Multiple Regression ala DMA

This transformation is based on the series of Multiple Regression developments published by the US Defense Mapping Agency (NIMA) in Technical Report 8350.2-B, December 1987. Essentially, these are formulas developed from applying linear regression techniques to a varying number of points where the local coordinates and WGS84 coordinates are rather precisely known.

These regression formulas are based on normalized input coordinates. It is assumed that the normalized coordinates define the useful range of the datum transformation. In theory, therefore, a geographic coordinate that produces a normalized coordinate greater than 1.0 or less than -1.0 would normally be considered to be outside the useful range of the transformation. In this implementation of the regression technique, a geographic coordinate is considered to be outside the useful range of a transformation if the absolute value of either normalized coordinate exceeds 1.4.

In the event that a coordinate is given that is outside of the useful range of the multiple regression formula as described above, a fallback technique is used to calculate a datum shift. In this case, the fallback technique is the Molodensky, the Six Parameter Transformation, or the Seven Parameter Transformation depending upon how many parameters have been defined in the base definition. That is, when defining the datum definition, temporarily set the technique specification to Seven Parameter and set the desired fallback parameters. Then, the technique can be set back to the Multiple Regression selection and the parameters values will be preserved.

Currently, the parameters to such a transformation consist of a preprocessed .MRT file. These files contain all of the coefficients of the multiple regression formula in a compact form. This form also facilitates the actual testing of each parameter file individually as the DMA-provided test case is included in the file. Currently, no provisions are made for users to implement their own multiple regression parameter files. This may change in the future.