The three important things to remember if you are going to apply a geoid model to a one-step transformation are:

* The geoid model must be selected before the points are matched.

* No points are to be matched vertically.

* The base must have a correct known ellipsoidal height.

* My thanks to Henri Ayers for the following information:

All of the following cases are valid as long as the Geoid Field File is coming from a "WGS84" Geoid Model and is being selected "before" matching the horizontal (2-D position only) coordinates of the local points with the corresponding WGS84 coordinates.

No points should be matched in vertical to prevent using the vertical (1-D vertical shift only or 1-D vertical shift with 2-D best-fit plane tilting parameters) transformation parameter(s) and therefore bypassing the use of Geoid Model to obtain Local (Orthometric) heights.

The WGS84 Geoid Model will be used to directly convert WGS84 Ellipsoid Heights to Orthometric Heights and vice versa without affecting the 1-Step Horizontal Transformation. It is then implicit that the reference station WGS84 Ellipsoid Height used as the RTK Base must be correctly known in WGS84 since no local shifts in heights can be applied in the transformation except the interpolated Geoid separations.

1. One Point matched in Horizontal with WGS84 Geoid Field File:

It is possible to manually enter an orientation, an elevation and/or an horizontal scale factor to a 1-point matched in horizontal only 1-Step transformation even if no orientation and scale factors are computed from the transformation (default to 0 degree and 0.0 ppm). The values should be applied from WGS84 to the Local Grid for the orientation and from the WGS84 ellipsoid to the Ground for the elevation scale factor. Without knowing both the orientation and the overall scale factor for horizontal distance, a 1-point 1-step transformation is not too practical to use and may lead to erroneous coordinates when moving several kilometers away from the meridian passing at the point.

2.Two or more points matched in Horizontal with WGS84 Geoid Field File:  

Two or more points can be matched in horizontal only to compute a complete 1-step transformation (2-D Helmert) so that two 2-D shifts, one rotation and one horizontal scale factor are simultaneously determined. If 3 or more points can be matched in horizontal, residuals in the north and east components can be displayed and later used to further constrain (match exactly the local known coordinates) by applying one of the distribution of residual interpolation methods.

Following are some screen captures about computing a 1-Step Transformation from Horizontal matched points with a WGS84 Geoid model.

Screen "Before" Matching Common Points. (WGS84 Geoid Model must be selected before calculations)

Screen for Horizontal Point Matching

Examination of North & East Residuals after calculations

Storage of the 1-Step Horizontal transformation with 1/Dist Distribution of Residual Interpolation

You can get into a State Plane system when your base is unknown (you positioned it with HERE or SPP) by occupying a known State Plane point with the rover and doing a one-point Classical transformation. In the example below, we have one job with WGS 84 positions and another job with the state plane coordinates. The steps are shown below:

* Again, thanks go to Henri Ayers for illuminating this process.

Select 01 Determine Coord System from the Applications submenu.

Select a name for your coordinate system and the appropriate jobs containing the WGS 84 and Local (State Plane) positions.

Press the F1 (CONT) key and then select Classical as the transformation type, something other than WGS 84 as the Ellipsoid, your state plane zone as the Projection, and the appropriate geoid model if you want orthometric heights.

* Note: The geoid model field file must be selected at this time if you plan on using orthometric heights.

* WARNING: The geoid field file name you enter here must be created from a geoid model using an ellipsoid other than WGS 84. It should be the same ellipsoid as entered in the Ellipsoid field in the screen below. This can be the GRS 80 ellipsoid, or a new ellipsoid with the same parameters as WGS 84 as shown.

* Entering WGS 84 as the ellipsoid here, and using a geoid model based on WGS 84 will cause the orthometric heights to be calculated from the WGS 84 ellipsoid heights from the SPP or HERE position of the base and not the transformed ellipsoid heights.

Press the F1 (CONT) key and match the point with the known state plane position.

Note: If you just press F1 (CONT) here, you will get a message that you don't have enough points to match. In order to do a one-point classical, we need to fix the rotations and scale to zero and solve only for the shifts.

Press the Shift key and then press the F5 (PARAM) key.

To display the parameter screen.

Move the highlight using the down-arrow key, until it is in the first rotation field. Then press the F4 (FIX) key to set the rotation to zero. Repeat for all three rotation values.

Move the highlight farther down to the Scale field and press the F4 (FIX) key to set the scale to 0 ppm (equals a scale factor of 1.0).

Now press the F1 (CONT) key to see the results.

Press the F1 (CONT) key again to return to the Main Menu.

Now your new State Plane coordinate system will be active. This system will contain a shift from the approximate WGS 84 coordinates produced from the base, to the true WGS 84 coordinates of State Plane point.

Summary on the Use of Distribution of Residuals in Coordinate Transformations:

Main Purpose on the Use of Residual Distribution in Coordinate Transformations:

The spatial distribution of residuals can be applied to estimate additional shifts to the transformed coordinates. Known coordinates can be matched exactly whereas other coordinates are slightly shifted from the spatial distribution of residuals within the transformation area. These shifts can be determined from different Distance Weighting or Multi-Quadratic Interpolation methods of residuals.

Two Methods of Residual Interpolation:

1) Distance Weighting Residual Interpolation Method:

The Distance Weighting Residual Interpolation Method uses 3 distance weighting schemes namely:

        - 1/Distance

        - 1/Distance**1.5

        - 1/Distance **2.0

The main purpose of the distance weighting interpolation method is to de-correlate slowly (1/Distance), moderately (1/Distance**1.5) or rapidly (1/Distance**2.0) the influence of residuals at the point of interpolation as per the plot of these functions in the attached tentative. This method appears to be appropriate for uneven (sparse or heterogeneous) distribution of points having different magnitude of residuals within the transformation area. This method is probably adequate and sufficient for very few points (3 to 5) having coordinates coming from different sources of information. More importance are considered for points in the close neighborhood of a known point compared to other known points located further away.

2) Multi-Quadratic Interpolation Method:

The Multi-Quadratic Interpolation Method is probably based on surface interpolation process. This method appears to be appropriate for even (homogeneous or well spaced) distribution of points having about the same magnitude of residuals within the transformation area. This method is probably adequate for a large number of points (10 or more) well distributed in the transformation area with residuals coming from the same or equivalent sources of information. The same importance will be considered for points within the whole transformation area coming from a surface smoothing process.

* Once more we have the "Amazing Henri" to thank for this information.