GIAA Mailbag: On Antenna Height Data, and U.S. and International Units of Length
Q: I use GPS to extend cadastral control for property boundary surveys, and occasionally to bring in State Plane coordinates for construction projects. I seldom use the elevation information, preferring to run levels from bench marks. Yet, I’m constantly reminded to measure my GPS antenna heights carefully and accurately. If I’m using GPS to extend horizontal control, why is antenna height data so critical?
A: This is a question many surveyors ask. Surveyors often ignore or use fictitious prism and instrument heights when working with optical instruments. This is not good practice with GPS measurements, even when the only purpose of the survey is to determine the horizontal positions of points. The reason for the importance of antenna heights is that all GPS observations are used to determine three-dimensional positions on the ellipsoid. When integer ambiguities are resolved, the first solution that is determined is the range (distance) from the antenna phase center to each satellite. This data, when used with each satellite’s three-dimensional position for the instant at which the range is applicable, permits the use of trilateration techniques to determine the antenna’s three-dimensional position. Regardless of whether the WGS-84 coordinates are Cartesian (X, Y, Z) or spherical (l, f, h) it should be intuitively apparent that using a fictitious antenna height value or zero will result in an erroneous horizontal position. This is best understood when imagining the reduction of two antenna positions to resolve a horizontal distance. Because the basic “language” of GPS uses the earth-centered, earth-fixed (ECEF) WGS-84, even when heights or elevations are of no interest to the surveyor, accurate antenna heights must be measured.
A: The French first developed the meter as a unit of measure in the late 1700s. Although Congress legalized the metric system in the United States in 1866, it was in 1893 that we formally made the meter the standard of length and defined 1 yd=3600/3937 m. This is equivalent to saying that the meter is equal to 39.37 in exactly or 1 ft=1200/3937 m exactly.
The problem with this definition was that other English-speaking nations have historically used English units and used different conversion factors. In 1959, the national standards laboratories from the various English-speaking countries agreed to establish the conversion as 1 yd=.9144 m (or 1 in=25.4 cm exactly). This was the birth of the international foot. At the same time, it was also decided in the United States that any measurements in feet that were derived from and published as a result of geodetic surveys would adhere to the old standard, the U.S. survey foot.
In most cases, the U.S. survey foot should be used. The most important consideration is to use the same standard throughout an entire project. Most projects utilize previously published information in feet, and in the vast majority of these cases, it will be the U.S. survey foot. Using the wrong unit will introduce a scale error in your measurements of 2ppm.
Thanks for the assistance of Matt Delano of Nikon and Joe Paiva for preparing this column.
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