Coordinate Geometry (COGO)
FAQs

The major difference between these two inverse types is the coordinate system origin. For the 3D Local NEU Inverse, the origin is the AT station. This origin is located at a position defined by its latitude, longitude and ellipsoidal height. If you were to measure an azimuth, zenith angle and chord (slope) distance from an AT station, you could compute a Local NEU vector from the results by applying the formulas:


Local North = chord distance * sin(zen) * cos(az)
Local East = chord distance * sin(zen) * sin(az)
Local Up = chord distance * cos(zen)


The 3D ECEF origin is based on the center of the ellipsoidal model being used (NAD 83, WGS 84, etc.). GPS observations (dx, dy, dz) are based on this inverse type.

For any two stations (an AT and TO station pair), the magnitude of a Local NEU Inverse results and the GPS dXYZ Inverse results are identical. That is:


dN squared + dE squared + dUP squared


is numerically the same as:


dX squared + dY squared + dZ squared.

For the 3D Astro Geodetic Inverse, 3D Geodetic Traverse or 3D Geodetic Network Adjustment, the deflection of vertical components (when known) are used to correct terrestrial observations measured in the field to geodetic observations used within the geodetic mathematical model.

Astronomic observations are measured in reference to the direction of gravity at the AT station. Geodetic observations are in reference to the ellipsoidal normal at the same AT station. The difference between the direction of gravity and the ellipsoidal normal can be as little as a few seconds to several seconds depending on the location of your survey project. The longer your measurements, the greater these differences will have on the computed coordinates of the TO station.

When computing the 3D Astro Geodetic Inverse, all computations are based on the reference ellipsoid (using latitude, longitude and height). The resulting Geodetic observations (azimuth, zenith, chord) are then corrected to Astronomic observations and reported. These corrections are based on the provided deflection of the vertical data. If these data are not provided, no correction is made and hence the computed Geodetic observations and Astronomic observations are assumed to be the same.

All inverse computation results are mark to mark observations. They can be utilized in the field if instrument and target heights are zero OR they are identical (and not very large - less than a couple meters). The latter is only a very close approximation.