are particularly useful when there are non-linear distortions that need to be built into the transformation model. However, the equations take the form of a one-way transformation, usually a local geodetic datum to a global datum. The standard procedure for applying the equations to obtain the reverse transformation only gives approximate results relative to the original model. This paper quantifies the problem and describes three methods for computing the reverse transformation (or inverse transformation) more accurately.

Keywords:

• Multiple regression equations
• Datum transformations
• Geodetic datums
• Reverse transformations

Acknowledgements

The author wishes to thank the two anonymous reviewers for their valuable comments which helped to improve this paper.